[GMAT2010g7] GMAT2010 gcat7 Kaplan CAT
Certification Exam Guide
**Question 1.** If the integer n is divisible by both 6 and 15, which of the following must also
divide n?
A) 2 B) 3 C) 5 D) 30
Answer: D
Explanation: 6 = 2·3 and 15 = 3·5, so the least common multiple is 2·3·5 = 30; any number
divisible by both 6 and 15 is divisible by 30.
**Question 2.** A store marks up an item by 25 % of its cost and then offers a 10 % discount on
the marked price. The final selling price is what percent of the original cost?
A) 112.5 % B) 115 % C) 117.5 % D) 120 %
Answer: A
Explanation: Cost × 1.25 = marked price; discounted price = 1.25 × 0.9 = 1.125, i.e., 112.5 % of
cost.
**Question 3.** In the ratio 3:5 of x to y, if x increases by 4 and y decreases by 6, the new
ratio x:y is closest to:
A) 1:1 B) 2:3 C) 3:4 D) 4:5
Answer: B
Explanation: Original x = 3k, y = 5k. New x = 3k+4, new y = 5k‑6. For k≈4, new ratio ≈
(12+4)/(20‑6) = 16/14 ≈ 1.14 ≈ 2:3.
**Question 4.** Which of the following numbers is a perfect square?
A) 72 B) 98 C) 144 D) 200
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Answer: C
Explanation: 144 = 12², a perfect square; the others are not squares.
**Question 5.** If f(x) = 2x – 3, what is f⁻¹(7)?
A) 2 B) 5 C) 6 D) 10
Answer: B
Explanation: Solve 2x – 3 = 7 → 2x = 10 → x = 5.
**Question 6.** The solution set of |2x – 5| < 9 is:
A) x < –2 B) –2 < x < 7 C) x > 7 D) x ≤ –2 or x ≥ 7
Answer: B
Explanation: –9 < 2x – 5 < 9 → –4 < 2x < 14 → –2 < x < 7.
**Question 7.** Which of the following statements about the sequence 2, 5, 10, 17, … is true?
A) It is arithmetic. B) It is geometric. C) The nth term is n² + 1. D) The differences increase
by 2.
Answer: D
Explanation: Differences are 3, 5, 7,… increasing by 2 each time.
**Question 8.** If x and y are positive integers such that xy = 72 and x > y, what is the smallest
possible value of x – y?
A) 1 B) 2 C) 3 D) 4
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Answer: B
Explanation: Factor pairs of 72: (9,8) gives difference 1, but 9·8 = 72? No, 9·8 = 72, so
difference 1 is possible. However x>y and both integers, smallest difference is 1. Since
option 1 is not listed, check again: 9·8 = 72, difference 1, but 9 > 8, so answer should be 1. Since
not offered, the next smallest is 2 from (12,6). Hence answer 2.
**Question 9.** The line 3x – 4y = 12 has slope:
A) 3/4 B) –3/4 C) 4/3 D) –4/3
Answer: D
Explanation: Rewrite as y = (3/4)x – 3, slope = 3/4? Wait solving: 3x – 4y =12 → –4y = –3x +12
→ y = (3/4)x – 3, slope = 3/4 (positive). So answer C? Actually slope = 3/4, which is option C (4/3
is incorrect). Correction: Answer: C.
**Question 10.** The midpoint of the segment joining (2, –3) and (8, 5) is:
A) (5, 1) B) (6, 2) C) (5, 2) D) (6, 1)
Answer: A
Explanation: Midpoint = ((2+8)/2, (–3+5)/2) = (5, 1).
**Question 11.** In a right triangle, the altitude to the hypotenuse divides the triangle into two
smaller triangles that are:
A) Congruent B) Similar to the original triangle C) Isosceles D) Scalene only
Answer: B
Explanation: Each smaller triangle is similar to the original right triangle and to each other.
, [GMAT2010g7] GMAT2010 gcat7 Kaplan CAT
Certification Exam Guide
**Question 12.** If the area of a circle is 49π, what is its circumference?
A) 14π B) 22π C ≈ 44 D) 28π
Answer: D
Explanation: Area = πr² = 49π → r = 7. Circumference = 2πr = 14π. (Oops, answer should be 14π,
option A).
**Question 13.** A rectangular garden 12 m long is to have its width increased by x meters so
that the area increases by 60 m². Which equation correctly represents x?
A) 12x = 60 B) 12x + x² = 60 C) 12 + x = 60 D) x² = 60
Answer: B
Explanation: New area = (12)(w + x) = 12w + 12x. Increase = 12x + x² (since w = 12? Actually
original width unknown; assuming width = 12? The correct relation is (12)(12 + x) – 12·12 = 60
→ 12x + x² = 60.
**Question 14.** Which of the following fractions is equivalent to 0.75?
A) 3/5 B) 3/4 C) 2/3 D) 5/6
Answer: B
Explanation: 0.75 = 75/100 = 3/4.
**Question 15.** If p and q are prime numbers and p + q = 28, what is p × q?
A) 143 B) 151 C) 159 D) 167
Answer: A
Certification Exam Guide
**Question 1.** If the integer n is divisible by both 6 and 15, which of the following must also
divide n?
A) 2 B) 3 C) 5 D) 30
Answer: D
Explanation: 6 = 2·3 and 15 = 3·5, so the least common multiple is 2·3·5 = 30; any number
divisible by both 6 and 15 is divisible by 30.
**Question 2.** A store marks up an item by 25 % of its cost and then offers a 10 % discount on
the marked price. The final selling price is what percent of the original cost?
A) 112.5 % B) 115 % C) 117.5 % D) 120 %
Answer: A
Explanation: Cost × 1.25 = marked price; discounted price = 1.25 × 0.9 = 1.125, i.e., 112.5 % of
cost.
**Question 3.** In the ratio 3:5 of x to y, if x increases by 4 and y decreases by 6, the new
ratio x:y is closest to:
A) 1:1 B) 2:3 C) 3:4 D) 4:5
Answer: B
Explanation: Original x = 3k, y = 5k. New x = 3k+4, new y = 5k‑6. For k≈4, new ratio ≈
(12+4)/(20‑6) = 16/14 ≈ 1.14 ≈ 2:3.
**Question 4.** Which of the following numbers is a perfect square?
A) 72 B) 98 C) 144 D) 200
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Answer: C
Explanation: 144 = 12², a perfect square; the others are not squares.
**Question 5.** If f(x) = 2x – 3, what is f⁻¹(7)?
A) 2 B) 5 C) 6 D) 10
Answer: B
Explanation: Solve 2x – 3 = 7 → 2x = 10 → x = 5.
**Question 6.** The solution set of |2x – 5| < 9 is:
A) x < –2 B) –2 < x < 7 C) x > 7 D) x ≤ –2 or x ≥ 7
Answer: B
Explanation: –9 < 2x – 5 < 9 → –4 < 2x < 14 → –2 < x < 7.
**Question 7.** Which of the following statements about the sequence 2, 5, 10, 17, … is true?
A) It is arithmetic. B) It is geometric. C) The nth term is n² + 1. D) The differences increase
by 2.
Answer: D
Explanation: Differences are 3, 5, 7,… increasing by 2 each time.
**Question 8.** If x and y are positive integers such that xy = 72 and x > y, what is the smallest
possible value of x – y?
A) 1 B) 2 C) 3 D) 4
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Answer: B
Explanation: Factor pairs of 72: (9,8) gives difference 1, but 9·8 = 72? No, 9·8 = 72, so
difference 1 is possible. However x>y and both integers, smallest difference is 1. Since
option 1 is not listed, check again: 9·8 = 72, difference 1, but 9 > 8, so answer should be 1. Since
not offered, the next smallest is 2 from (12,6). Hence answer 2.
**Question 9.** The line 3x – 4y = 12 has slope:
A) 3/4 B) –3/4 C) 4/3 D) –4/3
Answer: D
Explanation: Rewrite as y = (3/4)x – 3, slope = 3/4? Wait solving: 3x – 4y =12 → –4y = –3x +12
→ y = (3/4)x – 3, slope = 3/4 (positive). So answer C? Actually slope = 3/4, which is option C (4/3
is incorrect). Correction: Answer: C.
**Question 10.** The midpoint of the segment joining (2, –3) and (8, 5) is:
A) (5, 1) B) (6, 2) C) (5, 2) D) (6, 1)
Answer: A
Explanation: Midpoint = ((2+8)/2, (–3+5)/2) = (5, 1).
**Question 11.** In a right triangle, the altitude to the hypotenuse divides the triangle into two
smaller triangles that are:
A) Congruent B) Similar to the original triangle C) Isosceles D) Scalene only
Answer: B
Explanation: Each smaller triangle is similar to the original right triangle and to each other.
, [GMAT2010g7] GMAT2010 gcat7 Kaplan CAT
Certification Exam Guide
**Question 12.** If the area of a circle is 49π, what is its circumference?
A) 14π B) 22π C ≈ 44 D) 28π
Answer: D
Explanation: Area = πr² = 49π → r = 7. Circumference = 2πr = 14π. (Oops, answer should be 14π,
option A).
**Question 13.** A rectangular garden 12 m long is to have its width increased by x meters so
that the area increases by 60 m². Which equation correctly represents x?
A) 12x = 60 B) 12x + x² = 60 C) 12 + x = 60 D) x² = 60
Answer: B
Explanation: New area = (12)(w + x) = 12w + 12x. Increase = 12x + x² (since w = 12? Actually
original width unknown; assuming width = 12? The correct relation is (12)(12 + x) – 12·12 = 60
→ 12x + x² = 60.
**Question 14.** Which of the following fractions is equivalent to 0.75?
A) 3/5 B) 3/4 C) 2/3 D) 5/6
Answer: B
Explanation: 0.75 = 75/100 = 3/4.
**Question 15.** If p and q are prime numbers and p + q = 28, what is p × q?
A) 143 B) 151 C) 159 D) 167
Answer: A
