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mcq on Official GRE Practice Tests for Students
A group of students, when divided into groups of 4, leaves a remainder of 1, and when divided into groups of 5, leaves a remainder of 3. What is the total of the two smallest possible values of the group size?
a) 33
b) 46
c) 49
d) 53
e) 86
Option b – 46
If n is an integer and n raised to the power of 4 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
Organization P has 4096 members, and group Q has 4 members. Every 5 months, P doubles its membership, and every 10 months, Q increases by 700%. After how many months will both organizations have the same number of members?
a) 20
b) 40
c) 50
d) 100
Option d – 100
A positive number x gives a remainder of 5 when divided by 9. What is the remainder when 3x is divided by 9?
a) 0
b) 1
c) 3
d) 6
Option d – 6
1025 minus 560 is divisible by all of the following except
a) 11
b) 8
c) 5
d) 3
Option d – 3
Let p be a positive even number with a non-zero unit digit. If the units digit of p³ minus that of p² is zero, what is the units 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, what is the units digit of a + (13!)^4?
a) 0
b) 1
c) 3
d) 9
Option d – 9
How many months have exactly 28 days over a span of 400 years?
a) 40
b) 100
c) 103
d) 400
e) None of these
Option d – 400
If p and q are integers and the value of (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
A two-digit number G is given. When each digit is halved, a new two-digit number H is formed. Which of the following could be the total of G and H?
a) 153
b) 150
c) 137
d) 129
e) 89
Option d – 129
Let a be even and b be odd. Which of the following expressions must result in a number that is not even?
a) ab
b) a ÷ b
c) b ÷ a
d) ab
e) a²b + 1
Option c – b ÷ a
If x and y are prime numbers and x < y, which of the following cannot be true?
a) x is even
b) x + y is odd
c) xy is even
d) 2x + y is even
Option d – 2x + y is even
What is the unit digit of 1727?
a) 1
b) 2
c) 3
d) 7
e) 9
Option c – 3
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