Diagnostic Test with Answers and Explanations

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Section 3: Quantitative

Time: 75 minutes

37 questions

This section consists of two different types of questions: Problem-Solving and Data Sufficiency. To answer the questions, select the best answer from the answer choices given.

The Problem-Solving questions require you to solve the problem and select the best answer choice.

Numbers: All the numbers used are real numbers.

Figures: A figure given for a question provides information that can be used to solve the problem. Figures are drawn to scale, as accurately as possible, unless it is stated otherwise. A line that appears straight should be considered a straight line. All figures given in this section lie in a plane unless it is stated otherwise.

Each Data Sufficiency problem contains a question followed by two statements, (1) and (2). You are asked to determine whether the statements are sufficient to answer the question. You need to use the information given in the statements along with your knowledge of general mathematics and other common facts (such as the number of minutes in an hour or the number of days in a year) to determine which of the following is true:

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient to answer the question.
5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question, and additional data specific to the problem is needed.

In any Data Sufficiency problem that asks for the value of an unknown quantity, the statements are sufficient to answer the question only when you can determine exactly one value.

1. If Susan was 31 years old 5 years ago, how old was she x years ago?
1. x - 36
2. x - 26
3. 36 - x
4. 26 - x
5. 26 + x
2. Kendra works 5 days per week and earns d dollars per day. Which of the following represents the amount Kendra earns at this job in w weeks?
1. 5dw
3. A homeowner wants to put up fencing around three sides of a rectangular portion of his yard and leave 70 feet unfenced. If the rectangular portion of the yard being fenced has an area of 2,800 square feet, how many feet of fencing does he need?
1. 80
2. 150
3. 400
4. 2,730
5. 4,900
4. If rs ≠ 0, is t an integer?
1. t = 3 r - 2s
2. r = s
5. If n is a positive integer and p = 3.021 × 10n, what is the value of n?
1. 3,021 < p < 302,100
2. 103 < p < 105
6. Is the positive integer x a prime number?
1. x is even
2. 2 < x < 19
7. If 25 percent of 400 is 40 percent of x, then x =
1. 65
2. 160
3. 250
4. 260
5. 440
8. During the first week of May, a bicycle retailer sold 10 bicycles of a certain brand at \$250.00 each. If, during the second week of May, 15 bicycles were sold at the sale price of \$180.00 each, by what amount did the revenue from weekly sales of these bicycles increase during the second week?
1. \$70
2. \$86
3. \$100
4. \$200
5. \$430
9. If the diameter of a circle is 10, then the circumference of the circle is
1. 10π
2. 20π
3. 25π
4. 100π
10. What is the value of the sum of a list of n odd integers?
1. n = 7
2. The square of the number of integers on the list is 49
11. Commissioner R wants to schedule a 2-hour meeting on Friday for herself and three other commissioners, S, T, and U. Is there a 2-hour period on Friday that is open for all four commissioners?
1. On Friday, commissioners R and S have an open period from 10:00 a.m. to 2:00 p.m.
2. On Friday, commissioner T has an open period from 11:00 a.m. to 1:00 p.m. and commissioner U has an open period from 8:00 a.m. to 12:00 p.m.
12. If 13 painters participated in a certain art gallery opening featuring oil paintings, how many different oil paintings were there?
1. The art gallery opening lasted 90 minutes.
2. The ratio of the number of painters who participated in the opening to the number of different oil paintings was 1 to 5.
13. Franco purchased brand R pens for \$3.30 per box and brand S pens for \$2.00 per box. If Franco purchased a total of 12 boxes of pens for \$37.00, how many boxes of brand R pens did he purchase?
1. 2
2. 3
3. 5
4. 7
5. 10
14. If the length and the width of a patio were each increased by 30 percent, what would be the percent increase in the area of the patio?
1. 69%
2. 24%
3. 43%
4. 26%
5. 20%
15. Amanda is a salesperson. Each week, she earns a salary of \$480 plus 5 percent of the amount of her total sales that exceeds \$1,000 for the week. If Amanda earned a total of \$760 one week, what were her total sales that week?
1. \$2,900
2. \$3,300
3. \$4,800
4. \$5,000
5. \$6,600
16. Does xy = 50?
1. 4 x = 20 and 7y = 70
17. If x is a positive integer, is the square root of x an integer?
1. x is the square of an integer.
2. The square root of x is the square of an integer.
18. How many books were sold at a certain bookstore today?
1. A total of 200 books were sold at the bookstore yesterday, 20 fewer than twice the number sold today.
2. The number of books sold at the bookstore yesterday was 90 more than the number sold today.
19. If a2 = 4b2 and 3b = 9, what is the value of a2 + b?
1. 9
2. 27
3. 36
4. 39
5. 72
20. The number 0.825 is how much greater than ?
1. 0.75
2. 0.50
3. 0.250
4. 0.020
5. 0.025
21. If x picture frames cost \$6.00 each and y picture frames cost \$13.00 each, then the average (arithmetic mean) cost in dollars per picture frame is equal to
22. If p + q = r, what is the value of q?
1. p = 31
2. r + 31 = p
23. If R is an integer between 1 and 100, what is the value of R?
1. One of R’s digits is 2 more than the other, and the sum of the digits is 10.
2. R > 50
24. What is the units digit of (11)4(22)3(36)2?
1. 1
2. 4
3. 6
4. 8
5. 9
25. A flat triangular flower bed has the dimensions shown in the figure above. If x2 = 4, what is the area of the flower bed in square feet?
1. ¼
2. ½
3. 1
26. Is the value of a2 + ab equal to 0?
1. a = 0
2. b = 0
27. In isosceles triangle ABC, what is the measure of angle B?
1. The measure of angle A is 80°.
2. The measure of angle C is 50°.
28. What were the gross revenues from ticket sales for a certain movie during the second week that it ran?
1. Gross revenues during the second week were \$2.8 million less than during the first week.
2. Gross revenues during the third week were \$4.2 million less than during the first week.
29. If Jill loses 7 pounds, she will weigh half as much as her brother. Together, they now weigh 343 pounds. What is Jill’s present weight, in pounds?
1. 107
2. 119
3. 127
4. 133
5. 143
30. (x + y)2 - 2xy =
1. x2 + y2
2. x2
3. 0
4. x2 - y2
5. (x - y)2
31. What is the decimal equivalent of ?
1. 0.44
2. 0.16
3. 0.048
4. 0.0256
5. 0.0064
32. What is the value of x?
1. x6 = 729
2. x5 < x4
33. How many balloons does Kenny have?
1. If Kenny had 3 fewer balloons, he would have only half as many as he actually has.
2. Kenny has twice as many blue balloons as red balloons.
34. If n is a prime number greater than 3, which of the following could be a prime number?
1. n2
2. 3n
3. n - 6
4. n2 + 1
35. At a certain restaurant, a meal cost \$42, and there was no tax. If the tip was more than 15 percent but less than 20 percent of the cost of the meal, then the total amount paid must have been between
1. \$42 and \$45
2. \$45 and \$46
3. \$46 and \$47
4. \$47 and \$48
5. \$48 and \$51
36. If the sum of the lengths of the edges of a cube is 48, the volume of the cube is
1. 1,728
2. 512
3. 216
4. 64
5. 36
37. A certain highway has exits A, B, C, and D in that order. What is the distance from exit B to exit C?
1. The distance from exit A to exit C is 7 miles.
2. The distance from exit B to exit D is 9 miles.
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