Introduction: In the SBI PO exam you can get 5 to 7 questions from data sufficiency test. In this type of questions the candidates are required to find out whether a questions can be answered or not with the help of the given data.
Here, we will practice few questions of Data Sufficiency Test
Data sufficiency questions are associated more with quantitative ability. These questions require maximum clarity of understanding. In DS question we need to decide whether the data given is sufficient to answer the question or not.
Each problem consists of a question followed by two statement I and II. We have to determine whether the information given by the statements is sufficient to answer the question with this we should also rely on our knowledge of mathematics and ordinary facts. These are the five option generally provided in the question paper:
(a) Statement I alone is sufficient to answer the question.
(b) Statement II alone is sufficient to answer the question.
(c) Either statement I or II alone is sufficient to answer the question.
(d) Both the statement together are necessary to answer the question.
(e) Neither statement I nor II is sufficient to answer the question
61 SBI PO Exam Study Package Flow chart for solving DS questions:
Tricks:
To solve DS questions we should go through the following tricks
1. The given data should provide the unique answer only, then it will be considered as valid.
2. But the unique answer does not mean that it cannot have two different answers from two different statements separately.
3. The statement which simply states a mathematics formula is not sufficient to answer the question.
4. The data is not sufficient if a statement only repeats the information given in the question.
5. Each statement should be treated as a separate statement. The statement I can give us something useful and then may be the same information is given in statement II with some variation, what we generally do is we dump the statement II thinking that we already have the information in statement I and we do not need the statement II. But there is also an option that either of the two statements alone can solve the question.
So solve both the statement separately.
6. There is an option that either of the two statements alone can solve the question. Do not choose this option just because one statement is helpful. We positively need both the statement.
7. Do not forget to try both the statement together. In a big rush we often eliminate choice (a) because statement I does not work. Then we eliminate (b) as statement II
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does not work. And then immediately we mark the option that state that neither of the statement is sufficient. We forget that there is a choice that state both the statement together is necessary to solve the question.
8. As soon as we come to know that the data is sufficient to answer the question, stop. Do not try to solve these DS problems till the end as the section is called data sufficiency not problem solving.
Example 1. The remainder when x is divided by 30 is?
I. X is a multiple of 3.
II. X is a multiple of 7
Solution: (e) Neither statement I and II a one nor taken together can give us the remainder as in this case remainder will vary with the value of x.
Example 2. The average of 3 consecutive odd integers is?
I. One of the integer is -1
II. The sum of two of the integers is 4 Solution: (d) From statement I, we get
a-2 a a+2
-1 1 3
-3 -1 1
-5 -3 -1
So we cannot find the average from statement I only.
Using only II we can say that the numbers are -1, 1-, 3 or 1, 3, 5
Using both the only possibility is -1, 1, 3 and hence the average can be find out
63 SBI PO Exam Study Package Example 3. How many students appeared for the examination?
I. The passed students are only 40%.
II. The pass percentage would have been 42% if 10 more students passed the exam.
Solution: (d) Let the total number of student appeared in the exam be x Statement I gives the information of passed student i.e 40%.
Statement II is also not complete alone.
If both the statement are combined together we get , 40𝑥100+ 10 =42𝑥100
⟹ 1002𝑥 = 10 ⟹ 𝑥 = 500 Hence x can be calculated.
64 SBI PO Exam Study Package PRACTICE QUESTIONS
Directions: Each question is followed by two statements 'I' and 'II'. Mark your answer as (a) If the question can be answered with the help of statement 'I' alone.
(b) If the question can be answered with the help of statement `II' alone.
(c) If the question can be answered with the help of both the statements together but not with the help of either statement alone.
(d) If the question cannot be answered even with the help of both the statements taken together or separately.
(e) If the question can be answered with the help of either the statement ‘I’ or the statement ‘II’.
1. How far is town A from town B? Town C is 15 km west of town A.
I. It is 10 km from town B to town C.
II. There is a canal between town A and town B.
2. Adi had an average score of 85 in three tests. What was the Adi's lowest score?
I. Adi's highest score was 95.
II. The average of Adi's two highest scores was 92.
3. A shopkeeper sold an article for Rs. 100. How much profit did he earn?
I. 20% profit would have been earned if it were sold for Rs.90.
II. The profit was one-third of the purchase price.
4. What is Suman’s age today?
I. Today, Suman’s age is five times her son’s present age.
II. Two years hence, Suman’s age will be three times her daughter’s age at that time.
65 SBI PO Exam Study Package 5. Which is costlier – a cup of sweetened corn or a bottle of beer?
I. Sweetened corns are sold at 4 cups for a Rs. 100.
II. Two bottles of beer can be exchanged for 4 cups of corn.
6. Esha opened a savings account that gives simple annual interest by depositing Rs. 750.
What was the annual rate of interest?
I. The bank does not charge for service and she made no transactions for the first 3 years.
II. Three years later her savings were Rs. 999
7. A city doubles its population every 5 years. How long will it take to increase its population by 3,600 from its present size?
I. In 1972 the population was 475.
II. The present population is 900.
8. How many students appeared for the examination?
I. Only 50% of students passed the examination.
II. If 10 more students passed, the pass percentage would have been 51%.
9. The ratio of milk to water in a mixture is 5 : 1. How many litres of water should be added to make the ratio 5 : 3?
I. The amount of water to be added is one third of the original mixture.
II. The ratio of half the amount of milk to the amount of water in the original mixture is 5 : 2.
10. What is the speed of the boat in still water?
I. It takes 2 hours to travel from A to B downstream.
II. It takes 4 hours to travel B to A upstream.
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11. Sandhya’s house is 40km away from Delhi. How long does the round trip from home to delhi and back?
I. Sandhya travelled at a uniform rate of 30km/hr for the whole trip.
II. If Sandhya travelled 10km/hr faster, then it would have taken her three fourths of the time for the whole trip.
Answers:
1. (d) 2. (b) 3. (c)
4. (d) 5. (b) 6. (c)
7. (b) 8. (c) 9. (d)
10. (d) 11. (c)
Explanations:
1. Ans.
Given:
From the first statement, we realise that the distance between town B and town C is 10km;
but the direction is not known.
C 15 km A 10 km B
10 km C 15 km A B
C 15 km A
67 SBI PO Exam Study Package From second statement nothing is known about the direction.
Thus the question cannot be answered using the given statements. Option (d) 2. Ans.
Let the lowest score be 𝑙, the highest be ℎ, and the middle one be 𝑚 Then,
𝑙 + 𝑚 + ℎ
3 = 85
⇒ 𝑙 + 𝑚 + ℎ = 85 × 3 = 255 Statement I:
𝑙 = 95 ⇒ 𝑚 + ℎ = 255 − 95 = 160
Thus statement I alone is not sufficient to answer the question Statement II:
𝑚 + ℎ 2 = 92
⇒ 𝑚 + ℎ = 92 × 2 = 184
Also, 𝑙 + 𝑚 + ℎ = 85 × 3 = 255
Thus, 𝑙 = 255 − 𝑚 + ℎ = 255 − 184 = 71
Thus Statement II alone is sufficient to answer the question.
Option (b)
B 10 km
C 15 km A
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Thus, statement I alone gives the answer.
Statement II:
Thus, statement II alone also gives the answer. Option (c) 4. Ans.
Statement I:
Today,
Suman’s age = 5 × (Her son’s age).
Thus statement I alone is not sufficient to answer the question Statement II:
Two years hence,
Suman’s age = 3 x (her daughter’s age)
69 SBI PO Exam Study Package Thus statement II alone is not sufficient to answer the question
Clearly, data even in I and II is not sufficient to get Suman’s present age.
Option (d) 5. Ans.
Statement I:
A cup of corn costs Rs. 100/4 = Rs. 25.
The rate of a bottle of beer is unknown so comparison cannot be made.
Thus statement I alone is not sufficient to answer the question Statement II:
2 x (bottle of beer) = 4 x (Cup of corn) Bottle of beer = 2 x (Cup of corn)
Thus a bottle of beer is costlier than a cup of corn.
Thus statement II alone is sufficient to answer the question Option (b)
6. Ans.
Statement I:
Statement I indicates that the amount deposited initially remained unchanged for 3 years. It does not talk about anything else.
Thus statement I alone is not sufficient to answer the question Statement II:
It indicates the amount accumulated at the end of 3 years.
Here we are not sure if any transaction was made during the three years or not.
Thus statement II alone is not sufficient to answer the question.
Clearly, data in I and II is sufficient to answer the question as shown below:
70 SBI PO Exam Study Package Total interest in three years = 999-750 = 249
Interest per year = 249/3 = 83
Annual Rate of interest = 83/750 = 11.06%
(It should be noted here that the actual rate need not be calculated to answer this question) Option (c)
7. Ans.
Statement I:
Statement I is of no use since present year/population is not mentioned.
Thus statement I alone is not sufficient to answer the question Statement II:
Present population is 900 Population after 5 years = 1800 Population after 10 years = 3600 Thus, the answer is 10 years.
Thus statement II alone is sufficient to answer the question.
Option (b) 8. Ans.
Let the total number of students that appeared in the examination be x.
Statement I:
No of passed students = 50% of x = 0.5x
Thus, statement I alone is not sufficient to answer the question Statement II:
Let the passed number of students be p.
71 SBI PO Exam Study Package P + 10 = 51% of x
Thus statement II alone is not sufficient to answer the question.
Statement I and II together:
0.5x + 10 = 0.51x 0.01x = 10 X = 1000 Option (c) 9. Ans.
Since the volume is not given in any of the statements, the question cannot be solved using both the information together.
Option (d) 10. Ans.
Let the distance between A and B be D km and the speed of the boat and current in still water be x km/hr and y km/hr, respectively.
Statement I:
D = (x–y) 2
Thus, statement I alone is not sufficient to answer the question Statement II:
D = (x–y) 4
Thus statement II alone is not sufficient to answer the question.
Statement I and II together:
Even if we combine both statements, we cannot find out the answer, because we have two equations and three variables.
Option (d)
72 SBI PO Exam Study Package 11. Ans.
Let the speed of Sandhya be x km/hr.
Time for round trip = 80/x Statement I:
x = 30km/hr Time = 80/30 hrs.
Thus, statement I alone is sufficient to answer the question Statement II:
If speed = x + 10
Then, time = ¾ of 80/x = 60/x Also, distance = 40km
i.e. (x + 10) (60/x) = 40
From this equation x can be found out, and so can be time.
Thus statement II alone is sufficient to answer the question.
Option (c)
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