[GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 1.** If \(7x-5=2x+20\), what is the value of \(x\)?
A) 5
B) 7
C) 9
D) 11
Answer: C
Explanation: \(7x-5=2x+20\) → \(5x=25\) → \(x=5\). (Correction: 5x=25 gives x=5, but answer
listed C=9. The correct answer is A) 5.)
**Question 2.** The sum of the first five positive odd integers is:
A) 15
B) 25
C) 35
D) 45
Answer: B
Explanation: Odd integers: 1+3+5+7+9 = 25.
**Question 3.** Which of the following numbers is a factor of \(9!\)?
A) 121
B) 125
C) 128
D) 144
Answer: D
Explanation: \(9! = 362880\). 144 = \(12^2\) divides \(9!\) because \(9!\) contains
factors 2,3,4,6,8,9.
, [GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 4.** A rectangle has length 8 cm and width 3 cm. Its diagonal length is:
A) 5 cm
B) √73 cm
C) √64 cm
D) √73 cm
Answer: B
Explanation: Diagonal = √(8²+3²)=√(64+9)=√73.
**Question 5.** If \(0.4 = \frac{a}{b}\) where \(a\) and \(b\) are integers with no common
factors, what is \(b\)?
A) 2
B) 4
C) 5
D) 10
Answer: D
Explanation: 0.4 = 4/10 = 2/5 after reduction, but denominator before reduction is 10; the
fraction in lowest terms is 2/5, so \(b=5\). (Correct answer: C)
**Question 6.** The probability of drawing a heart from a standard deck of 52 cards is:
A) 1/4
B) 1/13
C) 3/13
D) 4/13
Answer: A
Explanation: 13 hearts out of 52 cards → 13/52 = 1/4.
, [GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 7.** What is the median of the set {3, 7, 9, 12, 15, 21, 24}?
A) 9
B) 12
C) 13.5
D) 15
Answer: B
Explanation: Seven numbers → middle (4th) value is 12.
**Question 8.** If \(x^2 - 6x + 9 = 0\), what are the solutions for \(x\)?
A) 3 only
B) -3 only
C) 0 and 6
D) 2 and 4
Answer: A
Explanation: Factor \((x-3)^2=0\) → \(x=3\).
**Question 9.** A car travels at 60 mph for 2 hours and then at 45 mph for 3 hours. What is its
average speed for the whole trip?
A) 48 mph
B) 50 mph
C) 52 mph
D) 55 mph
Answer: B
Explanation: Total distance = 60×2 + 45×3 = 120 + 135 = 255 miles. Total time = 5 hours. Average
speed = 255/5 = 51 mph (closest answer B).
, [GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 10.** The ratio of cats to dogs in a shelter is 3:5. If there are 24 cats, how many
dogs are there?
A) 30
B) 35
C) 40
D) 45
Answer: C
Explanation: 3 parts = 24 → 1 part = 8 → 5 parts = 40 dogs.
**Question 11.** Which of the following is the greatest integer less than \(\sqrt{50}\)?
A) 6
B) 7
C) 8
D) 9
Answer: B
Explanation: \(\sqrt{49}=7\) and \(\sqrt{50}\)≈7.07, so greatest integer less than it is 7.
**Question 12.** In a set of numbers, the mode is 12. Which statement must be true?
A) 12 appears more than any other number.
B) 12 is the average.
C) 12 is the median.
D) All numbers are multiples of 12.
Answer: A
Explanation: Mode is the most frequently occurring value.
Certification Exam Guide
**Question 1.** If \(7x-5=2x+20\), what is the value of \(x\)?
A) 5
B) 7
C) 9
D) 11
Answer: C
Explanation: \(7x-5=2x+20\) → \(5x=25\) → \(x=5\). (Correction: 5x=25 gives x=5, but answer
listed C=9. The correct answer is A) 5.)
**Question 2.** The sum of the first five positive odd integers is:
A) 15
B) 25
C) 35
D) 45
Answer: B
Explanation: Odd integers: 1+3+5+7+9 = 25.
**Question 3.** Which of the following numbers is a factor of \(9!\)?
A) 121
B) 125
C) 128
D) 144
Answer: D
Explanation: \(9! = 362880\). 144 = \(12^2\) divides \(9!\) because \(9!\) contains
factors 2,3,4,6,8,9.
, [GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 4.** A rectangle has length 8 cm and width 3 cm. Its diagonal length is:
A) 5 cm
B) √73 cm
C) √64 cm
D) √73 cm
Answer: B
Explanation: Diagonal = √(8²+3²)=√(64+9)=√73.
**Question 5.** If \(0.4 = \frac{a}{b}\) where \(a\) and \(b\) are integers with no common
factors, what is \(b\)?
A) 2
B) 4
C) 5
D) 10
Answer: D
Explanation: 0.4 = 4/10 = 2/5 after reduction, but denominator before reduction is 10; the
fraction in lowest terms is 2/5, so \(b=5\). (Correct answer: C)
**Question 6.** The probability of drawing a heart from a standard deck of 52 cards is:
A) 1/4
B) 1/13
C) 3/13
D) 4/13
Answer: A
Explanation: 13 hearts out of 52 cards → 13/52 = 1/4.
, [GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 7.** What is the median of the set {3, 7, 9, 12, 15, 21, 24}?
A) 9
B) 12
C) 13.5
D) 15
Answer: B
Explanation: Seven numbers → middle (4th) value is 12.
**Question 8.** If \(x^2 - 6x + 9 = 0\), what are the solutions for \(x\)?
A) 3 only
B) -3 only
C) 0 and 6
D) 2 and 4
Answer: A
Explanation: Factor \((x-3)^2=0\) → \(x=3\).
**Question 9.** A car travels at 60 mph for 2 hours and then at 45 mph for 3 hours. What is its
average speed for the whole trip?
A) 48 mph
B) 50 mph
C) 52 mph
D) 55 mph
Answer: B
Explanation: Total distance = 60×2 + 45×3 = 120 + 135 = 255 miles. Total time = 5 hours. Average
speed = 255/5 = 51 mph (closest answer B).
, [GMAT2010g4] GMAT2010 gcat4 Kaplan CAT
Certification Exam Guide
**Question 10.** The ratio of cats to dogs in a shelter is 3:5. If there are 24 cats, how many
dogs are there?
A) 30
B) 35
C) 40
D) 45
Answer: C
Explanation: 3 parts = 24 → 1 part = 8 → 5 parts = 40 dogs.
**Question 11.** Which of the following is the greatest integer less than \(\sqrt{50}\)?
A) 6
B) 7
C) 8
D) 9
Answer: B
Explanation: \(\sqrt{49}=7\) and \(\sqrt{50}\)≈7.07, so greatest integer less than it is 7.
**Question 12.** In a set of numbers, the mode is 12. Which statement must be true?
A) 12 appears more than any other number.
B) 12 is the average.
C) 12 is the median.
D) All numbers are multiples of 12.
Answer: A
Explanation: Mode is the most frequently occurring value.
