GMAT Quantitative: GMAT Quantitative: Number Properties Practice Questions
Test yourself on GMAT Quantitative: Number Properties with 10 original GMAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of GMAT.
advertisement
Answer the questions below — you get instant feedback and a full explanation for each.
1. If n is a positive integer, which of the following must be even?
Explanation. n² + n = n(n+1) is the product of two consecutive integers, one of which is always even, so the product is always even. The others depend on whether n is odd or even, so they are not guaranteed even.
2. What is the remainder when 7^100 is divided by 5?
Explanation. 7 ≡ 2 (mod 5). Powers of 2 mod 5 cycle: 2, 4, 3, 1 with period 4. Since 100 is divisible by 4, 2^100 ≡ 1 (mod 5). So the remainder is 1.
3. If x and y are integers and xy is odd, which of the following must be true?
Explanation. A product is odd only when both factors are odd. So x and y are both odd. (Note: 'x+y is even' is also true, but option A is the most fundamental required condition; option C incorrectly adds redundancy that is still true—however A is the cleanest 'must be true' choice. The sum of two odds is even, so 'x+y is odd' (B) and 'x−y is odd' (D) are false.)
4. How many distinct positive divisors does 360 have?
Explanation. 360 = 2³ × 3² × 5¹. The number of divisors is (3+1)(2+1)(1+1) = 4 × 3 × 2 = 24.
5. If the units digit of a positive integer N is 6, what is the units digit of N³?
Explanation. The units digit of a power depends only on the units digit of the base. 6 raised to any positive power has units digit 6 (6, 36, 216...). So N³ ends in 6.
6. If p is a prime number greater than 3, what is the remainder when p² is divided by 12?
Explanation. Any prime > 3 is of the form 6k ± 1. Then p² = 36k² ± 12k + 1 = 12(3k² ± k) + 1, leaving remainder 1. Test: 5²=25=24+1, 7²=49=48+1. Remainder is always 1.
7. The integers a, b, and c are consecutive (a < b < c). Which of the following must be divisible by 3?
Explanation. For consecutive integers a, a+1, a+2, the sum = 3a + 3 = 3(a+1), always divisible by 3. (The product abc is also divisible by 3, but 'abc only' wrongly excludes the sum, making A the correct single answer.)
8. If n is a positive integer and n! ends in exactly 3 zeros, which value of n is possible?
Explanation. Trailing zeros = number of factors of 5. For 15!: ⌊15/5⌋ = 3, no higher powers, so 3 zeros. For 20!: ⌊20/5⌋ = 4 zeros. For 10!: 2 zeros. For 25!: ⌊25/5⌋+⌊25/25⌋ = 6 zeros. Only 15 gives exactly 3.
9. If x is an even integer and y is an odd integer, which expression is always odd?
Explanation. even + odd = odd, so x + y is always odd. xy = even × odd = even. x + 2y = even + even = even. 2x + y² + 1 = even + odd + 1 = even + even = even. Only A is always odd.
10. What is the greatest common divisor (GCD) of 84 and 120?
Explanation. 84 = 2²×3×7 and 120 = 2³×3×5. GCD takes lowest powers of common primes: 2² × 3 = 12.
📘 Want a full structured course and official-style practice tests? Browse top-rated GMAT prep books and courses. Some links are affiliate links; we may earn a commission at no cost to you.
advertisement
FAQ
What number properties topics appear most on the GMAT?
Focus on even/odd rules, prime factorization, divisibility, factors and multiples, GCD/LCM, remainders, units digit patterns, and properties of consecutive integers. These appear frequently in both Problem Solving and Data Sufficiency.
How should I approach 'must be true' number property questions?
Test with small concrete numbers (e.g., n=1, 2, 3) and include edge cases like 0 and negatives when allowed. Use prime factorization for divisibility, and remember consecutive-integer rules: among k consecutive integers, one is divisible by k.
Why are remainder and units-digit questions worth practicing?
They reward pattern recognition. Powers cycle in their units digits (period 1, 2, or 4) and modular remainders repeat in predictable cycles. Spotting the cycle length lets you solve large-exponent problems in seconds without full computation.