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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  [#permalink]

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01 May 2017, 04:59
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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.

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Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

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01 May 2017, 05:38
2
ziyuen wrote:
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.

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.

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Posts: 3358
Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

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01 May 2017, 06:12
Top Contributor
1
ziyuen wrote:
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.

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

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Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

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19 Jul 2017, 20:16
hazelnut wrote:
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.

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

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Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

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02 Apr 2018, 09:35
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.

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Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl  [#permalink]

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02 Apr 2018, 11:56
hazelnut wrote:
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.

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

Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl &nbs [#permalink] 02 Apr 2018, 11:56
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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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