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Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl
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01 May 2017, 07:12

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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

Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl
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19 Jul 2017, 21:16

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

Re: If a, b, and c are positive integers and a/6+b/5 =c/30, is c divisibl
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02 Apr 2018, 10:35

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.