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If a is a multiple of 3 and b is a multiple of 4,

which of the following must be a multiple of 12 ?
A (ab) only
B (3a + 4b) only
C(4a + 3b) only
D (ab) and (3a + 4b)
E (ab) and (4a + 3b)

User Cald
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1 Answer

5 votes

Final answer:

To find the expression that is a multiple of 12, we need to analyze the given options. Option A (ab) is the only expression that is guaranteed to be a multiple of 12.

Step-by-step explanation:

To determine which expression is a multiple of 12, we need to look for the expression that can be divided evenly by 12. Let's analyze the given options:

A) (ab) only: Since both a and b are multiples of 3 and 4 respectively, their product ab will also be divisible by 12, making this option a multiple of 12.

B) (3a + 4b) only: This expression can be simplified to 3a + 4b, which is not necessarily divisible by 12. Therefore, this option is not a multiple of 12.

C) (4a + 3b) only: Similar to option B, this expression can be simplified to 4a + 3b, which is not necessarily divisible by 12. So, this option is not a multiple of 12.

D) (ab) and (3a + 4b): We already established that (ab) is a multiple of 12. However, (3a + 4b) may or may not be divisible by 12. Therefore, this option is not guaranteed to be a multiple of 12.

E) (ab) and (4a + 3b): Similar to option D, (ab) is a multiple of 12. And (4a + 3b) may or may not be divisible by 12. So, this option is also not guaranteed to be a multiple of 12.

Based on our analysis, only option A (ab) is guaranteed to be a multiple of 12.

User Dogweather
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