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Question 1. **What is the greatest common divisor of 84 and 126?**
A) 6 B) 12 C) 14 D) 42
Answer: D
Explanation: Prime factors 84=2·2·3·7, 126=2·3·3·7; common factors 2·3·7=42.
Question 2. **If 5x – 3 = 2, what is the value of x?**
A) 1 B) −1 C) 5 D) −5
Answer: A
Explanation: 5x = 5 ⇒ x = 1.
Question 3. **Which of the following is equivalent to √(50)?**
A) 5√2 B) √5 C) 10√5 D) 2√25
Answer: A
Explanation: √50=√(25·2)=5√2.
Question 4. **The sum of the interior angles of a hexagon is:**
A) 360° B) 540° C) 720° D) 900°
Answer: C
Explanation: (n‑2)·180 = (6‑2)·180 = 720°.
Question 5. **A line passes through (2, 3) and (5, k). If its slope is 2, what is k?**
A) 7 B) 9 C) 5 D) 11
Answer: A
Explanation: Slope = (k‑3)/(5‑2)=2 ⇒ k‑3=6 ⇒ k=9? Wait compute: (k‑3)/3=2 ⇒ k‑3=6 ⇒ k=9.
Actually option B is 9.
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Answer: B
Question 6. **What is the area of a circle with radius 4?**
A) 16π B) 8π C) 12π D) 4π
Answer: A
Explanation: Area = πr² = π·16 = 16π.
Question 7. **If a rectangular prism has length 3, width 4, height 5, its volume is:**
A) 60 B) 45 C) 30 D) 12
Answer: A
Explanation: Volume = l·w·h = 3·4·5 = 60.
Question 8. **A car travels 150 miles in 3 hours. Its average speed is:**
A) 35 mph B) 45 mph C) 50 mph D) 55 mph
Answer: C
Explanation: Speed = distance / time = 150/3 = 50 mph.
Question 9. **If 30% of a number is 18, the number is:**
A) 45 B) 54 C) 60 D) 72
Answer: C
Explanation: 0.30·x = 18 ⇒ x = 60.
Question 10. **How many ways can 3 books be arranged on a shelf?**
A) 3 B) 6 C) 9 D) 12
Answer: B
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Explanation: Permutations of 3 distinct items = 3! = 6.
Question 11. **What is the probability of drawing an ace from a standard deck?**
A) 1/13 B) 1/52 C) 4/52 D) 1/4
Answer: D
Explanation: 4 aces out of 52 cards → 4/52 = 1/4.
Question 12. **If the mean of 5 numbers is 12, what is the sum of the numbers?**
A) 50 B) 55 C) 60 D) 65
Answer: C
Explanation: Sum = mean × n = 12×5 = 60.
Question 13. **In a data set {4, 7, 7, 9, 12}, the median is:**
A) 7 B) 8 C) 9 D) 7.5
Answer: A
Explanation: Ordered set, middle value (3rd) = 7.
Question 14. **If f(x)=2x+5, what is f(−3)?**
A) −1 B) −11 C) 11 D) −7
Answer: B
Explanation: f(−3)=2(−3)+5=−6+5=−1? Wait compute: -6+5 = -1. Option A is -1.
Answer: A
Question 15. **Which inequality is true for all real x?**
A) x² ≥ x B) x² ≤ |x| C) x² + 1 > 0 D) x + 1 < x – 1
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Answer: C
Explanation: x² ≥ 0, so x² + 1 > 0 always.
Question 16. **The solution set of |2x‑6| = 4 is:**
A) {1, 5} B) {2, 4} C) {−1, 5} D) {−2, 6}
Answer: A
Explanation: 2x‑6 = ±4 ⇒ 2x = 10 or 2 ⇒ x = 5 or 1.
Question 17. **If the sum of the first n positive integers is 210, what is n?**
A) 19 B) 20 C) 21 D) 22
Answer: C
Explanation: n(n+1)/2 = 210 ⇒ n²+n‑420=0 ⇒ (n‑20)(n+21)=0 ⇒ n=20? Wait compute:
20*21/2=210, so n=20. Option B.
Answer: B
Question 18. **A right triangle has legs of length 6 and 8. Its hypotenuse is:**
A) 10 B) 12 C) 14 D) 15
Answer: A
Explanation: 6²+8²=36+64=100 ⇒ √100=10.
Question 19. **If two angles of a triangle are 35° and 65°, the third angle measures:**
A) 80° B) 85° C) 90° D) 95°
Answer: B
Explanation: Sum 180 ⇒ third = 180‑100 = 80? Wait 35+65=100, so third = 80. Option A.
Answer: A
CAT Certification Exam Preparation
Question 1. **What is the greatest common divisor of 84 and 126?**
A) 6 B) 12 C) 14 D) 42
Answer: D
Explanation: Prime factors 84=2·2·3·7, 126=2·3·3·7; common factors 2·3·7=42.
Question 2. **If 5x – 3 = 2, what is the value of x?**
A) 1 B) −1 C) 5 D) −5
Answer: A
Explanation: 5x = 5 ⇒ x = 1.
Question 3. **Which of the following is equivalent to √(50)?**
A) 5√2 B) √5 C) 10√5 D) 2√25
Answer: A
Explanation: √50=√(25·2)=5√2.
Question 4. **The sum of the interior angles of a hexagon is:**
A) 360° B) 540° C) 720° D) 900°
Answer: C
Explanation: (n‑2)·180 = (6‑2)·180 = 720°.
Question 5. **A line passes through (2, 3) and (5, k). If its slope is 2, what is k?**
A) 7 B) 9 C) 5 D) 11
Answer: A
Explanation: Slope = (k‑3)/(5‑2)=2 ⇒ k‑3=6 ⇒ k=9? Wait compute: (k‑3)/3=2 ⇒ k‑3=6 ⇒ k=9.
Actually option B is 9.
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Answer: B
Question 6. **What is the area of a circle with radius 4?**
A) 16π B) 8π C) 12π D) 4π
Answer: A
Explanation: Area = πr² = π·16 = 16π.
Question 7. **If a rectangular prism has length 3, width 4, height 5, its volume is:**
A) 60 B) 45 C) 30 D) 12
Answer: A
Explanation: Volume = l·w·h = 3·4·5 = 60.
Question 8. **A car travels 150 miles in 3 hours. Its average speed is:**
A) 35 mph B) 45 mph C) 50 mph D) 55 mph
Answer: C
Explanation: Speed = distance / time = 150/3 = 50 mph.
Question 9. **If 30% of a number is 18, the number is:**
A) 45 B) 54 C) 60 D) 72
Answer: C
Explanation: 0.30·x = 18 ⇒ x = 60.
Question 10. **How many ways can 3 books be arranged on a shelf?**
A) 3 B) 6 C) 9 D) 12
Answer: B
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Explanation: Permutations of 3 distinct items = 3! = 6.
Question 11. **What is the probability of drawing an ace from a standard deck?**
A) 1/13 B) 1/52 C) 4/52 D) 1/4
Answer: D
Explanation: 4 aces out of 52 cards → 4/52 = 1/4.
Question 12. **If the mean of 5 numbers is 12, what is the sum of the numbers?**
A) 50 B) 55 C) 60 D) 65
Answer: C
Explanation: Sum = mean × n = 12×5 = 60.
Question 13. **In a data set {4, 7, 7, 9, 12}, the median is:**
A) 7 B) 8 C) 9 D) 7.5
Answer: A
Explanation: Ordered set, middle value (3rd) = 7.
Question 14. **If f(x)=2x+5, what is f(−3)?**
A) −1 B) −11 C) 11 D) −7
Answer: B
Explanation: f(−3)=2(−3)+5=−6+5=−1? Wait compute: -6+5 = -1. Option A is -1.
Answer: A
Question 15. **Which inequality is true for all real x?**
A) x² ≥ x B) x² ≤ |x| C) x² + 1 > 0 D) x + 1 < x – 1
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Answer: C
Explanation: x² ≥ 0, so x² + 1 > 0 always.
Question 16. **The solution set of |2x‑6| = 4 is:**
A) {1, 5} B) {2, 4} C) {−1, 5} D) {−2, 6}
Answer: A
Explanation: 2x‑6 = ±4 ⇒ 2x = 10 or 2 ⇒ x = 5 or 1.
Question 17. **If the sum of the first n positive integers is 210, what is n?**
A) 19 B) 20 C) 21 D) 22
Answer: C
Explanation: n(n+1)/2 = 210 ⇒ n²+n‑420=0 ⇒ (n‑20)(n+21)=0 ⇒ n=20? Wait compute:
20*21/2=210, so n=20. Option B.
Answer: B
Question 18. **A right triangle has legs of length 6 and 8. Its hypotenuse is:**
A) 10 B) 12 C) 14 D) 15
Answer: A
Explanation: 6²+8²=36+64=100 ⇒ √100=10.
Question 19. **If two angles of a triangle are 35° and 65°, the third angle measures:**
A) 80° B) 85° C) 90° D) 95°
Answer: B
Explanation: Sum 180 ⇒ third = 180‑100 = 80? Wait 35+65=100, so third = 80. Option A.
Answer: A
