Q. A number is divisible by both 2 and 5. Which of the following must be true?
A.
It is even.
B.
It is odd.
C.
It is a prime number.
D.
It is a multiple of 10.
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Solution
If a number is divisible by both 2 and 5, it must be a multiple of 10.
Correct Answer:
D
— It is a multiple of 10.
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Q. A number is said to be a multiple of 4 if its last two digits form a number that is divisible by 4. Which of the following numbers is NOT a multiple of 4?
A.
124
B.
256
C.
378
D.
492
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Solution
The last two digits of 378 are 78, which is not divisible by 4 (78 ÷ 4 = 19.5). Therefore, 378 is not a multiple of 4.
Correct Answer:
C
— 378
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Q. A number is said to be a perfect square if it has an integer as its square root. Which of the following numbers is a perfect square?
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Solution
25 is a perfect square because its square root is 5, which is an integer.
Correct Answer:
C
— 25
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Q. Arrange the following numbers in ascending order based on their factors: 15, 12, 18, 10. (2023)
A.
10, 12, 15, 18
B.
12, 10, 15, 18
C.
15, 10, 12, 18
D.
18, 15, 12, 10
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Solution
The number of factors for each is: 10 (4), 12 (6), 15 (4), 18 (6). Arranging them gives 10, 12, 15, 18.
Correct Answer:
A
— 10, 12, 15, 18
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Q. If a number is a factor of 100, which of the following cannot be a factor?
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Solution
75 is not a factor of 100.
Correct Answer:
D
— 75
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Q. If a number is a factor of 24 and a multiple of 3, which of the following could be that number?
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Solution
6 is a factor of 24 and also a multiple of 3.
Correct Answer:
A
— 6
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Q. If a number is a factor of 24 and a multiple of 3, which of the following is the smallest such number?
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Solution
The smallest number that is both a factor of 24 and a multiple of 3 is 3.
Correct Answer:
A
— 3
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Q. If a number is a factor of 36 and a multiple of 4, which of the following numbers could it be?
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Solution
12 is a factor of 36 and also a multiple of 4, as 12 = 4 * 3.
Correct Answer:
B
— 12
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Q. If a number is a factor of 36, which of the following numbers is NOT a factor?
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Solution
All options are factors of 36 except for 9, which is a factor but not a multiple of 4.
Correct Answer:
D
— 9
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Q. If a number is a multiple of 15, which of the following cannot be true?
A.
It is a multiple of 3.
B.
It is a multiple of 5.
C.
It is an even number.
D.
It is a multiple of 30.
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Solution
A multiple of 15 is not guaranteed to be even, as 15 itself is odd.
Correct Answer:
C
— It is an even number.
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Q. If a number is a multiple of 15, which of the following must also be true?
A.
It is a multiple of 3.
B.
It is a multiple of 5.
C.
It is a multiple of 10.
D.
Both 1 and 2.
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Solution
Since 15 = 3 × 5, any multiple of 15 must also be a multiple of both 3 and 5.
Correct Answer:
D
— Both 1 and 2.
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Q. If a number is a multiple of 7 and 9, which of the following numbers could it be? (2023)
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Solution
63 is a multiple of both 7 and 9 (7*9=63), while the others are not.
Correct Answer:
A
— 63
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Q. If a number is a multiple of 8 and 12, which of the following is the smallest such number? (2023)
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Solution
The least common multiple of 8 and 12 is 24, making it the smallest number that is a multiple of both.
Correct Answer:
A
— 24
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Q. If a number is a multiple of 8, which of the following must also be true?
A.
It is a multiple of 4.
B.
It is a multiple of 2.
C.
It is an even number.
D.
All of the above.
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Solution
All statements are true as multiples of 8 are also multiples of 4, 2, and are even.
Correct Answer:
D
— All of the above.
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Q. If a number is a multiple of 9, which of the following must also be true?
A.
It is a multiple of 3.
B.
It is a multiple of 27.
C.
It is a prime number.
D.
It is an even number.
Show solution
Solution
All multiples of 9 are also multiples of 3.
Correct Answer:
A
— It is a multiple of 3.
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Q. If a number is a multiple of both 3 and 4, which of the following is guaranteed to be true?
A.
It is a multiple of 7.
B.
It is a multiple of 12.
C.
It is a multiple of 10.
D.
It is a multiple of 9.
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Solution
The least common multiple of 3 and 4 is 12, so any multiple of both must also be a multiple of 12.
Correct Answer:
B
— It is a multiple of 12.
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Q. If a number is a multiple of both 4 and 6, which of the following must also be true?
A.
It is a multiple of 12.
B.
It is a multiple of 24.
C.
It is a multiple of 10.
D.
It is a multiple of 8.
Show solution
Solution
The least common multiple of 4 and 6 is 12, so any number that is a multiple of both must also be a multiple of 12.
Correct Answer:
A
— It is a multiple of 12.
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Q. If a number is a multiple of both 4 and 6, which of the following must it also be a multiple of?
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Solution
The least common multiple of 4 and 6 is 12, so any multiple of both must also be a multiple of 12.
Correct Answer:
A
— 12
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Q. If a number is a multiple of both 5 and 7, which of the following is a possible value for this number?
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Solution
35 is a multiple of both 5 and 7 (5*7=35).
Correct Answer:
A
— 35
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Q. If a number is a multiple of both 5 and 7, which of the following is true?
A.
It is a multiple of 35.
B.
It is a multiple of 12.
C.
It is a multiple of 10.
D.
It is a multiple of 14.
Show solution
Solution
The least common multiple of 5 and 7 is 35, so any number that is a multiple of both must also be a multiple of 35.
Correct Answer:
A
— It is a multiple of 35.
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Q. If a number is a multiple of both 7 and 9, which of the following numbers is a possible candidate?
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Solution
63 is a multiple of both 7 (7x9) and 9 (9x7).
Correct Answer:
A
— 63
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Q. If a number is a multiple of both 8 and 14, which of the following numbers is guaranteed to be a factor of that number? (2023)
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Solution
Since any multiple of 8 and 14 must also be a multiple of their GCD, which includes 2 as a factor.
Correct Answer:
D
— 2
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Q. If a number is both a factor and a multiple of 6, which of the following could it be?
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Solution
The number 6 is a factor of itself and also a multiple of 6, making it the only valid option.
Correct Answer:
A
— 6
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Q. If a number is both a factor of 24 and a multiple of 3, which of the following could it be?
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Solution
12 is a factor of 24 and also a multiple of 3, as 12 = 3 * 4.
Correct Answer:
D
— 12
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Q. If a number is both a factor of 36 and a multiple of 4, which of the following could be that number?
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Solution
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Among these, 12 is a multiple of 4.
Correct Answer:
B
— 12
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Q. If a number is both a factor of 36 and a multiple of 6, which of the following is the largest such number?
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Solution
The factors of 36 that are also multiples of 6 are 6, 12, and 18. Among these, 18 is the largest.
Correct Answer:
C
— 18
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Q. If a number is both a multiple of 4 and a factor of 48, which of the following numbers could it be?
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Solution
The multiples of 4 that are also factors of 48 are 4, 8, 12, and 16. Among the options, 8 is valid.
Correct Answer:
A
— 8
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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.
Show solution
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
Show solution
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
Show solution
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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