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.
Show solution
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 the GCD of two numbers is 1, what can be inferred about the two numbers? (2023)
A.
They are both even.
B.
They are both odd.
C.
They are coprime.
D.
They are multiples of each other.
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Solution
If the GCD of two numbers is 1, it means they have no common factors other than 1, thus they are coprime.
Correct Answer:
C
— They are coprime.
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Q. If the GCD of two numbers is 1, which of the following statements is true?
A.
The numbers are multiples of each other
B.
The numbers are co-prime
C.
The numbers are both even
D.
The numbers are both odd
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Solution
If the GCD of two numbers is 1, it means they have no common factors other than 1, hence they are co-prime.
Correct Answer:
B
— The numbers are co-prime
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Q. If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
A.
It is 216.
B.
It is 72.
C.
It is 36.
D.
It is 6.
Show solution
Solution
The product of two numbers is equal to the product of their LCM and GCD: 36 * 6 = 216.
Correct Answer:
A
— It is 216.
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Q. If the least common multiple (LCM) of two numbers is 60 and one of the numbers is 15, what could be the other number?
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Solution
The LCM of 15 and 20 is 60, making 20 a valid option. 30 and 60 would not work as they would exceed the LCM.
Correct Answer:
B
— 30
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
A.
720
B.
180
C.
120
D.
60
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Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Correct Answer:
A
— 720
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
A.
(5, 12)
B.
(10, 30)
C.
(15, 20)
D.
(5, 15)
Show solution
Solution
The product of the two numbers is equal to the LCM multiplied by the GCD. Thus, 60 * 5 = 300. The pair (15, 20) satisfies this condition since 15 * 20 = 300.
Correct Answer:
C
— (15, 20)
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, what is the product of the two numbers?
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Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 5 = 300.
Correct Answer:
A
— 300
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?
A.
It is 720.
B.
It is 60.
C.
It is 12.
D.
It is 5.
Show solution
Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Correct Answer:
A
— It is 720.
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Q. If the number 36 is expressed in terms of its prime factors, which of the following is correct?
A.
2^2 * 3^2
B.
2^3 * 3^1
C.
3^2 * 4^1
D.
6^2
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Solution
The prime factorization of 36 is 2^2 * 3^2, as 36 = 2 * 2 * 3 * 3.
Correct Answer:
A
— 2^2 * 3^2
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Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?
A.
8 and 9
B.
6 and 7
C.
5 and 6
D.
9 and 10
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Solution
6 and 7 are consecutive integers whose product is 42, not 72.
Correct Answer:
B
— 6 and 7
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Q. If the product of two consecutive integers is 72, which of the following pairs could represent those integers?
A.
8 and 9
B.
6 and 7
C.
5 and 6
D.
4 and 5
Show solution
Solution
The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.
Correct Answer:
B
— 6 and 7
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Q. If the product of two numbers is 144 and one of the numbers is 12, what is the other number? (2023)
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Solution
The other number can be found by dividing the product by the known number: 144 / 12 = 12.
Correct Answer:
D
— 6
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Q. If the product of two numbers is 48 and one of the numbers is 6, what can be inferred about the other number?
A.
It is 8.
B.
It is 12.
C.
It is 6.
D.
It is 4.
Show solution
Solution
If the product is 48 and one number is 6, then the other number must be 48 ÷ 6 = 8.
Correct Answer:
A
— It is 8.
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Q. If the product of two numbers is 48, which of the following pairs could represent these numbers?
A.
(2, 24)
B.
(3, 16)
C.
(4, 12)
D.
(All of the above)
Show solution
Solution
All pairs listed multiply to 48, hence they are valid pairs.
Correct Answer:
D
— (All of the above)
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Q. If the product of two numbers is 72 and one of the numbers is 8, what is the other number?
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Solution
The other number is 72 divided by 8, which equals 9.
Correct Answer:
A
— 6
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Q. If the product of two numbers is a multiple of 15, which of the following must be true?
A.
At least one of the numbers is a multiple of 3.
B.
At least one of the numbers is a multiple of 5.
C.
Both numbers are even.
D.
Both numbers are odd.
Show solution
Solution
For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.
Correct Answer:
B
— At least one of the numbers is a multiple of 5.
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Q. If the sum of the factors of a number is 28, which of the following could be the number?
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Solution
The factors of 12 are 1, 2, 3, 4, 6, and 12. Their sum is 28.
Correct Answer:
A
— 12
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Q. If the sum of two multiples of 7 is 56, which of the following pairs could represent these multiples?
A.
21 and 35
B.
14 and 42
C.
28 and 28
D.
All of the above.
Show solution
Solution
All pairs listed are multiples of 7 that sum to 56.
Correct Answer:
D
— All of the above.
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Q. If the sum of two numbers is 30 and one of the numbers is a multiple of 5, which of the following could be the other number?
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Solution
If one number is 20 (a multiple of 5), the other number would be 10, making it a valid option.
Correct Answer:
C
— 20
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Q. If the sum of two numbers is 30 and one of them is a multiple of 5, which of the following pairs could represent these numbers?
A.
10 and 20
B.
15 and 15
C.
5 and 25
D.
12 and 18
Show solution
Solution
5 and 25 add up to 30, and 5 is a multiple of 5.
Correct Answer:
C
— 5 and 25
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Q. If the sum of two numbers is 30 and one of them is a multiple of 5, which of the following could be the two numbers?
A.
10 and 20
B.
15 and 15
C.
5 and 25
D.
12 and 18
Show solution
Solution
5 and 25 add up to 30, and 25 is a multiple of 5.
Correct Answer:
C
— 5 and 25
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Q. If the sum of two numbers is 30 and one of them is a multiple of 6, which of the following could be the two numbers?
A.
12 and 18
B.
10 and 20
C.
6 and 24
D.
15 and 15
Show solution
Solution
12 is a multiple of 6, and 12 + 18 = 30.
Correct Answer:
A
— 12 and 18
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Q. If the sum of two numbers is a multiple of 10, which of the following can be inferred?
A.
Both numbers are even.
B.
Both numbers are odd.
C.
At least one number is even.
D.
At least one number is odd.
Show solution
Solution
For the sum to be a multiple of 10, at least one of the numbers must be even.
Correct Answer:
C
— At least one number is even.
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Showing 31 to 60 of 122 (5 Pages)
