Number Properties

Number properties is the most GMAT-specific topic in Quant: odds and evens, primes and factors, remainders, units digits, and positive/negative reasoning. Almost every hard Quant question borrows from this toolbox. The questions here train you to characterize numbers instead of computing them — to see that a product is even because one factor must be, or that a remainder pattern cycles every four powers. Master this topic and both Problem Solving and Data Sufficiency get noticeably easier.

Primes, parity, integers.·Show:20 30 50

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555-605 (Medium)

On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?

555-605 (Medium)

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10 4 â 10 2) (0.00 12 Â¯ Â¯) (10 4 â 10 2) (0.00 12 Â¯) ?

505-555 (Easy)

In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

605-655 (Medium)

If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?

505-555 (Easy)

The positive integer n is divisible by 25. If â n n â is greater than 25, which of the following could be the value of n/25 ?

505-555 (Easy)

If n is a positive integer, then n(n+1)(n+2) is

Sub 505 (Easy)

If the quotient a/b positive, which of the following must be true?

Sub 505 (Easy)

For which of the following values of n is (100+n)/n NOT an integer?

Sub 505 (Easy)

If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true? I. c - a = 2 II. abc is an even integer. III. (a + b + c)/3 is an integer.

505-555 (Easy)

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

Sub 505 (Easy)

The sum of prime numbers that are greater than 60 but less than 70 is

Sub 505 (Easy)

A studentâs average (arithmetic mean) test score on 4 tests is 80. What must be the studentâs score on a 5th test for the studentâs average score on the 5 tests to be 82?

505-555 (Easy)

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2 i * 3 k * 5 m * 7 p , then i + k + m + p =

505-555 (Easy)

What is the units digit of 13 4 â 17 2 â 29 3 ?

Sub 505 (Easy)

Fermat primes are prime numbers that can be written in the form 2 k + 1 , where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

555-605 (Medium)

Which of the following CANNOT be a value of 1 x â 1 ?

Sub 505 (Easy)

If p is an even integer and q is an odd integer, which of the following must be an odd integer?

Sub 505 (Easy)

Which of the following is NOT equal to the square of an integer:

505-555 (Easy)

If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?

Sub 505 (Easy)

R is the set of positive odd integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?

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