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MCQ on Official GRE Practice Tests for Students
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
(a) 33
(b) 46
(c) 49
(d) 53
(e) 86
Option b – 46
If n is an integer and n4 is divisible by 32, which of the following could be the remainder when n is divided by 32?
(a) 2
(b) 4
(c) 5
(d) 6
(e) 10
Option b – 4
An old organization (P) has exactly 4096 members. A new organization (2) has exactly 4 members. Every 5 months the membership of P is increased by 100 percent. Every 10 months the membership of the Q by 700%. New members join the organization only on the last day of each 5 or 10-month period. Assuming that no member leaves the organization, after how many months will the two groups have exactly the same number of members?
(a) 20
(b) 40
(c) 50
(d) 80
(e) 100
Option e – 100
When the positive integer x is divided by 9, the remainder is 5. Find the remainder when 3x is divided by 9.
(a) 0
(b) 1
(c) 3
(d) 4
(e) 6
Option e – 6
1025-560 is divisible by all of the following EXCEPT
(a) 11
(b) 8
(c) 5
(d) 4
(e) 3
Option e – 3
Given that p is a positive even integer with a positive units digit if the units digit of p³ minus the unit digit of p2 is equal to zero, what is the unit digit of (p + 3)?
(a) 3
(b) 6
(c) 7
(d) 9
(e) Can’t say
Option d – 9
If ((13!)16-(13!)8) = ( (13!)8+ (13!)4]) = a, find the unit digit of a + (13!)4
(a) 0
(b) 1
(c) 3
(d) 5
(e) 9
Option e – 9
How many months will have 28 days in a 400-year calendar
(a) 40
(b) 100
(c) 103
(d) 400
(e) None of these
Option d – 400
If p and q are integers and (p+q + p) is odd, which of the following must be odd?
(a) p
(b) q
(c) p + q
(d) pq
(e) pq + p
Option b – q
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H?
(a) 153
(b) 150
(c) 137
(d) 129
(e) 89
Option d – 129
If a is an even integer and b is an odd integer, which cannot be an even integer?
(a) ab
(b) a/b
(c) b/a
(d) ab
(e) a2b + 1
Option c – b/a
If x and y are prime integers and x <y, which cannot be true?
(a) x is even
(b) x+y is odd
(c) xy is even
(d) y + xy is even
(e) 2x+y is even
Option e – 2x+y is even
1727 has a unit digit of
(a) 1
(b) 2
(c) 3
(d) 7
(e) 9
Option c – 3
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