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

Question

If a, b, and c are positive integers and  \frac{a}{6} + \frac{b}{5} = \frac{c}{30} , is c divisible by 5?

(1) b is divisible by 5.
(2) a is even.

vitaliyGMAT · Answer

Hi

Multiplying both sides by 30:

5a + 6b = c

(1) b is divisible by 5.

b=5x

5a + 6*5x = c

5(a + 6x) = c ----> c is a multiple of 5. Sufficient.

(2) a is even

a = 2y

10y + 6b = c

c is even, but depending on y and b it may o may not be multiple of 5. Insufficient.

Answer A.

BrentGMATPrepNow · Answer

Target question :    Is c divisible by 5?

Given : a/6 + b/5 = c/30  
First let's eliminate the fractions by multiplying both sides of the equation be the least common multiple of 6, 5 and 30. 
So, we'll multiply both sides by 30 to get:   5a + 6b = c

Statement 1 : b is divisible by 5  
We can apply a useful divisibility rule that says:   "If j is divisible by x and k is divisible by x, then (j+k) is divisible by x"  
We can ready see that  5a  is divisible by 5. 
And, if b is divisible by 5, then we know that  6b  is divisible by 5. 
So, by the above   rule  , we know that   5a + 6b   is divisible by 5. 
Since   5a + 6b = c  , we can conclude that   c IS divisible by 5  
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : a is even 
There are several cases that satisfy statement 2. Here are two: 
Case a: a = 2 and b = 5. we know that c = 5a + 6b. So, c = 5(2) + 6(5) = 40, which is divisible by 5. In this case,  c IS divisible by 5 
Case b: a = 2 and b = 1. we know that c = 5a + 6b. So, c = 5(2) + 6(1) = 16, which is NOT divisible by 5. In this case,  c is NOT divisible by 5 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer:  A

Nunuboy1994 · Answer

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

EMPOWERgmatRichC · Answer

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:  A

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

Mo2men · Answer

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

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

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