[GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
**Question 1.** Which of the following integers is a multiple of both 4 and 9?
A) 36
B) 48
C) 54
D) 72
Answer: D
Explanation: The least common multiple of 4 and 9 is 36; multiples are 36, 72, 108… Only 72
appears among the choices.
**Question 2.** What is the remainder when 7⁵ is divided by 5?
A) 0
B) 1
C) 2
D) 3
Answer: B
Explanation: 7 ≡ 2 (mod 5). 2⁵ = 32 ≡ 2 (mod 5). Actually 2⁵ = 32, 32 mod 5 = 2, but we need
remainder of 7⁵. Wait 7⁵ = 16807; 16807 mod 5 = 2. So answer should be C. Correct answer: C.
Explanation: Using modular arithmetic, 7 ≡ 2 (mod 5); 2⁵ = 32; 32 mod 5 = 2.
**Question 3.** Convert 0.125 into a fraction in simplest form.
A) 1/4
B) 1/8
C) 3/16
D) 5/40
Answer: B
Explanation: 0.125 = 125/1000 = 1/8 after dividing numerator and denominator by 125.
,[GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
**Question 4.** Which of the following decimals is a repeating decimal?
A) 0.250
B) 0.333...
C) 0.5
D) 0.875
Answer: B
Explanation: 0.333... repeats the digit 3 indefinitely; the others terminate.
**Question 5.** If 5 kg of a substance costs $45, what is the unit price per kilogram?
A) $5
B) $7
C) $9
D) $12
Answer: C
Explanation: $45 ÷ 5 kg = $9 per kg.
**Question 6.** In a mixture problem, 8 L of a 30% solution is mixed with 12 L of a 50%
solution. What is the concentration of the resulting solution?
A) 38%
B) 40%
C) 42%
D) 44%
Answer: B
Explanation: Total solute = 0.30·8 + 0.50·12 = 2.4 + 6 = 8.4 L. Total volume = 20 L. Concentration
= 8.4/20 = 0.42 = 42%; actually that's 42%, which corresponds to choice C. Correct answer: C.
,[GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
**Question 7.** If x varies directly as y and x = 24 when y = 3, what is x when y = 7?
A) 42
B) 48
C) 56
D) 63
Answer: C
Explanation: Direct variation: x = ky. k = 24/3 = 8. Then x = 8·7 = 56.
**Question 8.** The price of a stock increased from $40 to $52. What is the percent increase?
A) 20%
B) 25%
C) 30%
D) 35%
Answer: B
Explanation: Increase = $12; percent increase = 12/40 = 0.30 = 30%; Wait that's 30%, not 25%.
Actually 12/40 = 0.30 = 30%, so answer should be C. Correct answer: C. Explanation: Percent
increase = (52‑40)/40 = 12/40 = 0.30 = 30%.
**Question 9.** Simplify (2⁴ · 2⁻³)⁻².
A) 1/8
B) 1/16
C) 8
D) 16
Answer: A
, [GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
Explanation: Inside: 2⁴·2⁻³ = 2¹ = 2. Then (2)⁻² = 1/2² = 1/4. Wait compute: (2)⁻² = 1/4. But we
have (2⁴·2⁻³)⁻² = (2)⁻² = 1/4. None of the options match. Let's adjust: Actually (2⁴·2⁻³)⁻² = (2¹)⁻² =
2⁻² = 1/4. So correct answer should be 1/4, which is not listed. Replace options: A) 1/4 B) 1/8 C)
4 D) 8. Then answer A. Explanation as above.
**Question 10.** Solve for x: 3x – 7 = 2x + 5.
A) 2
B) 5
C) 12
D) –12
Answer: B
Explanation: Subtract 2x: x – 7 = 5 → x = 12. Wait that gives x = 12, which is choice C. Correct
answer: C. Explanation: 3x – 7 = 2x + 5 → x = 12.
**Question 11.** Which of the following is the solution set of the inequality |2t – 5| < 9?
A) t < –2 or t > 7
B) –2 < t < 7
C) –2 ≤ t ≤ 7
D) t ≤ –2 or t ≥ 7
Answer: B
Explanation: |2t – 5| < 9 → –9 < 2t – 5 < 9 → –4 < 2t < 14 → –2 < t < 7.
**Question 12.** If f(x) = 3x – 4, what is f⁻¹(y)?
A) (y + 4)/3
B) (y – 4)/3
C) 3y + 4
Certification Exam Preparation
**Question 1.** Which of the following integers is a multiple of both 4 and 9?
A) 36
B) 48
C) 54
D) 72
Answer: D
Explanation: The least common multiple of 4 and 9 is 36; multiples are 36, 72, 108… Only 72
appears among the choices.
**Question 2.** What is the remainder when 7⁵ is divided by 5?
A) 0
B) 1
C) 2
D) 3
Answer: B
Explanation: 7 ≡ 2 (mod 5). 2⁵ = 32 ≡ 2 (mod 5). Actually 2⁵ = 32, 32 mod 5 = 2, but we need
remainder of 7⁵. Wait 7⁵ = 16807; 16807 mod 5 = 2. So answer should be C. Correct answer: C.
Explanation: Using modular arithmetic, 7 ≡ 2 (mod 5); 2⁵ = 32; 32 mod 5 = 2.
**Question 3.** Convert 0.125 into a fraction in simplest form.
A) 1/4
B) 1/8
C) 3/16
D) 5/40
Answer: B
Explanation: 0.125 = 125/1000 = 1/8 after dividing numerator and denominator by 125.
,[GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
**Question 4.** Which of the following decimals is a repeating decimal?
A) 0.250
B) 0.333...
C) 0.5
D) 0.875
Answer: B
Explanation: 0.333... repeats the digit 3 indefinitely; the others terminate.
**Question 5.** If 5 kg of a substance costs $45, what is the unit price per kilogram?
A) $5
B) $7
C) $9
D) $12
Answer: C
Explanation: $45 ÷ 5 kg = $9 per kg.
**Question 6.** In a mixture problem, 8 L of a 30% solution is mixed with 12 L of a 50%
solution. What is the concentration of the resulting solution?
A) 38%
B) 40%
C) 42%
D) 44%
Answer: B
Explanation: Total solute = 0.30·8 + 0.50·12 = 2.4 + 6 = 8.4 L. Total volume = 20 L. Concentration
= 8.4/20 = 0.42 = 42%; actually that's 42%, which corresponds to choice C. Correct answer: C.
,[GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
**Question 7.** If x varies directly as y and x = 24 when y = 3, what is x when y = 7?
A) 42
B) 48
C) 56
D) 63
Answer: C
Explanation: Direct variation: x = ky. k = 24/3 = 8. Then x = 8·7 = 56.
**Question 8.** The price of a stock increased from $40 to $52. What is the percent increase?
A) 20%
B) 25%
C) 30%
D) 35%
Answer: B
Explanation: Increase = $12; percent increase = 12/40 = 0.30 = 30%; Wait that's 30%, not 25%.
Actually 12/40 = 0.30 = 30%, so answer should be C. Correct answer: C. Explanation: Percent
increase = (52‑40)/40 = 12/40 = 0.30 = 30%.
**Question 9.** Simplify (2⁴ · 2⁻³)⁻².
A) 1/8
B) 1/16
C) 8
D) 16
Answer: A
, [GMAT2013g8] GMAT2013 g12cat8 Kaplan CAT
Certification Exam Preparation
Explanation: Inside: 2⁴·2⁻³ = 2¹ = 2. Then (2)⁻² = 1/2² = 1/4. Wait compute: (2)⁻² = 1/4. But we
have (2⁴·2⁻³)⁻² = (2)⁻² = 1/4. None of the options match. Let's adjust: Actually (2⁴·2⁻³)⁻² = (2¹)⁻² =
2⁻² = 1/4. So correct answer should be 1/4, which is not listed. Replace options: A) 1/4 B) 1/8 C)
4 D) 8. Then answer A. Explanation as above.
**Question 10.** Solve for x: 3x – 7 = 2x + 5.
A) 2
B) 5
C) 12
D) –12
Answer: B
Explanation: Subtract 2x: x – 7 = 5 → x = 12. Wait that gives x = 12, which is choice C. Correct
answer: C. Explanation: 3x – 7 = 2x + 5 → x = 12.
**Question 11.** Which of the following is the solution set of the inequality |2t – 5| < 9?
A) t < –2 or t > 7
B) –2 < t < 7
C) –2 ≤ t ≤ 7
D) t ≤ –2 or t ≥ 7
Answer: B
Explanation: |2t – 5| < 9 → –9 < 2t – 5 < 9 → –4 < 2t < 14 → –2 < t < 7.
**Question 12.** If f(x) = 3x – 4, what is f⁻¹(y)?
A) (y + 4)/3
B) (y – 4)/3
C) 3y + 4
