GMAT QUANT Problem Solving Divisibility / Multiples / Factors

 

1) If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?

A. 10

B. 12

C. 15

D. 18

E. 20

 

2) What is the remainder when n^2+7 is divided by 8, where n is an odd prime number?

A. 0

B. 2

C. 3

D. 4

E. 6

 

3)If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

(A) four

(B) five

(C) six

(D) seven

(E) eight

 

4) 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?

(A) 6

(B) 9

(C) 10

(D) 11

(E) 14

 

5) The 180 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT

(A) 4

(B) 20

(C) 30

(D) 40

(E) 90

 

6) If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

(A) (x+z)/z

(B) (y+z)/x

(C) (x+y)/z

(D) (xy)/z

(E) (yz)/x

 

 

Answer: 1)D 2)A 3)A 4)D 5)D 6)B