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mcq on GRE Practice test Full for Students
If x is a whole number, the expression x(x−1)(x−k) is divisible by 3 for all values of k except?
a) -4
b) -2
c) -1
d) 2
e) 5
Option b – -2
Given that a, b, c, and d are consecutive integers with 1 < b < c < d, and b × c × d = 2 × a × b × c, then the value of b × c is?
a) 2
b) 6
c) 12
d) 20
e) 30
Option d – 20
For any positive number n, define its “length” as the number of prime factors (counted with multiplicity) whose product equals n. For example, the length of 78 is 3 since 78 = 2 × 3 × 13. How many two-digit numbers have a length of 6?
a) 0
b) 1
c) 2
d) 3
e) 4
Option c – 2
The sum x includes all three-digit numbers that can be formed using the non-zero digits a, b, and c exactly once in each number. What is the largest number that will divide x without a remainder?
a) 3
b) 6
c) 11
d) 222
Option d – 222
If k and m are both positive integers, which one of the following options cannot be the highest common factor of 35k and 20m?
a) 5
b) 5(k−m)
c) 20k
d) 20m
e) 35k
Option c – 20k
What is the smallest positive number that is divisible by all of the numbers 8, 9, 10, 11, and 12?
a) 7,920
b) 5,940
c) 3,960
d) 2,970
e) 890
Option c – 3,960
What is the largest prime number that divides 417 − 228?
a) 5
b) 7
c) 11
d) 13
e) 19
Option b – 7
What is the least positive number that is divisible by the first 7 multiples of 5?
a) 140
b) 210
c) 1,400
d) 2,100
e) 3,500
Option d – 2,100
Suppose that for every integer k > 1, the “length” is defined as the number of prime factors (not necessarily distinct) in its prime factorization. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the highest possible combined length of x and y?
a) 5
b) 6
c) 15
d) 16
e) 18
Option d – 16
Let q be a number such that the sum of its digits equals a three-digit number ending in 13. If q = 10^n − 49, find the value of n.
a) 24
b) 25
c) 26
d) 27
e) 28
Option b – 25
If n is a positive number that is divisible by both 4 and 21, which number must n also be divisible by?
a) 8
b) 12
c) 18
d) 24
e) 48
Option b – 12
Suppose a number x gives a quotient y and a remainder 3 when divided by 11. If x also gives a remainder of 3 when divided by 19, what will be the remainder when y is divided by 19?
a) 0
b) 1
c) 2
d) 3
e) 4
Option a – 0
Let n be a non-negative integer such that 12n is divisible by 43,75,953. What is the value of n^12 − 12n?
a) -11
b) -1
c) 0
d) 1
e) 11
Option b – -1
If the greatest common divisor of 16 and some positive integer n is 4, and the greatest common divisor of n and 45 is 3, which of the following could n be?
a) 6
b) 8
c) 9
d) 12
e) 15
Option d – 12
How many total divisors does 362 have?
a) 2
b) 8
c) 24
d) 25
e) 26
Option d – 25
In a game, colored chips are assigned values: blue = 1 point, green = 5 points, purple = x points, and red = 11 points. The purple chip’s value is more than green but less than red. If a group of selected chips has a total product of 88,000 points, how many purple chips were chosen?
a) 1
b) 2
c) 3
d) 4
e) 5
Option b – 2
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