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# If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ?

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Joined: 02 Sep 2009
Posts: 43851
If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ? [#permalink]

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18 Jun 2015, 01:53
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If $$K = \frac{\frac{1}{3a} + \frac{1}{b}}{\frac{5}{ab}}$$ and ab ≠ 0, what is the value of K ?

(1) a = 3
(2) b – 3(5 – a ) = 0

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ? [#permalink]

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18 Jun 2015, 02:08
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Simplified we do have 3a+b/15 so we need these values

A) insufficient we have only the value of a but not b

B) sufficient. we do have directly the value of 3a= -b + 15. The we do have 15/15=1

B wins
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Posts: 43851
Re: If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ? [#permalink]

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22 Jun 2015, 04:18
Bunuel wrote:
If $$K = \frac{\frac{1}{3a} + \frac{1}{b}}{\frac{5}{ab}}$$ and ab ≠ 0, what is the value of K ?

(1) a = 3
(2) b – 3(5 – a ) = 0

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

It should be evident that the two statements combined are sufficient to answer the question—you can plug the value of a from Statement (1) into Statement (2) to solve for the value of b, then you can plug those values into the question to solve for K.

Immediately be skeptical. C should seem too easy. After all, you didn't do anything to the question stem. So you should do some work to determine whether one of the two statements alone (or, in some cases, each statement alone) is sufficient to answer the question.

Let's start by rephrasing the question:

$$K = \frac{\frac{1}{3a} + \frac{1}{b}}{\frac{5}{ab}}=\frac{\frac{b}{3ab} + \frac{3a}{3ab}}{\frac{5}{ab}}=\frac{b+3a}{3ab}*\frac{ab}{5}=\frac{b+3a}{15}$$

“What is the value of K?” rephrases to “What is the value of b + 3a?” Statement (2) rephrases and gives us the answer:
b – 3(5 – a) =
b – 15 + 3a = 0
b + 3a = 15

This is not a tactic to use at lower levels of the test. On 500-600 level problems, the two statements may work together in straightforward ways to produce sufficiency. The C trap may be the C answer!
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Re: If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ? [#permalink]

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22 Jun 2017, 03:17
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Re: If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ? [#permalink]

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10 Sep 2017, 12:31
Bunuel wrote:
If $$K = \frac{\frac{1}{3a} + \frac{1}{b}}{\frac{5}{ab}}$$ and ab ≠ 0, what is the value of K ?

(1) a = 3
(2) b – 3(5 – a ) = 0

Kudos for a correct solution.

Always try to rewrite the original equation in ds suff to find the true question

St 1

Still cannot solve for b +3a

St 2

Distribute (though this was a foiling question at first).

b- 15+3a= -
b+3a= 15

suff

B
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Re: If K = (1/(3a) + 1/b)/(5/(ab)) and ab ≠ 0, what is the value of K ?   [#permalink] 10 Sep 2017, 12:31
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