[GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
**Question 1.** If 5x − 3 = 2x + 7, what is the value of x?
A) 2 B) 3 C) 4 D) 5
Answer: C
Explanation: Adding 3 to both sides gives 5x = 2x + 10; subtract 2x → 3x = 10; x = 10/3 ≈ 3.33,
but only integer choice is 4, so check: 5·4‑3=20‑3=17 and 2·4+7=8+7=15, not equal. Actually
solving correctly: 5x‑3=2x+7 → 5x‑2x=7+3 → 3x=10 → x=10/3, which is not listed; the closest
integer is 4, but since none match, correct answer is none; however typical GMAT expects exact
value, so answer is not listed. **(Correction: The correct answer is not among choices; this
question is a trick – discard.)**
**Question 2.** A store marks up an item by 25% of its cost and then offers a 20% discount on
the marked price. What is the final price as a percent of the original cost?
A) 100% B) 105% C) 110% D) 115%
Answer: B
Explanation: Let cost = 100. Markup → 125. Discount 20% → 125 × 0.8 = 100. So final price =
100% of cost. Actually that yields 100%; none of the given options match. The correct answer is
100%, which is not listed; the intended answer is A, but A is 100%.
**Question 3.** The sum of the first n positive integers is 210. What is n?
A) 19 B) 20 C) 21 D) 22
Answer: C
Explanation: Sum = n(n+1)/2 = 210 → n(n+1)=420. Testing n=20 gives 20·21=420, so n=20.
Actually 20·21=420, so n=20. Answer B.
**Question 4.** 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 P(A or B)?
A) 0.2 B) 0.5 C) 0.7 D) 0.9
Answer: C
,[GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
Explanation: P(A∪B)=P(A)+P(B)−P(A)P(B)=0.4+0.5−0.2=0.7.
**Question 5.** In a certain class, 12 students study French, 15 study German, and 5 study
both. How many students study at least one of the two languages?
A) 12 B) 15 C) 22 D) 27
Answer: C
Explanation: |F∪G|=|F|+|G|−|F∩G|=12+15−5=22.
**Question 6.** Which of the following is equivalent to √(50) − √(18)?
A) √2 + √3 B) √2 − √3 C) 2√2 − 3√2 D) 5√2 − 3√2
Answer: B
Explanation: √50=5√2, √18=3√2, difference = (5−3)√2=2√2 which is not listed; the closest
expression is √2 − √3, but that is not equal. The correct simplification is 2√2.
**Question 7.** If f(x)=3x − 4, what is f⁻¹(5)?
A) 3 B) 4 C) 5 D) 6
Answer: A
Explanation: Solve 3x−4=5 → 3x=9 → x=3.
**Question 8.** The average (arithmetic mean) of three numbers is 12. If two of the numbers
are 8 and 14, what is the third number?
A) 10 B) 12 C) 14 D) 16
Answer: B
Explanation: Sum = 3·12=36. Subtract 8+14=22 → third = 14. Actually 36‑22=14, so answer C.
,[GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
**Question 9.** A rectangular garden is twice as long as it is wide. If its perimeter is 60 m, what
is its area?
A) 200 B) 225 C) 250 D) 300
Answer: C
Explanation: Let width = w, length = 2w. Perimeter 2(w+2w)=60 → 6w=60 → w=10, length=20.
Area=10·20=200. Answer A.
**Question 10.** In a certain code, if “CAT” is written as “DBU”, how is “DOG” written?
A) EPF B) EPH C) EPF D) EPF
Answer: A
Explanation: Each letter shifted forward one alphabetic position: C→D, A→B, T→U. Apply to
D→E, O→P, G→H → “EPH”. The correct answer is B.
**Question 11.** If the ratio of the ages of Tom and Jerry is 4:5 and the sum of their ages is 72,
what is Tom’s age?
A) 28 B) 30 C) 32 D) 34
Answer: C
Explanation: Let ages be 4k and 5k, sum 9k=72 → k=8. Tom’s age =4·8=32.
**Question 12.** A bag contains 4 red, 5 blue, and 6 green marbles. If three marbles are drawn
without replacement, what is the probability that all are blue?
A) 1/91 B) 5/91 C) 10/91 D) 20/91
Answer: B
Explanation: Probability = (5/15)*(4/14)*(3/13)=60/2730=2/91≈0.022. None of the options
match; the closest is 5/91.
**Question 13.** Which of the following statements about the function g(x)=x² − 4x + 3 is true?
, [GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
A) g(x) has a minimum at x=2. B) g(x) is decreasing for all x. C) g(x) has roots at x=1 and x=3.
D) g(x) is always positive.
Answer: C
Explanation: Factoring gives (x‑1)(x‑3); roots are 1 and 3.
**Question 14.** 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
Answer: D
Explanation: Sum = (n‑2)·180 =1260 → n‑2 =7 → n=9. Actually 1260/180=7, so n‑2=7 → n=9.
Answer C.
**Question 15.** A car travels at a constant speed of 60 mi/h for 2 hours and then at 40 mi/h
for 3 hours. What is its average speed for the entire trip?
A) 45 mi/h B) 48 mi/h C) 50 mi/h D) 52 mi/h
Answer: B
Explanation: Total distance = 60·2 + 40·3 = 120 + 120 = 240 mi. Total time = 5 h. Average speed =
240/5 = 48 mi/h.
**Question 16.** In the sentence “The committee, which was appointed last year, will meet
tomorrow,” the phrase “which was appointed last year” is a...
A) restrictive clause B) non‑restrictive clause C) appositive D) dangling modifier
Answer: B
Explanation: The clause is set off by commas, providing non‑essential information.
**Question 17.** Choose the correctly punctuated sentence.
Certification Review Guide
**Question 1.** If 5x − 3 = 2x + 7, what is the value of x?
A) 2 B) 3 C) 4 D) 5
Answer: C
Explanation: Adding 3 to both sides gives 5x = 2x + 10; subtract 2x → 3x = 10; x = 10/3 ≈ 3.33,
but only integer choice is 4, so check: 5·4‑3=20‑3=17 and 2·4+7=8+7=15, not equal. Actually
solving correctly: 5x‑3=2x+7 → 5x‑2x=7+3 → 3x=10 → x=10/3, which is not listed; the closest
integer is 4, but since none match, correct answer is none; however typical GMAT expects exact
value, so answer is not listed. **(Correction: The correct answer is not among choices; this
question is a trick – discard.)**
**Question 2.** A store marks up an item by 25% of its cost and then offers a 20% discount on
the marked price. What is the final price as a percent of the original cost?
A) 100% B) 105% C) 110% D) 115%
Answer: B
Explanation: Let cost = 100. Markup → 125. Discount 20% → 125 × 0.8 = 100. So final price =
100% of cost. Actually that yields 100%; none of the given options match. The correct answer is
100%, which is not listed; the intended answer is A, but A is 100%.
**Question 3.** The sum of the first n positive integers is 210. What is n?
A) 19 B) 20 C) 21 D) 22
Answer: C
Explanation: Sum = n(n+1)/2 = 210 → n(n+1)=420. Testing n=20 gives 20·21=420, so n=20.
Actually 20·21=420, so n=20. Answer B.
**Question 4.** 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 P(A or B)?
A) 0.2 B) 0.5 C) 0.7 D) 0.9
Answer: C
,[GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
Explanation: P(A∪B)=P(A)+P(B)−P(A)P(B)=0.4+0.5−0.2=0.7.
**Question 5.** In a certain class, 12 students study French, 15 study German, and 5 study
both. How many students study at least one of the two languages?
A) 12 B) 15 C) 22 D) 27
Answer: C
Explanation: |F∪G|=|F|+|G|−|F∩G|=12+15−5=22.
**Question 6.** Which of the following is equivalent to √(50) − √(18)?
A) √2 + √3 B) √2 − √3 C) 2√2 − 3√2 D) 5√2 − 3√2
Answer: B
Explanation: √50=5√2, √18=3√2, difference = (5−3)√2=2√2 which is not listed; the closest
expression is √2 − √3, but that is not equal. The correct simplification is 2√2.
**Question 7.** If f(x)=3x − 4, what is f⁻¹(5)?
A) 3 B) 4 C) 5 D) 6
Answer: A
Explanation: Solve 3x−4=5 → 3x=9 → x=3.
**Question 8.** The average (arithmetic mean) of three numbers is 12. If two of the numbers
are 8 and 14, what is the third number?
A) 10 B) 12 C) 14 D) 16
Answer: B
Explanation: Sum = 3·12=36. Subtract 8+14=22 → third = 14. Actually 36‑22=14, so answer C.
,[GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
**Question 9.** A rectangular garden is twice as long as it is wide. If its perimeter is 60 m, what
is its area?
A) 200 B) 225 C) 250 D) 300
Answer: C
Explanation: Let width = w, length = 2w. Perimeter 2(w+2w)=60 → 6w=60 → w=10, length=20.
Area=10·20=200. Answer A.
**Question 10.** In a certain code, if “CAT” is written as “DBU”, how is “DOG” written?
A) EPF B) EPH C) EPF D) EPF
Answer: A
Explanation: Each letter shifted forward one alphabetic position: C→D, A→B, T→U. Apply to
D→E, O→P, G→H → “EPH”. The correct answer is B.
**Question 11.** If the ratio of the ages of Tom and Jerry is 4:5 and the sum of their ages is 72,
what is Tom’s age?
A) 28 B) 30 C) 32 D) 34
Answer: C
Explanation: Let ages be 4k and 5k, sum 9k=72 → k=8. Tom’s age =4·8=32.
**Question 12.** A bag contains 4 red, 5 blue, and 6 green marbles. If three marbles are drawn
without replacement, what is the probability that all are blue?
A) 1/91 B) 5/91 C) 10/91 D) 20/91
Answer: B
Explanation: Probability = (5/15)*(4/14)*(3/13)=60/2730=2/91≈0.022. None of the options
match; the closest is 5/91.
**Question 13.** Which of the following statements about the function g(x)=x² − 4x + 3 is true?
, [GMAT2013g4] GMAT2013 g12cat4 Kaplan CAT
Certification Review Guide
A) g(x) has a minimum at x=2. B) g(x) is decreasing for all x. C) g(x) has roots at x=1 and x=3.
D) g(x) is always positive.
Answer: C
Explanation: Factoring gives (x‑1)(x‑3); roots are 1 and 3.
**Question 14.** 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
Answer: D
Explanation: Sum = (n‑2)·180 =1260 → n‑2 =7 → n=9. Actually 1260/180=7, so n‑2=7 → n=9.
Answer C.
**Question 15.** A car travels at a constant speed of 60 mi/h for 2 hours and then at 40 mi/h
for 3 hours. What is its average speed for the entire trip?
A) 45 mi/h B) 48 mi/h C) 50 mi/h D) 52 mi/h
Answer: B
Explanation: Total distance = 60·2 + 40·3 = 120 + 120 = 240 mi. Total time = 5 h. Average speed =
240/5 = 48 mi/h.
**Question 16.** In the sentence “The committee, which was appointed last year, will meet
tomorrow,” the phrase “which was appointed last year” is a...
A) restrictive clause B) non‑restrictive clause C) appositive D) dangling modifier
Answer: B
Explanation: The clause is set off by commas, providing non‑essential information.
**Question 17.** Choose the correctly punctuated sentence.
