GMAT Quantitative: Number Properties 2 — Questions and Answers
Question 1: If n is a positive integer, which of the following must be even?
- n(n+1) (Correct answer)
- n+2
- 2n+1
- n^2
Correct answer: n(n+1)
The product of two consecutive integers is always even because one of them must be even.
Question 2: What is the units digit of 7^23?
- 1
- 3 (Correct answer)
- 7
- 9
Correct answer: 3
Powers of 7 cycle 7,9,3,1 with period 4, and 23 mod 4 = 3, giving units digit 3.
Question 3: How many positive divisors does 36 have?
- 6
- 8
- 9 (Correct answer)
- 12
Correct answer: 9
Since 36 = 2^2 * 3^2, the divisor count is (2+1)(2+1) = 9.
Question 4: If x is an odd integer, which expression is always odd?
- x+1
- 3x (Correct answer)
- 2x
- x^2-1
Correct answer: 3x
An odd number times an odd number is odd, so 3x stays odd.
Question 5: What is the remainder when 47 is divided by 6?
- 1
- 3
- 5 (Correct answer)
- 4
Correct answer: 5
Since 6 * 7 = 42, the remainder is 47 - 42 = 5.
Question 6: Which of the following is a prime number?
- 91
- 87
- 83 (Correct answer)
- House 51
Correct answer: 83
83 has no divisors other than 1 and itself, while 91=7*13, 87=3*29, and 51=3*17.
Question 7: If the sum of three consecutive integers is 72, what is the largest of them?
- 23
- 24
- 25 (Correct answer)
- 26
Correct answer: 25
The middle integer is 72/3 = 24, so the three are 23, 24, 25 and the largest is 25.
GMAT Quantitative: Number Properties 2
If n is a positive integer, which of the following must be even?