1. In the figure below, what is the value of y? (GEOMETRY) (A) (B) (C) (D) (E) 40 50 60 100 120 Answer:
Vertical angles being equal allows us to fill in two angles in the triangle that y° belongs to. Sum of angles in a triangle = 180°.
So, y° + 40° + 80° = 180° y° + 120° = 180° y° = 60°
2. What is the area of the following square, if the length of BD is ? (GEOMETRY)
(A) (B) (C) (D) (E) 1 2 3 4 5 Answer:
We need to find the length of the side of the square in order to get the area. The diagonal BD makes two 45°-45°-90° triangles with the sides of the square.
Using the 45°-45°-90° special triangle ratio . If the hypotenuse is then the legs must be 2. So the length of the side of the square is 2. Area of square = s2 = 22 = 4
SALES OF WILDLIFE TOURS
Price of Tour Number of Purchased Tours
$5.00 120,000
$10.00 95,000
$20.00 65,000
3. A wildlife company offered tours for three different prices during a single year. Based on the information above, how much more money did the company make when the price was $20.00 than when the price was $5.00? (STATISTICS) (A) $35,000 (B) $70,000 (C) $350,000 (D) $700,000 (E) $1,050,000 Answer:
Find the total sales of the $5.00 tickets and the $20.00 tickets: $5.00 × 120,000 = $600,000
$20.00 × 65,000 = $1,300,000
Now simply subtract the smaller amount from the larger amount: $1,300,000 – $600,000 = $700,000
4. Train A travels at 100 miles per hour. Train B travels at 150 miles per hour. Train B leaves station exactly 30 minutes after Train A. After how many minutes will Train B catch up to Train A? (ALGEBRA)
(A) Never. (B) 20. (C) 40. (D) 60. (E) 120. Answer:
Analyze the given: (30 minutes passed)
Train A: if in 1 hour it travels 100 miles then in half an hour it should travel 50 miles. Train B: 0 miles.
So the 20 minutes answer is canceled. (60 minutes passed)
Train A: in 1 hour it travels 100 miles.
Train B: it is considered that for every hour it travels 150 so for every half an hour it travels 75 miles. So less than 60 minutes is a wrong answer. Now we need to see if it is never or 120 minutes.
(120 minutes passed)
Train A: in 2 hours it travels 200 miles.
5. Marie purchased six bags of apples from the store at a price of $3.69 a bag. When she arrived home, she realized that they were on sale for $3.19 a bag, so she returned to the store to get a refund of the difference. The cashier gave her the difference in quarters. How many quarters did Marie receive? (ARITHMETIC) (A) 2. (B) 12. (C) 13. (D) 76. (E) 77. Answer: Each bag = $3.69 so 3.69 × 6 = $22.14 On Sale = $3.19 /bag so 3.19 ×6 = $19.14 $22.14 - $19.14 = 3 so 3 ÷ ¼ = 12.
6. The ratio of red marbles to green marbles is 4 to 3. If there are 28 marbles in the bag, how many marbles will need to be removed to make the ratio of red to green equal? (ARITHMETIC)
(A) 1. (B) 2. (C) 3. (D) 4. (E) 5. Answer:
28 marbles with a ratio of 4:3 so (4+3=7), 28 ÷ 7 = 4, so the red is 4×4=16, and the green 4×3=12. So 16-12=4.
7. According to the graphs above, how many seniors are enrolled at Taft High School? (STATISTICS) (A) 375 (B) 525 (C) 750 (D) 1500 (E) 2125 Answer:
You must use information from both graphs to solve this question. First, find the total student enrollment at Taft High School. According to the bar graph, total enrollment is 2500 students.
Now use the information in the pie graph. Fifteen percent of the students at Taft High School are seniors: 15% of 2500 = ? , 0.15 × 2500 = 375.
A box contains cards with one question on each card. There are 4 categories of questions.
Each category has some easy and some difficult questions. The table shows the probability of selecting a card at random from the box.
8. There are 40 cards in the box. How many of these are music questions? (PROBABILITY) (A) 15 (B) 14 (C) 40 (D) 20 (E) 35 Answer: Music: 0.2+0.15 = 0.35 40÷35%= 14. 9. If 2x - 3 = 9, what is x2 - 4x + 2? (ALGEBRA) (A) 12 (B) 14 (C) 16 (D) 32 (E) 36 Answer: 2x-3=9, 2x=12, x=6, then x2 - 4x + 2, (6)2 – 4(6) + 2, 36 – 24 + 2 = 14. 10. If x - (2 - x) = 2, x =? (ALGEBRA) (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Answer: x - (2 - x) = 2, x - 2 + x = 2, 2x - 2 = 2, 2x = 4, x = 2.
11. Two circles both of radii 6 have exactly one point in common. If A is a point on one circle and B is a point on the other circle, what is the maximum possible length for the line segment AB? (GEOMETRY)
(A) 12 (B) 15 (C) 18 (D) 20 (E) 24 Answer:
Sketch the two circles touching at one point.
The furthest that A and B can be would be at the two ends. If the radius is 6 then the diameter is 2 × 6 = 12 and the distance from A to B would be 2 × 12 = 24
12. A broken washing machine will cost you $100 to repair, and a new washing machine will cost $250. Luckily, the new energy-efficient washing machine will save you $6 per month on your water bill compared to your current washing machine. How many months of savings from the new washing machine will it take to equal the difference in cost between buying a new washing machine and repairing it?
A) 20 B) 25 C) 30 D) 35 E) 40 Answer:
So we are trying to solve for the NUMBER OF MONTHS, which we can call x. x months of savings = the DIFFERENCE in cost between buying a new washing machine and repairing it. The difference between buying and repairing a washing machine is found by subtraction, or $250 – $100 = $150. Now we have $6x = $150. We can then solve for x by division. Dividing both sides of the equation by $6 gives us x = 25.
13. The total cost of 6 of equally priced gloves is $12.00. If the cost per glove is increased by $1.50, how much will 11 gloves cost at the new price?
A) $40.00 B) $39.50 C) $38.50 D) $37.00 E) $21.00 Answer:
To do that, we take the TOTAL COST divided by the NUMBER of gloves, or = $2.00 per glove.
The price per glove is INCREASED by $1.50. So the new price per glove is now $2.00 + $1.50 = $3.50. To find the cost for the 11 gloves we multiply 11 × $3.50 = $38.50.
14. In the figure above, points A, D, E all lie on the same line. What is the value of x?
A) 135° B) 100° C) 130° D) 50° E) 180° Answer:
A quadrilateral is made up of two triangles, so the sum of all the angles must be 180° × 2 = 360°. Now we should be able to find the missing angle in the figure, CDA. To find CDA, we subtract the other three angles from 360°. Which gives us 360° – 75° – 100° – 135° = 50° = CDA. Now, notice that x and CDA form a straight line. And a straight line has 180°, 180° – 50° = 130°.
$12.00 6
15. A certain robot is capable of folding and stacking two towels per hour. If it works for five hours each day, how many days will it take to fold 10,000 towels?
A) 1,000 B) 10 C) 1 D) 6 E) 60 Answer:
We are given that the machine can fold 2 towels every hour. And that it runs for 5 hours per day. Multiplying them out gives us 2 × 5 = 10 towels produced each day.
So = 1,000
16. If = g, what is the value of g?
A) -12 B) -2 C) 6 D) -2 or 6 E) 6 or -12 Answer:
4g + 12 = g 2, Subtracting both sides by (4g + 12) gives us the equation 0 = g 2 – 4g – 12, solve the quadratic equation by factoring to get 0 = (g – 6)(g + 2). (g – 6)(g + 2) to equal zero, g = 6 OR g = -2, Trying -2 , gives us 2 = -2 which is NOT correct. So -2 is NOT the answer. And trying 6 gives us 6 = 6, which means that 6 is the ONLY possible answer.
17. If 4b + d = c and 4b + c + d = 6, what is the value of c? A) 7
B) 6 C) 4 D) 3
E) It cannot be determined from the information given.
Answer:
Notice in the first equation that 4b + d = c.
And you can rearrange the second equation to be 4b + d + c = 6. So you can substitute the value c for 4b + d in the SECOND equation. Which gives you the new equation, c + c = 6. Or 2c = 6.
And dividing both sides by 2, gives us c = 3, which happens to be the answer. 10,000
10 √
18. (4, 8, 12, 16, ..)
The first term in this sequence is 4, and each term after the first is determined by adding 4. What is the value of the 30th term? A) 120 B) 160 C) 200 D) 240 E) 280 Answer:
Apply the formula: = 4+4(n-1)
= 4+4(30-1) = 120.
19. The perimeter of equilateral triangle W is 3 times the perimeter of equilateral triangle X. If the perimeter of X = 15, what is the length of one side of W?
A) 25 B) 5 C) 15 D) 20 E) 30 Answer:
We know that all equilateral triangles have sides of EQUAL LENGTH. So we know that equilateral triangle W has a perimeter that is 3 times that of X. And what is that value? We are given the perimeter of X, so the perimeter of W is 15 × 3 = 45. Since equilateral triangle W has 3 sides of equal length that sum to 45, we can find the length of one side simply by dividing. Perimeter W is 45 ÷ 3 = 15
20. Barb goes on a 50-mile bike ride every Monday evening. Barb completes the distance in 5 hours. At this rate, how many miles can Barb pedal in 2 hours and 30 minutes?
A) 50 B) 25 C) 30 D) 5 E) 10 Answer:
If we had the SPEED at which Barb can pedal, we could just multiply it by the time. Since Barb can pedal 50 miles in 5 hours, we can get Barb's speed by dividing distance by time. So Barb's speed is 50 miles / 5 hours. We are trying to figure out how far Barb can travel in 2 hours and 30 minutes, so we can just multiply this time (in hours) by Barb's speed. So 5/2 × 50 miles/5 hours, can be simplified to 25 miles.
