Test Funda Nmat Mock-1

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In a developing country, since 1960, the number of millionaires in an urban city has been increasing by 100% every 10 years while the number of millionaires of a rural town has been increasing by 200% every 10 years. In the year 2000, the sum of the number of millionaires in both the places was 337. What was the absolute difference between the number of millionaires in the city and the town in the year 1960?

1) 15 2) 16 3) 1 4) 9 5) 0 Solution:

Let number of millionaires in the city and town in 1960 be x and y, respectively.

An increase of 100% in x will make it 2x, while an increase of 200% in y will make it 3y, and so on.

In 2000, the number of millionaires in the city = 2 × 2 × 2 × 2 × x = 16x And, the number of millionaires in the town = 3 × 3 × 3 × 3 × y = 81y ∴ Sum of millionaires in city and town = 16x + 81y = 337

The only set of integer values that satisfies this equation is x = 16, y = 1.

∴ Difference in number of millionaires in 1960 in the city and the town = 16 – 1 = 15 Hence, option 1.

2. 3 Marks

How many six-digit numbers are there such that the 3rd digit is the square of the 1st digit and the 4th digit is the square of the 2nd digit?

1) 256 2) 1000 3) 900 4) 6400 5) 1200 Solution:

We need to find the number which is of the form aba2b2cd where a, b, c and d can take any value from 0 to 9.

a and b cannot exceed 3 as the square of the two numbers then would exceed 9, which is not possible.

∴ a can have 3 values (1, 2 or 3) and b can have 4 values (0, 1, 2 or 3). c and d can have 10 values each.

Thus total count of numbers that satisfy the given conditions is 3 × 4 × 10 × 10 = 1200

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Hence, option 5. 3. 3 Marks

In the above figure, AB is the diameter and CD is parallel to AB. Also BC = AD = 2. AB = 8. What is the length of CD?

1) 5 2) 6 3) 7 4) 4 5) None of these Solution:

From the figure, O is the center of a circle and CE is perpendicular to OB. Let EB = x

∴ OE = 4 – x

Applying Pythagoras theorem to ∆ OCE, we get, 42 = (4 – x)2 + CE2

∴ CE2

= 8x – x2

Applying Pythagoras theorem to ∆ CEB, we get, 22 = x2 + 8x –x2

∴ x = 1/2

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Each question is followed by two statements, A and B. Answer each question using the following instructions:

Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.

Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.

Mark (3) if the question can be answered by using either statement alone. Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.

Mark (5) if the question cannot be answered on the basis of the two statements. If a and b are integers, what is the value of a + b?

A. LCM of a and b is 34.

B. One of the two numbers is 17. 1) 1 2) 2 3) 3 4) 4 5) 5 Solution:

Using Statement A alone: LCM(a, b) = 34

It is evident that the values of a and b are not unique.

Thus, the question cannot be answered using statement A alone. Using Statement B alone:

There is no information on the second number.

Thus, the question cannot be answer using statement B alone. Using both the statements together:

LCM(a, b) = 34 and one of these two numbers is 17. The other number could be 2 or 34.

Hence, the sum a + b can still not be determined.

Thus, the question cannot be answered on the basis of the two statements. Hence, option 5.

5. _{Equation of a pair of line passing through the origin is 2x}2

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3 Marks

are the separate equations of the lines? 1) 2x + y = 0 and x − y = 0 2) 2x − y = 0 and x − y = 0 3) 2x + y = 0 and x + y = 0 4) 2x − y = 0 and x + y = 0 5) None of these Solution:

2x2 + xy − y2 = 0 is a second degree equation that represents a pair of straight lines passing through the origin.

∴ 2x2

+ 2xy − xy − y2 = 0 2x(x + y) − y(x + y) = 0

∴ 2x − y = 0 and x + y = 0 are the separate equations of the line. Hence, option 4. 6. 3 Mark s 1) 2 2) 3.6 3) 4.2 4) 5 5) 4 Solution: the line 4x + 3y = 14. Hence, option 5. 7. 3 Marks

Mark (5) if the question cannot be answered on the basis of the two statements. Is 2x = y?

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A. B. (2x − 9)2 = (y − 9)2 1) 1 2) 2 3) 3 4) 4 5) 5 Solution:

Consider statement A alone:

Hence, (2x + y)2 = 8xy Thus, (2x − y)2 = 0 Or 2x = y

Hence statement A alone is sufficient to answer the question. Consider Statement B alone:

(2x − 9)2 = (y − 9)2

Thus, 2x − 9 = y − 9 or 2x − 9 = 9 − y Hence, 2x = y or 2x = 18 − y

Hence, no definite conclusion is possible.

Hence, we cannot answer the question using statement B alone. Hence, option 1. 8. 3 Marks

In Dexter‟s laboratory there is a specimen of bacteria that doubles its

number every minute. On certain day, the number of bacteria at 6.10 pm was 1048576. What was the number of bacteria present at 6.00 pm the same evening?

Let the number of bacteria present at 6.00 pm be n. Thus at 6.10 pm it will be,

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n(2)10 = 1048576 ∴ n = 1024 Hence, option 3. Group Question

Answer the following questions based on the information given below.

The following graph gives the sales revenue of five companies in the years from 2000 to 2004.

9. 3 Marks

The maximum absolute decrease in the sales revenue of CD occurred between which of the following years?

1) 2000 and 2001 2) 2001 and 2002 3) 2002 and 2003 4) 2003 and 2004 5) 2001 and 2004 Solution:

Note that the absolute decrease and not the percentage decrease is required. The sales revenue for CD has decreased only twice, i.e. between 2001 and 2002 and between 2002 and 2003. Also, the sales revenue for CD in 2004 is more than the sales revenue in 2001.

Hence, options 1, 3 and 4 can be eliminated.

From the year 2001 to 2002, absolute decrease registered for CD = 75 – 50 = 25

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∴ The absolute decrease in sales value of CD is maximum from 2002 to 2003. Hence, option 3. 10. 3 Marks

The absolute difference between the sales revenue of GH and IJ was the least in the year 1) 2000 2) 2001 3) 2002 4) 2003 5) 2004 Solution:

The absolute difference between the sales revenue of GH and IJ for each year is given below. For 2000 = 100 – 50 = 50 For 2001 = 125 – 75 = 50 For 2002 = 100 – 100 = 0 For 2003 = 125 – 75 = 50 For 2004 = 100 – 75 = 25

∴ The absolute difference between the sales revenue of GH and IJ was the least in the year 2002.

In which of the following years was the ratio of the sales revenue of GH to that of EF the maximum?

1) 2000 2) 2001 3) 2002 4) 2003 5) 2004 Solution:

The ratio of the sales revenue of GH to that of EF for each year is shown below. For 2000 : 100/25 = 4 For 2001 : 125/50 = 2.5 For 2002 : 100/75 = 1.33 For 2003 : 75/50 = 1.5 For 2004 : 75/75 = 1

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∴ The ratio of the sales revenue of GH to that of EF was maximum in the year 2000.

Hence, option 1.

Note: This question can be answered by direct observation as well. It is evident from the bar chart that the ratio is the highest in 2000.

12. 3 Marks

A boy, standing on top of a building 25 m high, notices a bird at some distance at an angle of elevation of 30°. At the same instant, he also notices reflection of the bird at an angle of depression of 45° in a small water pool, on the same level as the floor of the building and exactly vertically below the bird. What is the distance between the boy and the bird?

1) 2) 3) 4) 25 5) None of these Solution:

Given data can be represented as shown in the following diagram.

Let AB be the building, E be the location of the bird and C be the point on the pool on which the shadow of the bird is cast.

The measure of all four angles of the quadrilateral ABCD is 90°, therefore, ABCD is a rectangle.

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∴ AB = DC = 25 m

In right angled ∆ADC, ∠DAC = 45° ∴ ∠ADC = 45° ∴ AD = DC = 25 m In ∆ADE, ∠DAE = 30° Hence, option 2. 13. 3 Marks

The roots of the equation 4x4 − 4x3 − 72x2 − 4x + 4 = 0 are 1) 2) 3) 4) 5) Solution: 4x4 – 4x3 – 72x2 – 4x + 4 = 0 Dividing by x2 on both the sides

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∴ 4(a2 − 2) − 4(a) − 72 = 0 ∴ a2 − a − 20 = 0 ∴ a = 5 or a = −4 When a = 5 ∴ x2 − 5x + 1 = 0 When a = −4 ∴ x2 + 4x + 1 = 0 Hence, option 2. 14. 3 Marks

A piece of work when done by Amar, Akbar and Anthony respectively, costs Rs. 540, Rs.324 and Rs. 320 respectively. The daily wages of Amar, Akbar and

Anthony are Rs.36, Rs.18 and Rs.32 respectively. What will be the total cost when Amar, Akbar and Anthony are working together?

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2) 378 3) 387 4) 487

5) None of these Solution:

∴ The fraction of job that will be completed in a day when all three are working together is

∴ 4.5 days will be required to finish the job when all the three are working together.

Kishore owns a factory of plastic goods. His production cost comprises only the cost of raw material and labour . The cost of raw material increases by 20% and the labour cost also increases from 20% to 25% of the cost of raw material. By how much percent should he reduce his consumption of raw material and labour so that his production cost remains unchanged?

1) 20% 2) 15% 3) 17% 4) 25% 5) None of these Solution:

Let the cost of raw materials be Rs. 100 Then the labour cost will be Rs. 20 ∴ Production cost = 120

Due the increase in cost of raw materials and labour cost the revised cost of raw material and labour cost will be Rs. 120 and Rs. 30 respectively.

∴ The new production cost will be Rs. 150

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consumption of raw materials and labour.

∴ Percentage reduction in consumption of raw material and labour will be,

What is the number of sides of a polygon for which sum of interior angles is 5400°? 1) 20 2) 32 3) 19 4) 18 5) None of these Solution:

For an n sided polygon, there exist n vertices and therefore n interior angles. As we know, for every interior angle, there exists an exterior angle and thus n exterior angles exist.

Therefore, interior angle = 180 – exterior angle

It is given that the sum of the interior angles = 5400 ∴ 180(n – 2) = 5400 ∴ n = 32 Hence, option 2. 17. 3 Mark s

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Which of the statements is/are incorrect? 1) II only 2) III only 3) I only 4) I and II 5) II and III Solution:

Thus only statement II is incorrect. Hence, option 1. 18. 3 Marks

Jai and Veeru are two masons who are given the job of building a compound wall around a plot owned by Mr. Thakur. Jai working alone takes 8 hours more than the time that both Jai and Veeru would take working together. Veeru working alone takes 12.5 hours more than the time that both would take working together. How many hours would Jai alone take to build the wall?

1) 10 hours 2) 18 hours 3) 12 hours 4) 16 hours 5) None of these Solution:

Let the time taken to build the compound when both Jai and Veeru are working together be x.

Time taken by Jai to complete the job alone is x + 8 and the time taken by Veeru to complete the job alone is x + 12.5

Thus we get the following equation:

∴ 2x2 + 20.5x = x2 + 20.5x + 100 ∴ x2 = 100 ∴ x = 10

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Mark (5) if the question cannot be answered on the basis of the two statements. Six friends Aziz, Vivek, Nipun, Arun, Sahil and Navnit are sitting around a circular table such that Arun is two places to the left of Aziz. Who is opposite Vivek?

A. Sahil is adjacent to Nipun and Vivek B. Vivek is adjacent to Aziz and Sahil 1) 1 2) 2 3) 3 4) 4 5) 5 Solution:

The basic arrangement that can be obtained from the question is as shown below.

Using Statement A alone:

It is clear from the arrangement that either Arun or Aziz can be opposite Vivek. Thus, the question cannot be answered using statement A alone.

Using Statement B alone:

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The only way this is possible is if Vivek is adjacent to Aziz on his right and Sahil is to the immediate right of Vivek.

Now, Arun is opposite to Vivek as shown in the figure below.

Thus, the question can be answered using statement B alone.

Thus, the question can be answered using statement B alone but not by using statement A alone. Hence, option 2. 20. 3 Marks

The difference between simple interest and compound interest on a particular amount in 2 years at 30% is Rs.360. What is the principal?

1) Rs. 4000 2) Rs. 3500 3) Rs. 3000 4) Rs. 2500 5) None of these Solution:

The difference between the simple and compound interest for two years is the simple interest on the simple interest for one year.

∴ i = 1200

∴ Interest for the first year = Rs. 1200

nth term of an AP, consisting of only positive integers, is denoted by an. It is given that a3 = 4 and aN – 2 = 9. What is the value of (aN + 2N + 2)?

1) 29 2) 31 3) 33 4) 35

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5) Cannot be determined Solution:

Let common difference of the AP be d. ∴ We have a1 = a3 – 2d = 4 – 2d

We also have a1 = aN – 2 – (N – 3)d = 9 – d(N – 3) = 9 – Nd + 3d Equating these two values of a1, we get,

4 – 2d = 9 – Nd + 3d, or (N – 5) d = 5

Since both N and d are positive, we must have N – 5 = 1 and d = 5 or N – 5 = 5 and d = 1.

Thus, either N = 6 and d = 5 or N = 10 and d = 1.

In the first case, aN + 2N + 2 = a1 + (N – 1) d + 2N + 2 = 4 – 2 × 5 + 5 × 5 + 2 × 6

+ 2 = 33

In the second case, aN + 2N + 2 = a1 + (N – 1) d + 2N + 2 = 4 – 2 ×1 + 9 × 1 + 2 ×

10 + 2 = 33

In either case, the given expression = 33 Hence, option 3. 22. 3 Marks

Each question is followed by two quantities, A and B. Answer each question using the following instructions:

Mark (1) if quantity A is greater than quantity B. Mark (2) if quantity B is greater than quantity A. Mark (3) if the two quantities are equal.

Mark (4) if it is impossible to determine a relationship.

Mark (5) if the greater quantity cannot be determined but the two quantities are definitely not equal.

In a new dictionary, the position of alphabets is changed so as to arrange the words more concisely.

Let P be the old position of alphabets from 1 to 26, and let Pnew be the new

position.

Pnew is calculated using the function f(P), defined as follows:

f(P) = remainder of P × quotient of P, when divided by 3. ... If none of them are 0.

= quotient of P, when divided by 3. ... If the remainder is 0.

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ascending order in a set A.

If f(P) for two values of P is the same, then the one with a higher quotient is placed after the one with lower quotient, and if they have the same quotient, then one with higher P is placed after the one with lower P.

Now, the new position of a letter P is defined as the position of f(P) in the set A. A. Position of the word MAS in dictionary

B. Position of the word MAN in dictionary 1) 1 2) 2 3) 3 4) 4 5) 5 Solution:

Since the first two alphabets are the same, to find the order of the words, find the location of S and N in the new dictionary.

P for S and N is 19 and 14 respectively. ∴ f(14) = 2 × 4 = 8

and

f(19) = 1 × 6 = 6 ∴ f(19) < f(14)

Hence, the word MAS is placed before the word MAN in the new dictionary. ∴ Position of the word MAN > Position of the word MAS

Mark (5) if the question cannot be answered on the basis of the two statements. Is the 1st number in a series of 7 consecutive integers even?

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B. Sum of the numbers is divisible by 11. 1) 1 2) 2 3) 3 4) 4 5) 5 Solution:

Using Statement A alone:

Since the series consists of 7 consecutive integers, it forms an A.P. consisting of odd number of terms and the middle term of that A.P. is also the arithmetic mean of the A.P.

Thus, the arithmetic mean of the 7 numbers is the 4th number which is 2. Therefore, the 1st number in the series is 2 − 3 = −1.

Thus, the 1st number is odd.

Thus, the question can be answered using statement A alone. Using Statement B alone:

Sum of the 7 numbers = (x – 3) + (x – 2) +( x – 1) + x + (x + 1) + (x +2) + (x + 3) = 7x

Thus, the sum of the given numbers is divisible by 7.

Now, it is known this sum is also divisible by 11 which means that x has to be a multiple of 11.

But x can be odd or even which implies that the first term can also be odd or even.

Thus, the question cannot be answered using statement B alone.

Thus, the question can be answered using statement A alone but not by using statement B alone. Hence, option 1. 24. 3 Marks

A train moving at 54 kmph crosses a man standing on a platform in 10 seconds. What will be the time required by the train to cross a platform if the length of the platform is equal to the length of the train?

1) 30 seconds 2) 50 seconds 3) 25 seconds 4) 20 seconds 5) 45 seconds

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Solution:

Distance covered by the train to cross a man standing on the platform = Length of the train

∵ Distance = Speed × Time

∴ Distance covered = 15 × 10 = 150 m So the length of the train is 150 m.

Length of the platform = Length of the train = 150 m

Time taken by the train to cross the platform = Total Distance covered (Length of platform + Length of train)/Speed of train

Hence, option 4.

Alternatively,

As the length of the platform is equal to that of the train, the train will require twice the time to cross it as it takes to cross the man.

There are 3 friends competing against each other in a race. Mohit beats Purohit in a race of 1000 m by 50 m and Purohit beats Rohit in a race of 1200 m by 100 m. By what margin (in m)would Mohit beat Rohit in a race of 1500 m? (Round off the answer to closest integer.)

1) 190 2) 194 3) 197 4) 198 5) 199 Solution:

Let the speed of Mohit, Purohit and Rohit be m, p and r respectively. In a race of 1000 m,

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In a race of 1200 m,

Let Mohit beats Rohit by x in a race of 1500 m .

∴ 5225 = 6000 – 4x ∴ 4x = 775 or x = 193.75 Hence, option 2. 26. 3 Marks

What is the ratio of the right most digit preceding the zeros in the value of 2053 to the right most digit preceding the zeros in the value of 4053.

1) 1 : 2 2) 2 : 3 3) 2 : 1 4) 3 : 2 5) None of these Solution: 2053 = 253 × 1053

∴ The rightmost digit preceding zeros will be the unit's digit of 253

21 = 2, 22 = 4, 23 = 8, 24 = 16, 25 = 32 and so on.

Thus we can see that the units digit repeats after every 4th power. 53 = 52 + 1, where 52 is a multiple of 4.

∴ The unit's digit of 253

is same as the unit's digit of 21, which is 2.

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of 4053 is 4.

Hence, the ratio is 1 : 2 Hence, option 1. 27. 3 Marks

In the figure below, m∠ABC = 40°, m∠BAD = 140°, m∠ADE = 130° and DC = DE. Find m∠CDE + m∠DCB.

1) 160° 2) 170° 3) 210° 4) 150° 5) None of these Solution: In quadrilateral ABED,

m∠ABE + m∠BAD + m∠ADE + m∠DEB = 360° ∴ m∠DEC = 50°

Since DC = DE

∴ m∠DEC = m∠DCE = 50° Now, in ∆DCE,

m∠DCE + m∠DEC + m∠CDE = 180° ∴ m∠CDE = 80° Now, m∠DCE + m∠DCB = 180° ∴ m∠DCB = 130° ∴ m∠CDE + m∠DCB = 210° Hence, option 3.

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3 Marks

and the ratio of number of boys to the number of girls is 2 : 1. In class B, the ratio of average age of boys to the average age of girls is 3 : 2 and the ratio of number of boys to the number of girls is 1 : 2. The number of students in class A and class B are equal. If the average age of class A is equal to the average age of class B, then what is the ratio of the average age of girls of class A to the average age of boys of class B? 1) 7 : 6 2) 6 : 5 3) 5 : 3 4) 2 : 3 5) 5 : 4 Solution: For class A:

Let the average age of boys be x and the number of girls be y. ∴ Average age of girls is 2x and the number of boys is 2y.

For class B:

Let „z’ be the common variable for average age of boys and girls. ∴ Average age of boys is 3z and average age of girls is 2z.

Since, the total number of students is equal in both classes, the number of boys is y and the number of girls is 2y.

Now, since the average ages of both classes are equal

Ratio of average age of girls of class A to the average age of boys of class B is

Hence, option 1.

29.

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Marks variable component, such that the variable component depends on the number of members in the society. If there are 50 members, then each member has to pay Rs. 110 and if there are 30 more members then each member has to pay Rs. 80. If each member pays Rs. 130, then how many members are there in the society?

It is given that, expenditure = F + V From the condition given we can say that, (110)(50) = F + 50k ...(i)

(80)(80) = F + 80k ...(ii) On solving (i) and (ii) we get, F = 4000 and k = 30

Now,

130x = 4000 + 30x, where x is the number of members ∴ x = 40 Hence, option 3. Group Question

The graph below gives details of total exports as well as exports of herbal products for a company.

The abscissa represents the total exports for a given year in Rs. Lakhs, while the ordinate represents the exports of herbal products for that same year in Rs. Lakhs.

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30. 3 Marks

For 2006, herbal products formed what percentage of the total exports? 1) 13.50% 2) 13.64% 3) 14.28% 4) 12.50% 5) 11.11% Solution:

The abscissa and ordinate stand for the X-axis and Y-axis respectively. Thus, figures on the X-axis stand for the total exports for a given year while those on the Y-axis stand for the export of herbal products in that year. Thus, in 2006, the total exports were Rs. 5,500 lakhs, whereas the exports of herbal products were Rs. 750 lakhs.

The fall in herbal exports in 2007 from that in 2006 was nearly: 1) 13.65% 2) 12.78% 3) 13.33% 4) 86.66% 5) 90.25% Solution:

In 2006, the herbal exports were Rs. 750 lakhs, whereas in 2007, they were Rs. 650 lakhs.

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Hence, option 3. 32. 3 Mark s

Over the given period, the herbal exports rose by nearly: 1) 300% 2) 30% 3) 10% 4) 18.65% 5) 77% Solution:

In 2004, the herbal exports were Rs. 500 lakhs while at the end of the period, i.e. in 2007, they were Rs. 650 lakhs.

In how many ways can a committee of 4 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls?

Atleast 3 boys means the committee can be formed by 3 boys and 1 girl or all 4 boys.

Case 1: 3 boys and 1 girl

From 5 boys and 6 girls they can be selected in 5C3 × 6C1 ways = 10 × 6 = 60

ways

Case 2: All 4 boys

They can be selected from 5 boys in 5C4 ways = 5 ways

∴ Total number of ways = 60 + 5 = 65 ways Hence, option 1. 34. 3 Marks

A, B and C invest Rs. 4000, Rs. 15000 and Rs. 5000 respectively to set up a new business. A gets 20% of the total profit for running the business and the remaining profit is divided among the three in proportion to their investments. If in a year, A gets Rs. 3000 less than B and C together, the total profit for the year is

1) Rs. 5000 2) Rs. 6000 3) Rs. 7500 4) Rs. 9000 5) Rs. 10500 Solution:

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Ratio of investments of A, B and C ≡ 4000 : 15000 : 5000 ≡ 4 : 15 : 5 Let the profit for the year be Rs. x

Profit given to A for managing the business = 20% of x = 0.2x

80% of the total profit is divided between A, B and C in ratio 4 : 15 : 5 80% of total profit = 0.8x

A earns Rs. 3000 less than B and C.

∴ x = 9000 Hence option 4. 35. 3 Marks

In ∆PQR, a line is drawn from P to intersect the opposite side QR at S. What is m ∠QPS such that PR = RS and m ∠RPQ = m ∠PQR + 60°?

1) 15° 2) 30° 3) 20° 4) 25° 5) 45° Solution: m ∠QPS = m ∠RPQ − m ∠RPS

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∵ PR = RS

∴ m ∠QPS = m ∠RPQ – m ∠PSR Using exterior angle theorem, we get, m ∠PSR = m ∠QPS + m ∠PQS ∴ m ∠QPS = m ∠RPQ – (m ∠QPS + m ∠PQS) ∵ m ∠PQS = m ∠PQR ∴ 2(m ∠QPS) = m ∠RPQ − m ∠PQR ∴ 2(m ∠QPS) = 60° ∴ m ∠QPS = 30° Hence, option 2. 36. 3 Marks

A field is in the form of a circle of radius 100 m; the field is covered with grass except for an area in the form of a circle concentric with the field, and of radius 50 m. A parachutist is falling towards the field because his parachute has failed to open; he knows that he will die unless he falls on grass. He may fall anywhere on the field. What is the probability that he will live?

1) 2) 3) 4) 5) 1 Solution:

The probability that the parachutist will fall at any point on the field is equal to the probability that he will fall at any other point on the field.

Thus, the probability that he will fall on grass (and hence live) is equal to the area of the grassy portion of the field divided by the total area of the field.

The area (in sq. m.) of the grassy portion = π[1002

– 502] The area (in sq. m.) of the entire field = π[1002

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Gayathri and Savithri sell apples. Savithri sells two apples for one rupee. The apples that Gayathri sells are a bit smaller; she sells three apples for one rupee. At a certain moment, when both ladies have the same amount of apples left, Gayathri is called away. She asks her neighbour to take care of her goods. To make

everything not too complicated, Savithri simply puts all apples together, and starts selling five apples for Rs. 2. When Gayathri returns the next day, all apples have been sold. But when they start dividing the money, there appears to be a shortage of Rs. 7. Supposing they divide the amount equally, how much does Savithri lose in this deal? 1) 12 2) 21 3) 0 4) 25 5) Cannot be determined Solution:

The big pile of apples contains the same number of large apples of half a rupee each (from Savithri), as smaller apples of one third a rupee each (from Gayathri).

∴ The apples should be sold at Rs. (5/12) each.

But the apples were sold for Rs. (2/5) each (5 apples for Rs. 2). ∴ Each apple is sold at Rs. (1/60) less.

The total shortage is Rs. 7,

∴ After combining there were 7 × 60 = 420 apples.

∵ They divided the money equally amongst themselves, each of them got Rs. 84. If Savithri would have sold the apples herself, she would have received Rs. 105 for 210 apples.

∴ Savithri loses Rs. 21 in this deal. Hence, option 2. 38. 3 Marks

A number which reads the same when read forward and backward is called a palindrome.

How many four-digit numbers are palindromes? 1) 81

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3) 99 4) 100 5) 115 Solution:

A 4-digit palindrome will be of the form abba where a > 0 and b can take integer values from 0 to 9.

∴ a can take 9 values and b can take 10 values.

∴ The total number of 4-digit palindromes is 9 × 10 = 90 Hence, option 2. 39. 3 Marks

Seven lotuses, sixteen roses and nine lilies cost Rs. 338. Four lotuses, six roses and seven lilies cost Rs. 169. What is the cost of nine lotuses, thirty roses and six lilies? 1) Rs. 169 2) Rs. 507 3) Rs. 496 4) Rs. 570 5) Cannot be determined Solution:

Let the price of a lotus, a rose and a lily be Rs. x, y and z respectively. ∴ 7x + 16y + 9z = 338 ...(i)

and

4x + 6y + 7z = 169 ...(ii)

Subtracting (ii) from (i) and multiplying the resulting equation by 3, we get 9x + 30y + 6z = 507

So the cost of 9 lotuses, 30 roses and 6 lilies is Rs. 507. Hence, option 2. 40. 3 Marks

In a survey conducted 70% watched CNN, 75% watched BBC, 20% watched neither of the channels and 325 people watched both the channels. How many people were surveyed?

1) 500 2) 382 3) 50 4) 492 5) 491 Solution:

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Let x be the total number of people surveyed. From the figure above,

0.7x – 325 + 325 + 0.75x – 325 + 0.2x = x ∴ x = 500 Hence, option 1. 41. 3 Marks

The length of the side of a cubical box is equal to twice the length of the longest rod that can be placed in a rectangular box of dimensions 3 cm × 4 cm × 12 cm. What is the maximum number of spheres of diameter 32.5 mm that can be kept in the cubical box?

1) 64 2) 512 3) 216 4) 1000 5) 324 Solution:

The length of the longest rod that can fit in the cuboid = The diagonal of the cuboid

Side of the cubical box = 2 × 13 = 26 cm

∴ Along one face of the cube 8 × 8 sheres can be fitted as shown in the figure given below.

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Also, there will be 8 such vertical slabs in the cube.

∴ The total number of spheres that can be fitted in the cube = 8 × 8 × 8 = 512 Hence, option 2. 42. 3 Marks

If m and n are two natural numbers, ratio of m to n is x and ratio of n to m is y, then (x + y) will be 1) Less than 1 2) Greater than 1 3) Equal to 1 4) Depends on m and n 5) Data insufficient Solution: ∴ x + y > 1 Even then x + y > 1

∴ x + y is always greater than 1. Hence, option 2.

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43. 3 Marks

There are three identical circles of radii 10 units touching each other. What is circumference of the biggest circle that can fit in the gap formed by the intersection of all three circles and touching all three of them?

1) 2) 3) 4) 5) None of these Solution:

Let the radius of a smaller circle be r. ∆ABC is an equilateral triangle.

∵ the centroid divides the median of a triangle in the ratio 2 : 1,

∴ Circumference = 2πr

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On a busy Monday morning a certain number of cyclists started from Borivali towards Churchgate. At the Malad junction, half of these cyclists entered Malad while 1/5 of the remaining cyclists joined the cyclists going towards Chuchgate. The same thing happened at Andheri, Santacruz, Bandra and Dadar. No cyclist joined or left the group thereafter. Finally 243 cyclists reached Churchgate. How many cyclists started from Borivali?

There are 243 cyclists at Churchgate. So 243 cyclists left Dadar. Let there be x cyclists before Dadar.

Since half of the cyclists left, there were x/2 cyclists remaining. These were joined by 1/5 of remaining cyclists.

This has to be equal to 243.

∴ x = 405

Using the same logic, we have the number of cyclists before Bandra to be 675, before Santacruz to be 1125, before Andheri to be 1875 and before Malad to be 3125.

Thus total cyclists leaving Borivali is 3125. Hence, option 1. 45. 3 Marks

Ram invested Rs. 10,000 each in two bank schemes. In scheme A he earns an interest of 10% p.a., compounded semi-annually, while in scheme B he gets a simple interest of 6% every six months. What is the difference in the interest that he will earn at the end of 2 years?

1) 245 2) 200 3) 260 4) 243 5) 267

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Solution: Scheme A:

The interest is compounded semi-annually. Interest earned at the end of 2 years

= 10000 × 1.054 – 10000 ≈ 10000 × 1.2155 – 10000 = 2155

Scheme B:

The rate of interest is 6% per 6 months i.e. 12% p.a.

∴ The interest earned in 2 years = 0.12 × 2 × 10000 = 2400 ∴ Difference between the interest earned = 2400 – 2155 = Rs. 245 Hence, option 1. Group Question

In the year 2004, Deepesh and Devesh together purchased 20 acres of land from Dinesh. They paid amounts in the ratio 4 : 1. Further Devesh spent Rs. 3 lakhs more on the land for its development, and thereby they spent equal amounts. They

cultivated mango and orange trees in equal areas. However the ratio of number of mango trees to that of orange trees was 3 : 2. In the year 2008, the trees yielded fruits. They sold each mango for Rs. 10. The revenue obtained from the total sale of mangoes and oranges was 25% of the purchase value of the land. They agreed to share the realised value equally. The total amounts generated from the sale of mangoes and oranges were in the ratio of 3 : 2.

46. 3 Marks

What is the ratio of revenue per acre of oranges to that of mangoes? 1) 3 : 2 2) 2 : 3 3) 1 : 1 4) 4 : 9 5) 9 : 4 Solution:

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per acre of oranges to that of mangoes is the same as the ratio of revenue from oranges to that of mangoes, which is 2 : 3.

The amount received (in Rs.) by Devesh in the year 2008 is 1) 62500 2) 750000 3) 100000 4) 125000 5) 300000 Solution:

Let Deepesh pay 4x lakhs and let Devesh pay x lakhs for the land. Devesh spends Rs. 3 lakhs more.

∴ 4x = x + 3 i.e. x = 1

Total purchase value of the land = 4x + x = 5 lakhs

Total amount realized from sale of both mangoes and oranges = 25% of 5 lakhs = Rs. 1.25 lakhs

Amount received by Devesh in the year 2008 = 125000/2 = Rs. 62,500 Hence, option 1. 48. 3 Marks

The total number of mangoes produced is 1) 5000 2) 50000 3) 6250 4) 62500 5) 7500 Solution:

From the solution to the previous question we get that the total revenue generated from the sale of mangoes and oranges = Rs. 1.25 lakhs Revenue from mangoes = (3/5) × 1.25 lakhs = Rs. 75,000

Revenue from oranges = (2/5) × 1.25 lakhs = Rs. 50,000 Total revenue from mangoes = Rs. 75,000

Selling price of each mango = Rs. 10 Number of mangoes = 75000/10 = 7500 Hence, option 5. Section II 1.

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Marks With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes

religion.

The above argument rests on which of the following assumptions?

1) Religious people do evil things.

2) Good people are incapable of doing evil things. 3) Every evil deed has religion behind it.

4) People are either good or evil.

5) Good and evil can be measured quantitatively. Solution:

It is not assumed that religious people generally do evil things, as stated in option 1. The given information only states that for good people to do evil, it requires religion - this cannot be generalized to ALL religious people.

Option 3 is not assumed because evil people without religion can also commit evil deeds.

Option 4 is not an assumption because although the argument is about good and evil people, it does not assume that these are the only two classes in which people can fall.

Option 5 introduces „quantitative‟- no relation to maindata.

Option 2 is an assumption because the paragraph states if good people have to do evil things, they are forced by religion to do so- hence they are generally

incapable of doing evil (incapable means: lacking capacity, ability, or qualification for the purpose or end in view).

Hence, the correct answer is option 2.

2. 3 Marks

During the Physical Training session in a school, some girls were made to stand in a straight line. Asha was the 4th girl from the front, while Nisha was the 3rd last girl. The instructor then asked 5 consecutive girls from the center of the line to move out of the line. This left exactly 4 girls between Asha and Nisha. How many girls were in the line initially?

1) 14 2) 15 3) 16 4) 17 5) 18 Solution:

Asha was the 4th girl from the front which means that there were 3 girls in front of Asha.

Nisha was the 3rd last girl which means that there were 2 girls behind Nisha. Thus, the number of girls who are always present in the line are 3 + 1 + 1 + 2 i.e. 7.

After the instructor asked 5 consecutive girls to move out, there were 4 girls left between Asha and Nisha.

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Thus, the number of girls initially in the line = 7 + 9 = 16. Hence, option 3. 3. 3 Marks

Given below is a passage followed by several statements that can be drawn from the facts stated in the passage. Examine each statement separately in the context of the passage and decide whether they are implied from the passage.

First, let us do away with the myth that parents teach language to their children. No one supposes that parents provide explicit grammar lessons, of course, but many parents (and some child psychologists who should know better) think that mothers provide children with implicit lessons. These lessons take the form of a special speech variety called Motherese: intensive sessions of conversational give-and-take, with repetitive drills and simplified grammar. („Look at the doggie! See the doggie? There‟s a doggie!‟)

Statements:

I. Some parents mistakenly think that they teach their children language. II. Motherese may not particularly helpful.

III. Child psychologists are expected to be aware that parents provide children with only implicit language lessons.

1) Only I is implicit. 2) Only III is implicit. 3) Both I and II are Implicit. 4) Both II and III are Implicit. 5) All are implicit.

Solution:

I is very much implicit in the first sentence, and forms the basis for the whole argument.

Since the idea of parents teaching their children language is called a „myth‟, we can infer that even a special variety of speech like Motherese is not particularly helpful in doing so. So II is implicit.

III directly contradicts the parenthetical observation in the second sentence, so it cannot be said to be implicit.

Therefore only assumptions I and II are implicit. Hence, the correct answer is option 3.

Group Question

In Ramraj society, it is known that only three brands of vehicles are used, i.e. Hero Honda, Yamaha and Bajaj. 42 families use only one brand, 23 families use exactly two brands and 10 families use all three brands. It is assumed that each family uses at least one of these brands.

4. 3 Marks

If 8 families stop using Yamaha and start using Bajaj, then what can be the maximum number of families that use exactly two brands?

1) 26 2) 32 3) 30

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4) 31 5) 23 Solution:

Since every family uses atleast one brand, there is no family that does not use any brand.

42 families use only one brand ∴ a + b + c = 42

23 families use exactly two brands ∴ d + f + e = 23

10 families use all the three brands. ∴ g = 10

The 8 families that stop using the Yamaha brand and start using the Bajaj brand can be from any one of the three categories : single brand users, two brand users or all brand users.

Since the maximum number of families that use two brands is required, this can happen only if all the 8 families are from the same category.

Therefore, there are three cases possible. Case 1 : All 8 families are single brand users.

In this case, a + b + c is still 42 because the 8 families get reduced from „Yamaha only‟ and get added to „Bajaj only‟.

Thus, there is no impact on the number of families using two brands i.e. its value still remains 23.

Case 2 : All 8 families are two brand users.

In this case, d + e + f can have a maximum value of 23 because in a best case scenario, there are originally no families in the „Yamaha and Bajaj only‟

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category and the 8 families get reduced from the „Hero Honda and Yamaha only‟and get added to „Bajaj and Hero Honda only‟ category. If there were some families in the „Yamaha and Bajaj only‟ category, then after the shift, the number of families in this category would have become zero while the number of families in the „Bajaj only‟ category would have increase by 8. Thus, the number of families that use two brands would have reduced by 8 i.e. become 15.

Thus, in this case, the value becomes either 15 or remains 23. Case 3 : All 8 families use all three brands.

Here, the value of g definitely decreases by 8 to become 2. This is because the families in this category now become two brand users i.e. they fall in the category „Bajaj and Hero Honda only‟.

Hence, the number of families using two brands becomes 23 + 8 = 31. Hence, the maximum value is 31.

How many families do not use all the three brands? 1) 50

2) 60 3) 54 4) 65

5) None of the above Solution:

Since every family uses at least one brand, the total number of families that uses any one of the brands is 42 + 23 + 10 = 75.

The number of families that uses all three brands = 10

∴ Number of families that don‟t use all three brands = 75 – 10 = 65 Hence, option 4. 6. 3 Marks

Answer the question based on the information given in the passage.

One reason given by those who are pro-zoos is that zoos have a very important role to play in breeding endangered animals in captivity. According to pro-zoo people, if animals were being taken care of in their natural environment, i.e. in forests and oceans, then there would have been no need for zoos. But so many animals are now becoming extinct and it is up to the zoos to somehow salvage the situation.

Which of the following statements further weakens the argument presented in the passage?

1) Zoos are primarily seen as entertainment centres.

2) Zoos do not offer guided tours to visitors, therefore there has been no rise in awareness.

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3) Studies have found that city zoos play an important role in protecting endangered species from poachers.

4) Zoos have been able to save many species from the brink of extinction. 5)

Studies show that zoos have a very low success rate when it comes to conserving endangered animals, due to diseases and defects caused due to inter-breeding.

Solution:

The main idea expressed in the passage is that zoos play a very important role in conserving endangered species. To weaken this argument we need a statement that shows that zoos are not doing this, or are somehow incapable of doing this. Option 1 is ruled out as it is not relevant to the argument in the passage about conserving endangered species.

Option 2 is ruled out as there is no relation between awareness and wildlife conservation in this passage.

Option 3 is ruled out as this is just a rephrasing of what has been stated in the passage; it doesn‟t weaken the argument.

Option 4 is ruled out as this would not weaken the argument, rather it would strengthen it.

If the zoos have a very low success rate in conserving animals and inter-breeding is leading to diseases and defects, then zoos are not playing a role in conserving endangered species. This certainly weakens the given argument.

7. 3 Marks

Given below are two statements. Analyze them and mark the option that correctly states their relationship.

A. I wrote pages after pages on the experiences of my travels. B. The ink-pot fell from the table and the ink in the pen ran dry. 1) A is the cause and B is the effect.

2) B is the cause and A is the effect.

3) Both A and B are effects of a common cause. 4) Both A and B are the causes of a common effect. 5) Cannot be determined.

Solution:

This is an abstract set of statements that connect logically only on the basis of certain assumptions. On the face of it, statement A looks like the cause to the fact mentioned in statement B. However, we have to assume that the author was using to write the very pen that ran out of ink and he did something for the ink-pot to fall. These two statements cannot be assumed to be related to each other as it would render the relationship ambiguous.

8. 3 Marks

Read the two statements given below and choose the statement that logically follows from the first two.

A. All pygmies are brown. B. All pygmies are black. 1) Brown is same as black. 2) Some brown is black. 3) Some black are not brown. 4) Some brown are pygmies.

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5) Every brown is black. Solution:

The two given statements can be represented in the form of a Venn diagram. Option 1 is incorrect because brown and black may not be the same set.

Option 2 is correct because there has to be some brown that are common to black (the set of all pygmies).

Option 3 is incorrect because brown and black could be the same set. Option 4 is derived only from statement A and is hence, incorrect. Option 5 is incorrect as seen in the Venn Diagram.

The statement given below is followed by two statements. Analyze all of them and determine the correct combination of a course of action.

Illegal hunting of tigers has caused the tiger population of India to reach alarming levels.

A. Environmental groups should spread awareness about this fact.

B. The government should enforce stricter measures towards upholding the existing tiger poaching laws.

1) A is the best course of action. 2) B is the best course of action.

3) A followed by B is the best course of action. 4) Either A or B is the best course of action. 5) Neither A nor B are relevant courses of action.

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Solution:

Both of these statements seem useful as courses of action when it comes to tiger poaching. However, this situation is very specific and so generic actions are not relevant in this case.

Statement A will definitely result in people being more aware of dropping tiger populations and start caring more but such awareness among the general population may or may not actually reduce the number of tigers being hunted illegally. Statement B, on the other hand, targets the crux of the problem, that is upholding laws more strictly so that the people who hunt these tigers are caught and stopped from hunting any more tigers. Between these two, statement B is more relevant as a course of action than statement A.

10. 3 Marks

In each of the following questions, there is a statement followed by a set of arguments. You are expected to classify the argument as Strong or Weak. Strong arguments are important and directly related to the question. Weak arguments may not be directly related or may be related to trivial aspects of the question and may be of lesser importance.

Choose the best option as per this classification.

Should there be a statutory limit on the amount spent on weddings, in view of the display of wealth witnessed at the weddings of politicians and industrialists?

I. Yes. Conspicuous consumption by public authorities undermines efforts to cultivate healthy economic habits across all classes, which is important for the success of the nation.

II. No. A large wedding creates jobs for people in several industries, from florists to caterers to photographers to bridal fairs. It boosts the local economy.

1) Only I is strong. 2) Only II is strong. 3) Both I and II are strong. 4) Either I or II is strong. 5) Neither I nor II is strong. Solution:

Argument I is not supported by strong facts. Firstly, in a democracy, one cannot lay a limit on the personal spending behaviour of a person. Secondly, across all classes is incorrect. People from the middle and lower economic classes will not have lavish spending habits, therefore, do not need to take an effort to cultivate healthy economic habits with respect to lavish weddings. Hence, argument I is weak.

Argument II is supported with unimpeachable facts. Therefore, argument II is strong.

Group Question

A clerk has been given the task of arranging a round table conference that will be attended by 8 delegates from different countries : A, B, C, D, E, F, G and H.

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The main job of the clerk is to assign the name of the delegate to the chair meant for that delegate.

The clerk has been given the following information – i. The chairs are numbered from 1 to 8.

ii. The delegate from country A will sit opposite to the delegate from country E. iii. The delegate from country C sits adjacent to the delegate from country D. iv. The delegate from country F sits opposite to the delegate from country G.

v. The delegate from country B sits on the right hand side of the delegate from country A.

vi. The delegate from country H sits adjacent to the delegate from country E. The clerk has been further informed that the delegate from country A sits on the seat numbered 1 and that the seats have been arranged in clockwise fashion.

Try helping the clerk in this job by answering the following.

11. 3 Marks

Whose name will the clerk write on seat number 2? 1) Delegate from G 2) Delegate from F 3) Delegate from D 4) Delegate from C 5) Cannot be determined Solution:

Since it is given that the delegate from country A sits on seat number 1 and that the seats are numbered in clockwise order, fix A's position and number the other seats accordingly.

Now, the delegate from country E sits exactly opposite to the delegate from country A.

Thus, the delegate from country E sits on seat number 5.

Since the delegate from country B sits on the right hand side of the delegate from A, the delegate from B can sit on any one seat from seat numbers 6, 7 and 8.

Now, the delegates from countries C and D sit adjacent to each other and the delegates from countries G and F are exactly opposite each other.

This implies that the delegates from countries C, D and one out of countries G and F have to occupy three adjacent seats.

Hence, the three delegates mentioned above have to occupy seat numbers 2, 3 and 4 (in no particular order).

Now, the delegate from country H sits adjacent to the delegate from country E.

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This means that the delegate from country H can sit on one of seats 4 and 6. But, as seen above, seat 4 will be occupied by one delegate from C, D and G/F.

Hence, the delegate from country H will be on seat number 6.

Consequently, the delegate from country G or F cannot be opposite to seat number 6 i.e. on seat number 2.

Similarly, this delegate cannot be on seat number 3 because the delegates from C and D have to be together.

Hence, one delegate from country G and F will be on seat number 4 while the other will be opposite him i.e. on seat number 8.

Consequently, the delegates from countries C and D will be on seat numbers 2 and 3 (in no particular order).

Hence, the delegate from country B can only be in seat number 7. Thus, the final arrangement is as shown below.

Therefore, it is clear from the figure that seat number 2 will be occupied by either C or D. Hence, option 5. 12. 3 Marks

Who will sit on the seat number 7? 1) Delegate from G 2) Delegate from H 3) Delegate from F 4) Delegate from B 5) Cannot be determined Solution:

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It is evident that the delegate from country B sits on the seat numbered 7. Hence, option 4. 13. 3 Marks

On which seat number will H be seated? 1) 4 2) 6 3) 7 4) 2 5) Cannot be determined Solution:

Consider the final arrangement obtained in the solution to the first question. You can observe that H sits on seat number 6.

Read the two statements given below and choose the statement that logically follows from the first two.

A. All Foreigners are Stupid. B. All Stupid are Awkward. 1) Some Awkward are Stupid.

2) Some Foreigners may be Stupid but not Awkward. 3) Some Stupid are Foreigners.

4) All Awkward are Foreigners. 5) Some Awkward are Foreigners. Solution:

The two given statements can be represented in the form of a Venn diagram as shown.

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Options 1 and 3 are incorrect as they are derived from one of the given statements only.

Option 2 is incorrect as such a case is not possible (as seen in the Venn Diagram).

Option 4 is not correct. Though it may be one of the possible cases, it is not necessarily true.

Option 5 is correct as can be seen from the diagram. Hence, option 5. 15. 3 Marks

A coding machine generates a code for words in a certain manner such

that the code for „STRANGER‟ is 19-T-18-A-14-G-5-R. What will be the code generated by this machine for the word „IMPORTANT‟?

1) 10-M-16-O-18-T-1-N-20 2) 9-M-16-O-18-T-1-N-21 3) 9-M-14-O-18-T-1-N-20 4) 9-M-16-O-18-T-1-N-20 5) 4-I-1-L-16-G-21-E Solution:

Looking at the code for „STRANGER‟, it is clear that starting from the first letter, every alternate letter is replaced by its position in the alphabet. The other set of alternate letters stay as they are.

Word: S T R A N G E R Position: 19 na 18 na 14 na 5 na

Code: 19 T 18 A 14 G 5 R Now, consider the word „IMPORTANT‟.

Word: I M P O R T A N T

Position: 9 na 16 na 18 na 1 na 20 Code: 9 M 16 O 18 T 1 N 20

∴ The code for „IMPORTANT‟ is 9-M-16-O-18-T-1-N-20. Hence, option 4. 16. 3 Marks

Read each of the passages and answer the questions that follow.

Today‟s society is reeling from the effects of constant advertising messages. These advertisements promote harmful and dangerous things that weaken social fabric and lead to the ill-health of young people. Advertisers promote unhealthy things and are not genuinely concerned about society. Fast food adverts are a

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major reason why children today are overweight.

Which of the following statements, if true, best weakens the argument presented in the passage?

1) Advertising affecting obesity is just a myth.

2) Society cannot deal with the pressure of advertising. 3) Fast food is the leading cause of obesity.

4) Researchers have found that most young people tend to be quite lean till the age of 20.

5)

Advertisements that promote unhealthy products are not as common as believed and fast food companies are now promoting their healthier dishes on offer.

Solution:

The main idea presented in the passage is that advertisements promote dangerous things that have a negative impact on people. The example is that of fast food advertisements targeted at young people. To weaken the argument we need a statement that shows that all advertisements do not promote unhealthy things and that fast food companies do not promote fattening food products which leads to children being overweight.

Option 1 does not weaken the argument as there is no concrete data. Option 2 simply rephrases what has already been stated in the passage. Option 3 supports the passage.

Option 4 is unrelated to the effects of advertising and merely adds more data to the passage.

Option 5 is the correct answer since it weakens the argument by stating that advertisements that promote unhealthy products are rare (this goes against the statement that, „Today‟s society is reeling from the effects of constant advertising messages‟). Secondly, it also says that fast-food companies have been promoting their healthier dishes, so the advertisements promoting these kinds of food cannot be held accountable for obesity among the young.

Group Question

Ten friends go to watch the IPL match. The seating arrangement is such that 5 people sit in one row while the other 5 sit in the other row. The following information is known about them.

1. The rows are one behind another.

2. There are only 4 girls in the group - Shalini, Priya, Priyanka and Sonia. 3. Each row has an equal number of girls.

4. Shalini does not sit in the same row as Ram. 5. Priya and Priyanka sit in different rows.

6. Ramesh and Suresh have to sit together if Karan and Sonia sit together and vice versa.

7. Karan sits in the 1st row.

8. If Abeer sits in the 1st row, then Prem sits behind Suresh otherwise Suresh sits behind Prem.

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9. Shalini always sits to the left of Ramesh.

17. 3 Marks

If Ram sits in the 1st row, who can sit to his left from the following? 1) Suresh 2) Abeer 3) Ramesh 4) Prem 5) Cannot be determined Solution:

If Ram is sitting in the 1st row, Shalini has to sit in the 2nd row.

Shalini always sits to the left of Ramesh and hence Ramesh is also sitting in the 2nd row.

Now, one of Priya or Priyanka must sit in the 2nd row.

Now, if Karan and Sonia sit separately, then Sonia has to sit in the 2nd row (as Karan always sits in the 1st row).

However, this is not possible as there are already 2 girls in the 2nd row. Thus, Karan and Sonia sit together in 1st row which means Suresh has to sit with Ramesh in the 2nd row.

Thus, Prem has to sit in the 1st row which means Abeer is in the 2nd row. Of the given options, only Prem is seated in the 1st row.

If Sonia sits in the 2nd row, who will definitely be seated in the 1st row? 1) Ramesh 2) Suresh 3) Abeer 4) Priya 5) Cannot be determined Solution:

Now, one of Priya or Priyanka would be seated with Sonia in the 2nd row. ∴ Shalini has to sit in the 1st

row which means Ramesh would also sit in the 1st row.

Also, Ram has to sit in the 2nd row.

Since Karan always sits in the 1st row and Sonia is now in the 2nd row, they are sitting separately.

∴ Ramesh and Suresh should be sitting in different rows i.e. Suresh has to sit in the 2nd row.

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But, since Suresh is in the 2nd row, Prem has to sit in the 1st row which means Abeer is in the 2nd row.

Boys and girls are alternately seated in the 1st row. If Sonia sits in the 1st row and Suresh is sitting at the right most end of one of the rows, who will occupy the 3rd place in the 1st row?

1) Prem 2) Abeer 3) Karan 4) Ram 5) Cannot be determined Solution:

If Sonia sits in 1st row, she and Karan are sitting together. ∴ Ramesh and Suresh are also sitting together.

Let us assume that Suresh is in the right most end of the 1st row. Now, one of Priya or Priyanka have to sit in the 1st row.

Since all the five seats in the 1st row are occupied, Shalini will have to sit in the 2nd row with Ram, which contradicts the given data.

∴ Suresh is sitting in the right most end of the 2nd

row.

Now, Prem must sit ahead of Suresh and hence he occupies the right most end of the 1st row.

i.e. Abeer is in the 2nd row.

Ramesh will sit in the 2nd row with Suresh and Shalini will be to the left of Ramesh and the remaining vacant spot will be occupied by one of

Priya/Priyanka.

∴ People sitting in the 1st

row: Karan, Sonia, Ram, Priya/Priyanka, Prem. We only know Prem's position and that girls and boys are sitting alternately. ∴ One of Karan or Ram can sit in the 3rd

place. Hence, option 5. 20. 3 Marks

If “CHIKU” = 20 and “BRINJAL” = 42, what is the value of “PINEAPPLE”? 1) 50

2) 72 3) 44 4) 69 5) 41

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Solution:

The logic here is that the number of letters in the word is multiplied by 1 less than the count.

The word “CHIKU” has 5 letters. ∴ It is coded as 5 × 4 = 20.

Similarly, the word “BRINJAL” has 7 letters, hence coded as 7 × 6 = 42. Using the same logic, “PINEAPPLE” is coded as 9 × 8 = 72.

Four of the five options are equal in magnitude. Which of the options has a magnitude different from the others?

1. 5465 − 4287 2. 1178 + 2145 − 1015 − 1130 3. (1100 ÷ 2) + (1884 ÷ 3) 4. 9 × 99 + 6 × 66 – 3 × 33 5. 666 + 333 + 111 + 66 + 2 1) 1 2) 2 3) 3 4) 4 5) 5 Solution: 1. 5465 − 4287 = 1178 2. 1178 + 2145 − 1015 − 1130 = 1178 + 2145 − 2145 = 1178 3. (1100 ÷ 2) + (1884 ÷ 3) = 550 + 628 = 1178 4. 9 × 99 + 6 × 66 − 3 × 33 = 891 + 396 − 99 = 1287 − 99 = 1188 5. 666 + 333 + 111 + 66 + 2 = 1178 Hence, option 4. Group Question

Four friends Ajay, Bob, Chetan and Dan live in house numbers 1, 2, 3 and 4, though not necessarily in the same order. They own the following brand of cars : Skoda, Sumo, Santro and Swift among them. No two persons own the same brand of car. The following information is known about them.

A. Neither Ajay nor Dan live in an even numbered house. B. The person in house 2 drives a Skoda.

C. The owner of the Swift is in house number 4. D. Ajay does not own a Sumo.

E. Bob drives the Swift.

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22. 3 Marks

In what house number does Ajay live? 1) 1 2) 3 3) 1 or 3 4) 2 5) 2 or 4 Solution:

There are 3 parameters here : Person, Brand of Car and House number. Now, Bob drives the Swift and the owner of the Swift stays in house number 4.

Therefore, Bob lives in house number 4. ∴ Bob - Swift - House 4.

Neither Ajay nor Dan stay in even numbered houses.

Therefore, these two stay in house numbers 1 and 3 (in no specific order). Hence, Chetan has to stay in house no 2.

Since the person in house number 2 drives a Skoda, Chetan drives a Skoda. ∴ Chetan - Skoda - House 2.

Now, Ajay can drive a Sumo or a Santro.

However, it is given that Ajay does not drive a Sumo. Therefore, Ajay drives a Santro and Dan drives a Sumo.

However, it cannot be determined whether Ajay stays in house number 1 or 3. He can stay in any one of the two.

Which car does Dan drive? 1) Santro 2) Sumo 3) Swift 4) Skoda 5) Cannot be determined Solution:

From the solution to the first question of this set, it is obvious that Dan drives the Sumo. Hence, option 2. 24. 3 Marks

If Ajay lives in house 1, then in which house does Dan live? 1) 2

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3) 4 4) 3 or 4

5) None of these Solution:

From the solution to the first question of this set, Ajay and Dan stay in house numbers 1 and 3 (in no specific order).

Therefore, if Ajay stays in house number 1, Dan has to stay in house number 3. Hence, option 2. 25. 3 Marks

On a particular evening, Mansi was heading home from office, walking towards the north. She crossed her daughter Latika mid way on the route. Mansi observed that her shadow was falling towards Latika‟s right. In which direction was Latika moving? 1) North 2) South 3) East 4) West 5) Indeterminate Solution:

In the evening, since the sun is in the west, the shadow of an object will fall towards the east.

Since Mansi was walking towards the north, her shadow fell on her right hand side.

For this shadow to fall on Latika's right, there can be two possiblities: Case 1 : Latika was walking towards the north.

If Latika was also walking towards the north and was either on the left of Mansi or parallel to Mansi (on the right side) such that the distance between Latika and Mansi (at the point of crossing) was less than the length of the shadow, Mansi's shadow would fall on Latika's right.

Hence, the given condition would be satisfied. Case 2 : Latika was walking towards the south.

If Latika was walking towards the south and was parallel to Mansi (on the right side) such that the distance between Latika and Mansi (at the point of crossing) was more than the length of the shadow, Mansi's shadow would fall on Latika's right.

Hence, the given condition would still be satisfied.

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Hence, option 5. Group Question

The columns and rows of matrix 1 are numbered 0 to 4 and that of matrix 2 from 5 to 9. A letter from these matrices is represented first by its row and next by column number e.g. O can be represented as 23, 34 and so on. In each of the questions that follow, find the set of codes that represents the word in that corresponding question.

26. 3 Marks MORAL 1) 43, 11, 77, 02, 96 2) 32, 33, 75, 44, 85 3) 22, 23, 66, 21, 65 4) 01, 23, 55, 03, 77 5) 14, 23, 55, 33, 69 Solution: M can be coded as 01, 14, 22, 32 and 43 O can be coded as 00, 11, 23, 34 and 40.

Hence, option 2 can be eliminated. R can be coded as 55, 66, 75, 88 and 99.

Hence, option 1 can be eliminated. A can be coded as 02, 10, 21, 33 and 44.

Hence, option 4 can be eliminated. L can be coded as 56, 69, 77, 85 and 96.

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Hence, option 3 can be eliminated. Only option 5 contains all the correct codes. Hence, option 5. 27. 3 Marks TONE 1) 31, 23, 59, 68 2) 04, 11, 76, 59 3) 20, 32, 67, 89 4) 31, 00, 87, 57 5) 31, 43, 59, 65 Solution:

T can be coded as 04, 12, 20, 31 and 42. O can be coded as 00, 11, 23, 34 and 40. Hence, options 3 and 5 can be eliminated. N can be coded as 59, 67, 78, 86 and 95. Hence, options 2 and 4 can be eliminated. E can be coded as 57, 68, 76, 89 and 98. Only option 1 contains all the correct codes. Hence, option 1. 28. 3 Marks KITE 1) 87, 31, 04, 76 2) 65, 13, 24, 89 3) 97, 24, 02, 57 4) 65, 03, 12, 98 5) 79, 30, 98, 12 Solution:

K can be coded as 58, 65, 79, 87 and 97. I can be coded as 03, 13, 24, 30 and 41. Hence, option 1 can be eliminated. T can be coded as 04, 12, 20, 31 and 42. Hence, options 2, 3 and 5 can be eliminated. Only option 4 contains all the correct codes. Hence, option 4.

29.