If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl

We don't really mind the equation here we just have to focus on

5a + 6b =30

Basically- the only thing you need to know in this question is whether 6 is a multiple of 5- if 6 is a multiple of 5 then C must be divisible by five because the sum of the two numbers that share a common multiple will always be divisible by that common multiple

Statement 1 is all you need

A

Hi All,

This DS question can be solved in a number of different ways. It's perfect for TESTing Values, but there's also a Number Property built into it that you might find useful. To start, "rewriting" the given equation is a must:

5A + 6B = C

We're also told that A, B and C are positive integers. We're asked if C is a multiple of 5? This is a YES/NO question.

1) B is a MULTIPLE of 5.

You can absolutely TEST Values here, but here's the Number Property worth knowing…

Since A is an integer, 5A is a MULTIPLE of 5
We're told that B is a multiple of 5, so 6B is also MULTIPLE of 5

If you add a multiple of 5 to another multiple of 5, then you will end up with a MULTIPLE of 5.
So, C will ALWAYS be a multiple of 5
Fact 1 is SUFFICIENT

2) A is even

5A will be multiple of 5, since 5(even) is a multiple of 5
However, 6B may or may not be a multiple of 5, depending on what B is.
For example, if B=1, then 6B = 6; if B = 5, then 6B = 30

There's no way to know if we'll end up with a sum that is a multiple of 5 or not.
Fact 2 is INSUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Analyzing the question stem:

\(\frac{a}{6} + \frac{b}{5} = \frac{c}{30}\)........Multiply by 30

\(5a + 6b = c\)

C is multiple of 5, if both terms are multiple of 5....... We see that (5a) is multiple of 5, so (6b) must be multiple of b to make c divisible by 5

The question could rephrased:

Is B multiple of 5??

(1) b is divisible by 5.

This directly answers the question.

Sufficient

(2) a is even.

It does not affect b so it does not help answer the question

Insufficient

Answer: A

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