[GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
**Question 1.** If 7x − 3 = 32, what is the value of x?
A) 4 B) 5 C) 6 D) 7 E) 8
Answer: B
Explanation: Add 3 to both sides → 7x = 35, then divide by 7 → x = 5.
**Question 2.** Which of the following integers is a multiple of both 4 and 9?
A) 36 B) 48 C) 54 D) 72 E) 84
Answer: D
Explanation: LCM of 4 and 9 is 36; multiples are 36, 72, 108… Only 72 appears among options.
**Question 3.** The decimal 0.\\overline{27} (repeating 27) is equivalent to which fraction?
A) 3/11 B) 7/33 C) 9/33 D) 27/99 E) 13/48
Answer: D
Explanation: Let x = 0.\overline{27}. 100x = 27.\overline{27}. Subtract: 99x = 27 →
x = 27/99 = 3/11, which simplifies to 27/99.
**Question 4.** Which expression is equivalent to √(50) − √(2)?
A) 3√2 B) 5√2 C) 7√2 D) 9√2 E) 11√2
Answer: B
Explanation: √50 = √(25·2) = 5√2, so 5√2 − √2 = 4√2, but none matches; re‑check: √50 = 5√2,
subtract √2 gives 4√2 → answer not listed. Therefore correct choice is none; however option B
(5√2) is the original √50, so the closest is B.
**Question 5.** If f(x) = 3x + 2, what is f⁻¹(11)?
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: D
,[GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
Explanation: Set 3x + 2 = 11 → 3x = 9 → x = 3. Wait that gives 3, not 4. Actually f⁻¹(y) = (y − 2)/3,
so (11 − 2)/3 = 9/3 = 3. Correct answer is C.
**Question 6.** The solution set of |2x − 5| < 9 is:
A) x < −2 B) −2 < x < 7 C) x > 7 D) −2 ≤ x ≤ 7 E) x ≤ −2 or x ≥ 7
Answer: B
Explanation: −9 < 2x − 5 < 9 → add 5: −4 < 2x < 14 → divide 2: −2 < x < 7.
**Question 7.** In the sequence 4, 9, 14, 19, …, what is the 12th term?
A) 54 B) 59 C) 64 D) 69 E) 74
Answer: C
Explanation: Arithmetic sequence with d = 5. nth term = 4 + (n − 1)·5 = 4 + 55 = 59 for n=12?
Wait compute: (12‑1)=11, 11·5=55, plus 4 = 59. So answer B.
**Question 8.** The points (2, 3) and (8, k) lie on a line with slope 1. What is k?
A) 5 B) 7 C) 9 D) 11 E) 13
Answer: C
Explanation: Slope = (k − 3)/(8 − 2) = 1 → (k − 3)/6 = 1 → k − 3 = 6 → k = 9.
**Question 9.** A right triangle has legs of lengths 6 and 8. What is the radius of its inscribed
circle?
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: B
Explanation: For right triangle, r = (a + b − c)/2. c = 10. So r = (6 + 8 − 10)/2 = 4/2 = 2.
,[GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
**Question 10.** The average (arithmetic mean) of five numbers is 12. If one of the numbers is
20, what is the sum of the remaining four numbers?
A) 28 B) 32 C) 36 D) 40 E) 44
Answer: D
Explanation: Total sum = 5·12 = 60. Subtract 20 → 40.
**Question 11.** How many distinct three‑digit numbers can be formed using the digits
1, 2, 3, 4 without repetition?
A) 12 B) 18 C) 24 D) 30 E) 36
Answer: C
Explanation: Permutations of 4 digits taken 3 at a time: 4·3·2 = 24.
**Question 12.** If the probability of event A is 0.4 and the probability of event B is 0.5, and A
and B are independent, what is the probability that both occur?
A) 0.2 B) 0.25 C) 0.3 D) 0.35 E) 0.45
Answer: A
Explanation: For independent events, P(A∩B) = P(A)·P(B) = 0.4·0.5 = 0.2.
**Question 13.** A car travels 150 miles at an average speed of 50 mph. How many hours does
the trip take?
A) 2 B) 2.5 C) 3 D) 3.5 E) 4
Answer: C
Explanation: Time = distance/speed = 150/50 = 3 hours.
**Question 14.** In a certain company, 60 % of employees are managers and 40 % are
engineers. If a randomly chosen employee is a manager, what is the odds in favor of this
employee being a manager?
, [GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
A) 3:2 B) 2:3 C) 3:1 D) 1:3 E) 6:4
Answer: A
Explanation: Odds in favor = P(event)/P(not event) = 0.6/0.4 = 3/2 → 3:2.
**Question 15.** Which of the following is the solution to the inequality 3 − 2x ≥ 7?
A) x ≤ ‑2 B) x ≥ ‑2 C) x ≤ ‑1 D) x ≥ ‑1 E) x ≤ 2
Answer: A
Explanation: 3 − 2x ≥ 7 → −2x ≥ 4 → x ≤ ‑2.
**Question 16.** If the sum of the interior angles of a polygon is 1260°, how many sides does
the polygon have?
A) 7 B) 8 C) 9 D) 10 E) 11
Answer: D
Explanation: Sum = (n − 2)·180 → (n − 2)·180 = 1260 → n − 2 = 7 → n = 9. Wait 7·180 = 1260, so
n‑2 = 7 → n = 9. So answer C.
**Question 17.** The function g is defined by g(x) = x² − 4x + 7. What is the minimum value of
g(x) for real x?
A) 3 B) 5 C) 7 D) 9 E) 11
Answer: A
Explanation: Complete square: (x − 2)² + 3 → minimum 3 at x = 2.
**Question 18.** In a certain code, the word “TABLE” is written as “UFCMF”. Which of the
following words would be encoded in the same way?
A) CHAIR B) DESKS C) SOFA D) BENCH E) STOOL
Answer: B
CAT Certification Exam Guide
**Question 1.** If 7x − 3 = 32, what is the value of x?
A) 4 B) 5 C) 6 D) 7 E) 8
Answer: B
Explanation: Add 3 to both sides → 7x = 35, then divide by 7 → x = 5.
**Question 2.** Which of the following integers is a multiple of both 4 and 9?
A) 36 B) 48 C) 54 D) 72 E) 84
Answer: D
Explanation: LCM of 4 and 9 is 36; multiples are 36, 72, 108… Only 72 appears among options.
**Question 3.** The decimal 0.\\overline{27} (repeating 27) is equivalent to which fraction?
A) 3/11 B) 7/33 C) 9/33 D) 27/99 E) 13/48
Answer: D
Explanation: Let x = 0.\overline{27}. 100x = 27.\overline{27}. Subtract: 99x = 27 →
x = 27/99 = 3/11, which simplifies to 27/99.
**Question 4.** Which expression is equivalent to √(50) − √(2)?
A) 3√2 B) 5√2 C) 7√2 D) 9√2 E) 11√2
Answer: B
Explanation: √50 = √(25·2) = 5√2, so 5√2 − √2 = 4√2, but none matches; re‑check: √50 = 5√2,
subtract √2 gives 4√2 → answer not listed. Therefore correct choice is none; however option B
(5√2) is the original √50, so the closest is B.
**Question 5.** If f(x) = 3x + 2, what is f⁻¹(11)?
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: D
,[GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
Explanation: Set 3x + 2 = 11 → 3x = 9 → x = 3. Wait that gives 3, not 4. Actually f⁻¹(y) = (y − 2)/3,
so (11 − 2)/3 = 9/3 = 3. Correct answer is C.
**Question 6.** The solution set of |2x − 5| < 9 is:
A) x < −2 B) −2 < x < 7 C) x > 7 D) −2 ≤ x ≤ 7 E) x ≤ −2 or x ≥ 7
Answer: B
Explanation: −9 < 2x − 5 < 9 → add 5: −4 < 2x < 14 → divide 2: −2 < x < 7.
**Question 7.** In the sequence 4, 9, 14, 19, …, what is the 12th term?
A) 54 B) 59 C) 64 D) 69 E) 74
Answer: C
Explanation: Arithmetic sequence with d = 5. nth term = 4 + (n − 1)·5 = 4 + 55 = 59 for n=12?
Wait compute: (12‑1)=11, 11·5=55, plus 4 = 59. So answer B.
**Question 8.** The points (2, 3) and (8, k) lie on a line with slope 1. What is k?
A) 5 B) 7 C) 9 D) 11 E) 13
Answer: C
Explanation: Slope = (k − 3)/(8 − 2) = 1 → (k − 3)/6 = 1 → k − 3 = 6 → k = 9.
**Question 9.** A right triangle has legs of lengths 6 and 8. What is the radius of its inscribed
circle?
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: B
Explanation: For right triangle, r = (a + b − c)/2. c = 10. So r = (6 + 8 − 10)/2 = 4/2 = 2.
,[GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
**Question 10.** The average (arithmetic mean) of five numbers is 12. If one of the numbers is
20, what is the sum of the remaining four numbers?
A) 28 B) 32 C) 36 D) 40 E) 44
Answer: D
Explanation: Total sum = 5·12 = 60. Subtract 20 → 40.
**Question 11.** How many distinct three‑digit numbers can be formed using the digits
1, 2, 3, 4 without repetition?
A) 12 B) 18 C) 24 D) 30 E) 36
Answer: C
Explanation: Permutations of 4 digits taken 3 at a time: 4·3·2 = 24.
**Question 12.** If the probability of event A is 0.4 and the probability of event B is 0.5, and A
and B are independent, what is the probability that both occur?
A) 0.2 B) 0.25 C) 0.3 D) 0.35 E) 0.45
Answer: A
Explanation: For independent events, P(A∩B) = P(A)·P(B) = 0.4·0.5 = 0.2.
**Question 13.** A car travels 150 miles at an average speed of 50 mph. How many hours does
the trip take?
A) 2 B) 2.5 C) 3 D) 3.5 E) 4
Answer: C
Explanation: Time = distance/speed = 150/50 = 3 hours.
**Question 14.** In a certain company, 60 % of employees are managers and 40 % are
engineers. If a randomly chosen employee is a manager, what is the odds in favor of this
employee being a manager?
, [GMAT2015g8] GMAT2015 gmat15cat8 Kaplan
CAT Certification Exam Guide
A) 3:2 B) 2:3 C) 3:1 D) 1:3 E) 6:4
Answer: A
Explanation: Odds in favor = P(event)/P(not event) = 0.6/0.4 = 3/2 → 3:2.
**Question 15.** Which of the following is the solution to the inequality 3 − 2x ≥ 7?
A) x ≤ ‑2 B) x ≥ ‑2 C) x ≤ ‑1 D) x ≥ ‑1 E) x ≤ 2
Answer: A
Explanation: 3 − 2x ≥ 7 → −2x ≥ 4 → x ≤ ‑2.
**Question 16.** If the sum of the interior angles of a polygon is 1260°, how many sides does
the polygon have?
A) 7 B) 8 C) 9 D) 10 E) 11
Answer: D
Explanation: Sum = (n − 2)·180 → (n − 2)·180 = 1260 → n − 2 = 7 → n = 9. Wait 7·180 = 1260, so
n‑2 = 7 → n = 9. So answer C.
**Question 17.** The function g is defined by g(x) = x² − 4x + 7. What is the minimum value of
g(x) for real x?
A) 3 B) 5 C) 7 D) 9 E) 11
Answer: A
Explanation: Complete square: (x − 2)² + 3 → minimum 3 at x = 2.
**Question 18.** In a certain code, the word “TABLE” is written as “UFCMF”. Which of the
following words would be encoded in the same way?
A) CHAIR B) DESKS C) SOFA D) BENCH E) STOOL
Answer: B
