Q. If a number is divisible by 4, which of the following must be true?
A.
It ends in 0
B.
It ends in 2
C.
Its last two digits form a number divisible by 4
D.
It is even
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Solution
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Correct Answer:
C
— Its last two digits form a number divisible by 4
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Q. If a number is divisible by 7, which of the following is NOT necessarily true?
A.
It is odd
B.
It is not a prime number
C.
It can be a multiple of 14
D.
It can be a two-digit number
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Solution
A number can be divisible by 7 and still be even, such as 14.
Correct Answer:
A
— It is odd
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Q. If a number is divisible by 8, which of the following must also be true?
A.
It is divisible by 2
B.
It is divisible by 4
C.
It is a multiple of 16
D.
It is a prime number
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Solution
Any number divisible by 8 is also divisible by 4, as 8 is a multiple of 4.
Correct Answer:
B
— It is divisible by 4
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Q. If a number is divisible by 8, which of the following must be true?
A.
It is divisible by 2
B.
It is divisible by 3
C.
It is divisible by 5
D.
It is divisible by 10
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Solution
A number divisible by 8 is also divisible by 2, as 8 is a multiple of 2.
Correct Answer:
A
— It is divisible by 2
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Q. If a number is divisible by 9, what can be inferred about the sum of its digits?
A.
It is even
B.
It is divisible by 3
C.
It is divisible by 9
D.
It is a prime number
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Solution
A number is divisible by 9 if the sum of its digits is also divisible by 9.
Correct Answer:
C
— It is divisible by 9
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Q. If a number is divisible by both 2 and 3, which of the following is true?
A.
It is divisible by 5
B.
It is divisible by 6
C.
It is odd
D.
It is a prime number
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Solution
A number that is divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— It is divisible by 6
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Q. If a number is divisible by both 2 and 3, which of the following must also be true?
A.
It is divisible by 5.
B.
It is divisible by 6.
C.
It is an odd number.
D.
It is a prime number.
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Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— It is divisible by 6.
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Q. If a number is divisible by both 2 and 3, which of the following must it also be divisible by?
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Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— 6
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Q. If a number is divisible by both 2 and 5, what can be said about it?
A.
It is odd
B.
It is a multiple of 10
C.
It is a prime number
D.
It is a multiple of 20
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Solution
A number divisible by both 2 and 5 must end in 0, making it a multiple of 10.
Correct Answer:
B
— It is a multiple of 10
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Q. If a number is divisible by both 2 and 5, which of the following must be true?
A.
It is divisible by 10
B.
It is divisible by 15
C.
It is divisible by 20
D.
It is divisible by 25
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Solution
A number divisible by both 2 and 5 is also divisible by 10, as 10 is the least common multiple of 2 and 5.
Correct Answer:
A
— It is divisible by 10
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Q. If a number is divisible by both 3 and 4, which of the following must also be true?
A.
It is divisible by 12.
B.
It is divisible by 7.
C.
It is divisible by 6.
D.
It is divisible by 9.
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Solution
The least common multiple of 3 and 4 is 12, so any number divisible by both must also be divisible by 12.
Correct Answer:
A
— It is divisible by 12.
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Q. If a number is divisible by both 3 and 5, which of the following is guaranteed to be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is divisible by 6
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Solution
A number divisible by both 3 and 5 is also divisible by their least common multiple, which is 15.
Correct Answer:
A
— It is divisible by 15
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Q. If a number is divisible by both 3 and 5, which of the following must also be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is not divisible by 6
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Solution
A number divisible by both 3 and 5 is also divisible by their LCM, which is 15.
Correct Answer:
A
— It is divisible by 15
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Q. If a number is divisible by both 4 and 6, which of the following must also be true? (2023)
A.
It is divisible by 12.
B.
It is divisible by 24.
C.
It is divisible by 10.
D.
It is not divisible by 2.
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Solution
The least common multiple of 4 and 6 is 12, so any number divisible by both must also be divisible by 12.
Correct Answer:
A
— It is divisible by 12.
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Q. If a number is divisible by both 5 and 10, which of the following can be concluded?
A.
It is a multiple of 15.
B.
It is a multiple of 20.
C.
It is a multiple of 50.
D.
It is a multiple of 10.
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Solution
Any number divisible by 10 is also a multiple of 10.
Correct Answer:
D
— It is a multiple of 10.
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Q. If a number is divisible by both 6 and 8, which of the following must it also be divisible by?
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Solution
The least common multiple of 6 and 8 is 24, so any number divisible by both must also be divisible by 24.
Correct Answer:
B
— 24
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Q. If a number is divisible by both 8 and 12, what is the smallest number it could be?
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Solution
The least common multiple of 8 and 12 is 24, so the smallest number divisible by both is 24.
Correct Answer:
B
— 48
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Q. If a number is divisible by both 8 and 12, which of the following must also be true?
A.
It is divisible by 24.
B.
It is divisible by 16.
C.
It is divisible by 20.
D.
It is divisible by 32.
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Solution
The least common multiple of 8 and 12 is 24, so any number divisible by both must also be divisible by 24.
Correct Answer:
A
— It is divisible by 24.
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Q. If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
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Solution
The least common multiple of 8 and 12 is 24, so the number must be divisible by 24.
Correct Answer:
B
— 24
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Q. If a number is divisible by both 9 and 12, which of the following is guaranteed to be true?
A.
It is divisible by 36.
B.
It is divisible by 108.
C.
It is divisible by 27.
D.
It is divisible by 18.
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Solution
The least common multiple of 9 and 12 is 36, and since 36 is divisible by 18, the number must also be divisible by 18.
Correct Answer:
D
— It is divisible by 18.
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Q. If a number is expressed as 5k + 3 for some integer k, what is the remainder when this number is divided by 5? (2023)
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Solution
The term 5k is divisible by 5, so the remainder is solely from 3, which is 3.
Correct Answer:
D
— 3
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Q. If a number is expressed as 5k + 3, where k is an integer, what is the remainder when this number is divided by 5?
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Solution
The remainder is 3, as 5k is divisible by 5.
Correct Answer:
D
— 3
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Q. If a number is increased by 15% and the result is 115, what is the original number?
A.
90
B.
100
C.
105
D.
110
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Solution
Let the original number be x. Then, x + 0.15x = 115, or 1.15x = 115. Thus, x = 115 / 1.15 = 100.
Correct Answer:
B
— 100
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Q. If a number is increased by 20% and then decreased by 20%, what is the net change in the number?
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Solution
Let the number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 96. Net change = (96-100)/100 * 100% = -4%.
Correct Answer:
A
— 0%
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Q. If a number leaves a remainder of 1 when divided by 3 and a remainder of 2 when divided by 4, what is the smallest positive integer that satisfies these conditions?
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Solution
The smallest number that satisfies both conditions is 11 (11 % 3 = 2 and 11 % 4 = 3).
Correct Answer:
C
— 11
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Q. If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5, what is the maximum possible value of this number? (2023)
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Solution
The maximum number satisfying both conditions is 19 (19 % 4 = 3 and 19 % 5 = 4).
Correct Answer:
C
— 19
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Q. If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5, what is the smallest positive integer that satisfies these conditions?
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Solution
The smallest number satisfying both conditions is 9, as 9 mod 4 = 1 and 9 mod 5 = 4.
Correct Answer:
A
— 6
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Q. If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5, what is the smallest such number?
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Solution
The smallest number that satisfies both conditions is 9.
Correct Answer:
A
— 9
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Q. If a number leaves a remainder of 2 when divided by 4 and a remainder of 3 when divided by 5, what is the smallest such number?
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Solution
The smallest number that satisfies both conditions is 7 (7 % 4 = 3 and 7 % 5 = 2).
Correct Answer:
B
— 7
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Q. If a number leaves a remainder of 2 when divided by 5 and a remainder of 3 when divided by 7, what is the smallest such number?
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Solution
The smallest number satisfying both conditions is 12, as 12 mod 5 = 2 and 12 mod 7 = 5.
Correct Answer:
A
— 12
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