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MCQ on GRE Practice Test Full for Students
If x is an integer, then x(x-1)(x-k) must be evenly divisible by 3 for k having any of the following values EXCEPT?
(a) -4
(b) -2
(c) -1
(d) 2
(e) 5
Option b – -2
a,b,c, and d are consecutive integers such that 1 <b<c<d. Also bcd=2abc; then bc =?
(a) 2
(b) 6
(c) 12
(d) 20
(e) 30
Option d – 20
For any positive integer n, the length of n is defined as a number of prime factors whose product is n. e.g. length of 78=3 as 78=2×3×13; How many two-digit positive integers have length 6?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
Option c – 2
If x represents the sum of all the positive three-digit numbers that can be constructed using each distinct non-zero digit a, b, and c exactly once. What is the largest integer by which x must be divisible?
(a) 3
(b) 6
(c) 11
(d) 22
(e) 222
Option e – 222
If k and m are positive integers, which of the following CANNOT be the greatest common divisor of 35k and 20m?
(a) 5
(b) 5(k-m)
(c) 20k
(d) 20m
(e) 35k
Option c – 20k
Which of the following is the lowest positive integer divisible by 8,9,10,11 and 12?
(a) 7,920
(b) 5,940
(c) 3,960
(d) 2.970
(e) 890
Option c – 3,960
Find the greatest prime factor of 417-228.
(a) 5
(b) 7
(c) 11
(d) 13
(e) 19
Option b – 7
Which is the lowest +ve integer divisible by the first 7 positive integer multiples of 5?
(a) 140
(b) 210
(c) 1400
(d) 2100
(e) 3500
Option d – 2100
For an integer k> 1, the term length of an integer refers to the number of positive prime factors, may not be different, whose product is = k. e.g. if k= 36, the length of k is 4, as 36 = 2×2×3×3. are positive integers such that x > 1, y> 1, and x + 3y < 1000, what is the maximum If x and y possible sum of the lengths of both x and of y?
(a) 5
(b) 6
(c) 15
(d) 16
(e) 18
Option d – 16
The sum of all the digits of the positive integer q is equal to the three-digit number X13. If q = 10n-49, what is the value of n?
(a) 24
(b) 25
(c) 26
(d) 27
(e) 28
Option b – 25
If positive integer n is divisible by both 4 and 21, then n must be divisible by?
(a) 8
(b) 12
(c) 18
(d) 24
(e) 48
Option b – 12
When a positive integer x is divided by 11, the quotient is y, and the remainder is 3. When x is divided by 19, the remainder is again 3. Find the remainder when y is divided by 19.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
Option a – 0
If n is a non-negative integer such that 12n is divided by 43,75,953, what is the value of n12-12n?
(a) -11
(b) -1
(c) 0
(d) 1
(e) 11
Option b – -1
The greatest common factor of 16 and the positive integer n is 4. And the greatest common factor of n and 45 is 3. Which could be the value of n?
(a) 6
(b) 8
(c) 9
(d) 12
(e) 15
Option d – 12
How many factors 362 has?
(a) 2
(b) 8
(c) 24
(d) 25
(e) 26
Option d – 25
In a certain game, a large bag is filled with blue, green, purple, and red chips worth 1,5, x, and 11 points each respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is INR 88,000, how many purple chips were selected?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Option b – 2
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