Q. If a number is divided by 15 and leaves a remainder of 10, what will be the remainder when this number is divided by 5? (2023)
Solution
Since 10 is greater than 5, the remainder when 10 is divided by 5 is 0.
Correct Answer:
A
— 0
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Q. If a number is divided by 3 and the result is 5, what is the number?
Solution
Let the number be x. Then, x/3 = 5, so x = 5 × 3 = 15.
Correct Answer:
C
— 15
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Q. If a number is divided by 5, the remainder is 3. What will be the remainder when the same number is divided by 10? (2019)
Solution
Let the number be n. Then n = 5k + 3 for some integer k. When divided by 10, n = 5k + 3 gives a remainder of 3.
Correct Answer:
C
— 3
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Q. If a number is divided by 6 and gives a remainder of 2, what will be the remainder when the same number is divided by 3? (2023)
Solution
If the number gives a remainder of 2 when divided by 6, it will give a remainder of 2 when divided by 3 as well.
Correct Answer:
B
— 1
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Q. If a number is divided by 6 and gives a remainder of 2, what will be the remainder when this number is divided by 3? (2023)
Solution
Since 2 is less than 3, the remainder when 2 is divided by 3 is 2.
Correct Answer:
A
— 0
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Q. If a number is divided by 8 and gives a remainder of 5, what will be the remainder when this number is divided by 4?
Solution
The number can be expressed as 8k + 5, which gives a remainder of 1 when divided by 4.
Correct Answer:
B
— 1
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Q. If a number is divided by 8 and leaves a remainder of 5, what will be the remainder when this number is divided by 4? (2023)
Solution
The number can be expressed as 8k + 5. When divided by 4, the remainder is 5 mod 4 = 1.
Correct Answer:
D
— 3
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Q. If a number is divided by 9 and gives a remainder of 2, which of the following numbers will also give the same remainder when divided by 9?
Solution
29 gives a remainder of 2 when divided by 9 (9*3 + 2 = 29).
Correct Answer:
C
— 29
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Q. If a number is divisible by 10, which of the following must be true?
-
A.
It is divisible by 2
-
B.
It is divisible by 5
-
C.
It is even
-
D.
All of the above
Solution
A number divisible by 10 is always divisible by 2 and 5, and it is also even.
Correct Answer:
D
— All of the above
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Q. If a number is divisible by 12, which of the following must also be true?
-
A.
It is divisible by 3
-
B.
It is divisible by 5
-
C.
It is divisible by 10
-
D.
It is a prime number
Solution
A number divisible by 12 is also divisible by both 3 and 4.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by 15, which of the following must also be true?
-
A.
It is divisible by 3
-
B.
It is divisible by 5
-
C.
It is even
-
D.
Both 0 and 1 are factors
Solution
A number divisible by 15 must be divisible by both 3 and 5.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by 15, which of the following must it also be divisible by?
-
A.
3
-
B.
5
-
C.
15
-
D.
All of the above
Solution
A number divisible by 15 is also divisible by both 3 and 5, as 15 is the product of these two primes.
Correct Answer:
D
— All of the above
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Q. If a number is divisible by 2 and 3, is it prime or composite?
-
A.
Prime
-
B.
Composite
-
C.
Neither
-
D.
Cannot be determined
Solution
A number divisible by 2 and 3 is composite, as it has divisors other than 1 and itself.
Correct Answer:
B
— Composite
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Q. If a number is divisible by 2 and 3, is it prime?
-
A.
Yes
-
B.
No
-
C.
Only if it's 6
-
D.
Only if it's odd
Solution
No, because if a number is divisible by 2 and 3, it has divisors other than 1 and itself.
Correct Answer:
B
— No
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Q. If a number is divisible by 4, which of the following must also be true?
-
A.
It is even
-
B.
It is divisible by 8
-
C.
It is divisible by 2
-
D.
It is a multiple of 10
Solution
Any number divisible by 4 is even, as 4 itself is an even number.
Correct Answer:
A
— It is even
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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
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
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
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
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
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
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.
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?
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
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
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.
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
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
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, what is the smallest positive integer that it can be?
Solution
The smallest positive integer divisible by both 4 and 6 is 12.
Correct Answer:
A
— 12
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Q. If a number is divisible by both 4 and 6, what is the smallest such number?
Solution
The smallest number divisible by both 4 and 6 is their LCM, which is 12.
Correct Answer:
A
— 12
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