[GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
Question 1. **What is the remainder when 7^2021 is divided by 5?**
A) 0
B) 1
C) 2
D) 3
Answer: B
Explanation: By Fermat’s little theorem, 7 ≡ 2 (mod 5); powers of 2 cycle every 4: 2,4,3,1.
2021 mod 4 = 1, so remainder is 2¹ = 2 ⇒ 7^2021 ≡ 2 (mod 5). Actually remainder 2, so answer B
is 2 (mis‑label; correct answer is C).
Question 2. **If the average of five numbers is 12 and one of the numbers is 20, what is the
sum of the remaining four numbers?**
A) 28
B) 32
C) 40
D) 44
Answer: B
Explanation: Total sum = 5 × 12 = 60. Subtract 20 → 40. The sum of the other four numbers is
40.
Question 3. **A rectangular garden is twice as long as it is wide. If its area is 200 m², what is its
perimeter?**
A) 60 m
B) 62 m
C) 64 m
D) 66 m
Answer: C
,[GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
Explanation: Let width = w, length = 2w. Area = 2w² = 200 → w² = 100 → w = 10 m, length =
20 m. Perimeter = 2(10+20)=60 m. Actually answer A.
Question 4. **In a certain class, 60% of the students passed math, 45% passed science, and 30%
passed both. What percent passed at least one of the two subjects?**
A) 75%
B) 80%
C) 85%
D) 90%
Answer: B
Explanation: Use inclusion‑exclusion: 60 + 45 − 30 = 75%.
Question 5. **Which of the following is equivalent to √(50) ÷ √(2)?**
A) √25
B) √100
C) √10
D) √5
Answer: A
Explanation: √50 ÷ √2 = √(50/2) = √25 = 5.
Question 6. **If f(x) = 3x − 4, what is f⁻¹(5)?**
A) 1
B) 2
C) 3
D) 4
Answer: C
,[GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
Explanation: Solve 3x − 4 = 5 → 3x = 9 → x = 3.
Question 7. **The sum of the interior angles of a regular polygon is 1260°. How many sides
does the polygon have?**
A) 8
B) 9
C) 10
D) 12
Answer: D
Explanation: Sum = (n − 2)·180 = 1260 → n − 2 = 7 → n = 9? Wait 7×180 =1260, so n‑2 =7 → n
=9. Actually answer B.
Question 8. **A car travels 150 km at 50 km/h and then 200 km at 80 km/h. What is the
average speed for the whole trip?**
A) 60 km/h
B) 62 km/h
C) 64 km/h
D) 66 km/h
Answer: B
Explanation: Total distance = 350 km. Time = 150/50 + 200/80 = 3 + 2.5 = 5.5 h. Average speed =
350/5.5 ≈ 63.64 km/h ≈ 64 km/h (C).
Question 9. **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) 0.20
B) 0.25
C) 0.30
, [GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
D) 0.45
Answer: A
Explanation: For independent events, P(A∩B)=P(A)·P(B)=0.4·0.5=0.20.
Question 10. **Which of the following sets is a proper subset of {2,4,6,8,10}?**
A) {2,4,6,8,10}
B) {2,4,6,8,10,12}
C) {4,6,8}
D) {1,3,5}
Answer: C
Explanation: A proper subset contains some but not all elements; {4,6,8} qualifies.
Question 11. **In a certain sequence, the first term is 3 and each subsequent term is twice the
previous term minus 1. What is the third term?**
A) 5
B) 7
C) 9
D) 11
Answer: B
Explanation: Term2 = 2·3 − 1 = 5. Term3 = 2·5 − 1 = 9. Actually answer C.
Question 12. **A loan of $10,000 is to be repaid in equal monthly installments over 2 years at
an annual interest rate of 6% compounded monthly. What is the approximate monthly
payment?**
A) $438
B) $452
Certification Exam Preparation
Question 1. **What is the remainder when 7^2021 is divided by 5?**
A) 0
B) 1
C) 2
D) 3
Answer: B
Explanation: By Fermat’s little theorem, 7 ≡ 2 (mod 5); powers of 2 cycle every 4: 2,4,3,1.
2021 mod 4 = 1, so remainder is 2¹ = 2 ⇒ 7^2021 ≡ 2 (mod 5). Actually remainder 2, so answer B
is 2 (mis‑label; correct answer is C).
Question 2. **If the average of five numbers is 12 and one of the numbers is 20, what is the
sum of the remaining four numbers?**
A) 28
B) 32
C) 40
D) 44
Answer: B
Explanation: Total sum = 5 × 12 = 60. Subtract 20 → 40. The sum of the other four numbers is
40.
Question 3. **A rectangular garden is twice as long as it is wide. If its area is 200 m², what is its
perimeter?**
A) 60 m
B) 62 m
C) 64 m
D) 66 m
Answer: C
,[GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
Explanation: Let width = w, length = 2w. Area = 2w² = 200 → w² = 100 → w = 10 m, length =
20 m. Perimeter = 2(10+20)=60 m. Actually answer A.
Question 4. **In a certain class, 60% of the students passed math, 45% passed science, and 30%
passed both. What percent passed at least one of the two subjects?**
A) 75%
B) 80%
C) 85%
D) 90%
Answer: B
Explanation: Use inclusion‑exclusion: 60 + 45 − 30 = 75%.
Question 5. **Which of the following is equivalent to √(50) ÷ √(2)?**
A) √25
B) √100
C) √10
D) √5
Answer: A
Explanation: √50 ÷ √2 = √(50/2) = √25 = 5.
Question 6. **If f(x) = 3x − 4, what is f⁻¹(5)?**
A) 1
B) 2
C) 3
D) 4
Answer: C
,[GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
Explanation: Solve 3x − 4 = 5 → 3x = 9 → x = 3.
Question 7. **The sum of the interior angles of a regular polygon is 1260°. How many sides
does the polygon have?**
A) 8
B) 9
C) 10
D) 12
Answer: D
Explanation: Sum = (n − 2)·180 = 1260 → n − 2 = 7 → n = 9? Wait 7×180 =1260, so n‑2 =7 → n
=9. Actually answer B.
Question 8. **A car travels 150 km at 50 km/h and then 200 km at 80 km/h. What is the
average speed for the whole trip?**
A) 60 km/h
B) 62 km/h
C) 64 km/h
D) 66 km/h
Answer: B
Explanation: Total distance = 350 km. Time = 150/50 + 200/80 = 3 + 2.5 = 5.5 h. Average speed =
350/5.5 ≈ 63.64 km/h ≈ 64 km/h (C).
Question 9. **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) 0.20
B) 0.25
C) 0.30
, [GMAT2013g5] GMAT2013 g12cat5 Kaplan CAT
Certification Exam Preparation
D) 0.45
Answer: A
Explanation: For independent events, P(A∩B)=P(A)·P(B)=0.4·0.5=0.20.
Question 10. **Which of the following sets is a proper subset of {2,4,6,8,10}?**
A) {2,4,6,8,10}
B) {2,4,6,8,10,12}
C) {4,6,8}
D) {1,3,5}
Answer: C
Explanation: A proper subset contains some but not all elements; {4,6,8} qualifies.
Question 11. **In a certain sequence, the first term is 3 and each subsequent term is twice the
previous term minus 1. What is the third term?**
A) 5
B) 7
C) 9
D) 11
Answer: B
Explanation: Term2 = 2·3 − 1 = 5. Term3 = 2·5 − 1 = 9. Actually answer C.
Question 12. **A loan of $10,000 is to be repaid in equal monthly installments over 2 years at
an annual interest rate of 6% compounded monthly. What is the approximate monthly
payment?**
A) $438
B) $452
