[GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
Certification Exam Preparation
**Question 1.** If 5 x − 3 = 2 x + 7, what is the value of x?
A) 2 B) 5 C) 10 D) −2
Answer: A
Explanation: Adding 3 to both sides gives 5x = 2x + 10; subtract 2x → 3x = 10; x = 10/3 ≈ 3.33.
Wait calculation error – correct solving: 5x‑3=2x+7 → 5x‑2x=7+3 → 3x=10 → x=10/3 ≈3.33,
which is not listed. Re‑check options: none match; thus answer is none – but given options, the
closest integer is 2? Actually mis‑step: The equation was 5x‑3=2x+7 → 5x‑2x=7+3 → 3x=10 →
x=10/3. Since not an option, the test expects integer, so maybe a typo. Assuming answer B) 5 is
wrong. **Correction:** The correct answer is not listed; however, based on the intended
integer solution, the correct answer is **B) 5** if the constant on right were 2 instead of 7.
*[Explanation demonstrates solving linear equations.]*
**Question 2.** What is 45% of 200?
A) 80 B) 90 C) 100 D) 110
Answer: B
Explanation: 45% = 0.45; 0.45 × 200 = 90.
**Question 3.** The sum of the interior angles of a polygon with n sides is 1260°. What is n?
A) 6 B) 7 C) 8 D) 9
Answer: C
Explanation: Sum = 180(n‑2)=1260 → n‑2=7 → n=9. Wait 180×7=1260, so n‑2=7 → n=9. Correct
answer D) 9.
**Question 4.** If the ratio of cats to dogs is 3:5 and there are 24 dogs, how many cats are
there?
A) 12 B) 14 C) 15 D) 18
Answer: C
, [GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
Certification Exam Preparation
Explanation: 5 dogs correspond to 3 cats; 24 dogs → (3/5)×24 = 14.4, not integer. Actually ratio
3:5 means cats/dogs =3/5, cats = (3/5)×24=14.4 → not integer, so likely mis‑statement.
Assuming whole numbers, answer C) 15 if dogs were 25. *[Illustrates ratio scaling.]*
**Question 5.** Which of the following numbers is a prime?
A) 51 B) 57 C) 59 D) 63
Answer: C
Explanation: 59 has no divisors other than 1 and itself.
**Question 6.** A circle has a radius of 7 cm. What is its area (π ≈ 3.14)?
A) 154 cm² B) 153.86 cm² C) 147 cm² D) 154.0 cm²
Answer: A
Explanation: Area = πr² = 3.14 × 49 ≈ 153.86 ≈ 154 cm².
**Question 7.** If f(x)=2x−5, what is f(−3)?
A) −11 B) −1 C) 1 D) 11
Answer: A
Explanation: f(−3)=2(−3)−5=−6−5=−11.
**Question 8.** The probability of drawing a red marble from a bag is 0.4. If there are 10
marbles total, how many are red?
A) 2 B) 3 C) 4 D) 5
Answer: C
Explanation: 0.4 × 10 = 4 red marbles.
**Question 9.** Solve for x: |2x − 5| = 9.
, [GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
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A) −2 B) 2 C) 7 D) −7
Answer: A and C (two solutions)
Explanation: 2x‑5=9 → x=7; 2x‑5=‑9 → x=‑2.
**Question 10.** In a right triangle, one leg is 6 and the hypotenuse is 10. What is the length of
the other leg?
A) 4 B) 6 C) 8 D) √64
Answer: C
Explanation: By Pythagoras: a²+6²=10² → a²=100‑36=64 → a=8.
**Question 11.** Which of the following is equivalent to (3x³y²)⁴?
A) 81x¹²y⁸ B) 12x³y² C) 3⁴x³y² D) 81x⁴y⁴
Answer: A
Explanation: (3)⁴=81; (x³)⁴=x¹²; (y²)⁴=y⁸.
**Question 12.** If the average (arithmetic mean) of five numbers is 14, what is the sum of the
numbers?
A) 56 B) 70 C) 84 D) 100
Answer: B
Explanation: Sum = mean × count = 14 × 5 = 70.
**Question 13.** A store discounts a $120 item by 15% and then offers a coupon for an
additional $10 off. What is the final price?
A) $92 B) $94 C) $96 D) $98
Answer: B
, [GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
Certification Exam Preparation
Explanation: 15% of 120 = 18; price after discount = 102; minus 10 = 92. Wait that gives $92,
which is option A. So answer A) $92.
**Question 14.** Which of the following statements is logically equivalent to “If it rains, the
ground gets wet”?
A) If the ground is not wet, it does not rain. B) If the ground gets wet, it rains. C) It rains only
if the ground gets wet. D) If it does not rain, the ground gets wet.
Answer: A
Explanation: Contrapositive of “If P then Q” is “If not Q then not P”.
**Question 15.** In a certain code, the word “CAT” is written as “DBU”. How would “DOG” be
coded?
A) EPE B) EPO C) EPF D) EOG
Answer: C
Explanation: Each letter is shifted forward by 1 (C→D, A→B, T→U). Apply to D→E, O→P, G→H →
“EPH”. None matches; maybe shift by 2? C→D (+1), A→B (+1), T→U (+1). So DOG → EP H? D→E,
O→P, G→H → “EPH”. Not listed; likely answer C) EPF if shift pattern is +1 for first two, +0 for
last? *[Shows pattern recognition.]*
**Question 16.** If 7ⁿ = 343, what is n?
A) 2 B) 3 C) 4 D) 5
Answer: B
Explanation: 7³ = 343, so n = 3.
**Question 17.** A sequence is defined by a₁ = 4 and aₙ₊₁ = 2aₙ + 1. What is a₃?
A) 9 B) 19 C) 21 D) 39
Answer: B
Certification Exam Preparation
**Question 1.** If 5 x − 3 = 2 x + 7, what is the value of x?
A) 2 B) 5 C) 10 D) −2
Answer: A
Explanation: Adding 3 to both sides gives 5x = 2x + 10; subtract 2x → 3x = 10; x = 10/3 ≈ 3.33.
Wait calculation error – correct solving: 5x‑3=2x+7 → 5x‑2x=7+3 → 3x=10 → x=10/3 ≈3.33,
which is not listed. Re‑check options: none match; thus answer is none – but given options, the
closest integer is 2? Actually mis‑step: The equation was 5x‑3=2x+7 → 5x‑2x=7+3 → 3x=10 →
x=10/3. Since not an option, the test expects integer, so maybe a typo. Assuming answer B) 5 is
wrong. **Correction:** The correct answer is not listed; however, based on the intended
integer solution, the correct answer is **B) 5** if the constant on right were 2 instead of 7.
*[Explanation demonstrates solving linear equations.]*
**Question 2.** What is 45% of 200?
A) 80 B) 90 C) 100 D) 110
Answer: B
Explanation: 45% = 0.45; 0.45 × 200 = 90.
**Question 3.** The sum of the interior angles of a polygon with n sides is 1260°. What is n?
A) 6 B) 7 C) 8 D) 9
Answer: C
Explanation: Sum = 180(n‑2)=1260 → n‑2=7 → n=9. Wait 180×7=1260, so n‑2=7 → n=9. Correct
answer D) 9.
**Question 4.** If the ratio of cats to dogs is 3:5 and there are 24 dogs, how many cats are
there?
A) 12 B) 14 C) 15 D) 18
Answer: C
, [GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
Certification Exam Preparation
Explanation: 5 dogs correspond to 3 cats; 24 dogs → (3/5)×24 = 14.4, not integer. Actually ratio
3:5 means cats/dogs =3/5, cats = (3/5)×24=14.4 → not integer, so likely mis‑statement.
Assuming whole numbers, answer C) 15 if dogs were 25. *[Illustrates ratio scaling.]*
**Question 5.** Which of the following numbers is a prime?
A) 51 B) 57 C) 59 D) 63
Answer: C
Explanation: 59 has no divisors other than 1 and itself.
**Question 6.** A circle has a radius of 7 cm. What is its area (π ≈ 3.14)?
A) 154 cm² B) 153.86 cm² C) 147 cm² D) 154.0 cm²
Answer: A
Explanation: Area = πr² = 3.14 × 49 ≈ 153.86 ≈ 154 cm².
**Question 7.** If f(x)=2x−5, what is f(−3)?
A) −11 B) −1 C) 1 D) 11
Answer: A
Explanation: f(−3)=2(−3)−5=−6−5=−11.
**Question 8.** The probability of drawing a red marble from a bag is 0.4. If there are 10
marbles total, how many are red?
A) 2 B) 3 C) 4 D) 5
Answer: C
Explanation: 0.4 × 10 = 4 red marbles.
**Question 9.** Solve for x: |2x − 5| = 9.
, [GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
Certification Exam Preparation
A) −2 B) 2 C) 7 D) −7
Answer: A and C (two solutions)
Explanation: 2x‑5=9 → x=7; 2x‑5=‑9 → x=‑2.
**Question 10.** In a right triangle, one leg is 6 and the hypotenuse is 10. What is the length of
the other leg?
A) 4 B) 6 C) 8 D) √64
Answer: C
Explanation: By Pythagoras: a²+6²=10² → a²=100‑36=64 → a=8.
**Question 11.** Which of the following is equivalent to (3x³y²)⁴?
A) 81x¹²y⁸ B) 12x³y² C) 3⁴x³y² D) 81x⁴y⁴
Answer: A
Explanation: (3)⁴=81; (x³)⁴=x¹²; (y²)⁴=y⁸.
**Question 12.** If the average (arithmetic mean) of five numbers is 14, what is the sum of the
numbers?
A) 56 B) 70 C) 84 D) 100
Answer: B
Explanation: Sum = mean × count = 14 × 5 = 70.
**Question 13.** A store discounts a $120 item by 15% and then offers a coupon for an
additional $10 off. What is the final price?
A) $92 B) $94 C) $96 D) $98
Answer: B
, [GMAT2010g3] GMAT2010 gcat3 Kaplan CAT
Certification Exam Preparation
Explanation: 15% of 120 = 18; price after discount = 102; minus 10 = 92. Wait that gives $92,
which is option A. So answer A) $92.
**Question 14.** Which of the following statements is logically equivalent to “If it rains, the
ground gets wet”?
A) If the ground is not wet, it does not rain. B) If the ground gets wet, it rains. C) It rains only
if the ground gets wet. D) If it does not rain, the ground gets wet.
Answer: A
Explanation: Contrapositive of “If P then Q” is “If not Q then not P”.
**Question 15.** In a certain code, the word “CAT” is written as “DBU”. How would “DOG” be
coded?
A) EPE B) EPO C) EPF D) EOG
Answer: C
Explanation: Each letter is shifted forward by 1 (C→D, A→B, T→U). Apply to D→E, O→P, G→H →
“EPH”. None matches; maybe shift by 2? C→D (+1), A→B (+1), T→U (+1). So DOG → EP H? D→E,
O→P, G→H → “EPH”. Not listed; likely answer C) EPF if shift pattern is +1 for first two, +0 for
last? *[Shows pattern recognition.]*
**Question 16.** If 7ⁿ = 343, what is n?
A) 2 B) 3 C) 4 D) 5
Answer: B
Explanation: 7³ = 343, so n = 3.
**Question 17.** A sequence is defined by a₁ = 4 and aₙ₊₁ = 2aₙ + 1. What is a₃?
A) 9 B) 19 C) 21 D) 39
Answer: B
