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

All

Start Practice

555-605 (Medium)

How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?

505-555 (Easy)

A computer routine was developed to generate two numbers, ( x,y), the first being a random number between 0 and 100 inclusive, and the second being less than or equal to the square root of the first. Each of the following pairs satisfies this routine EXCEPT:

505-555 (Easy)

If a, b, and c are three consecutive odd integers such that 10 < a < b < c < 20 and if b and c are prime numbers, what is the value of a + b?

Sub 505 (Easy)

If x, y, and z are single-digit integers and 100(x) + 1,000(y) + 10(z) = N, what is the units' digit of the number N?

Sub 505 (Easy)

If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

Sub 505 (Easy)

How many of the integers between 25 and 45 are even?

Sub 505 (Easy)

If x is an even integer, which of the following is an odd integer?

505-555 (Easy)

p

q

r

, and

s

are as shown on the number line above, which of the following products is greatest?

505-555 (Easy)

Set

X

consists of eight consecutive integers. Set

Y

consists of all the integers that result from adding 4 to each of the integers in Set

X

and all the integers that result from subtracting 4 from each of the integers in Set

X

. How many more integers are there in Set

Y

than in Set

X

505-555 (Easy)

The positive two-digit integers

x

and

y

have the same digits, but in reverse order. Which of the following must be a factor of

x + y

505-555 (Easy)

In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number. If the first number is

- 5

, how many of the numbers in the sequence are positive?

505-555 (Easy)

x

and

y

are positive integers such that

y

is a multiple of 5 and

3 x + 4 y = 200

, then

x

must be a multiple of which of the following?

505-555 (Easy)

Which of the following expressions can be written as an integer? I.

(82 + 82)^{2}

II.

(82) (82)

III.

\frac{( 82 ) ( 82 )}{82}

605-655 (Medium)

N

and

M

are each 3-digit integers. Each of 1, 2, 3, 6, 7, and 8 is a digit of either

N

M

. What is the smallest possible positive difference between

N

and

M

605-655 (Medium)

The number line shown contains three points

R

S

, and

T

, whose coordinates have absolute values

r

s

, and

t

, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points

R

S

, and

T

605-655 (Medium)

n = 20! + 17

, then

n

is divisible by which of the following? I. 15 II. 17 III. 19

605-655 (Medium)

A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer

n

is divisible by 3 and

n

is of the form

1 k 2, k 24

, where

k

represents a digit that occurs twice, how many values could

n

have?

655-705 (Hard)

3 < x < 100

, for how many values of

x

\frac{x}{3}

the square of a prime number?

655-705 (Hard)

[x]

is the greatest integer less than or equal to

x

, what is the value of

[- 1.6] + [3.4] + [2.7]

655-705 (Hard)

n = (33)^{43} + (43)^{33}

, what is the units digit of

n

← PreviousPage 4 of 5Next →