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# What is the value of k?

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Math Expert
Joined: 02 Sep 2009
Posts: 54376
What is the value of k?  [#permalink]

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05 Jul 2017, 00:32
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Difficulty:

45% (medium)

Question Stats:

67% (01:20) correct 33% (01:58) wrong based on 38 sessions

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What is the value of k?

(1) $$\frac{a}{4} = \frac{2b}{5} = \frac{(3a − 4b)}{k}$$

(2) $$a + b = 2k$$

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Re: What is the value of k?  [#permalink]

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05 Jul 2017, 00:37
Bunuel wrote:
What is the value of k?

(1) $$\frac{a}{4} = \frac{2b}{5} = \frac{(3a − 4b)}{k}$$

(2) $$a + b = 2k$$

(1) gives us
$$a/4 = (3a-4b)/k$$
$$k= 12-16(b/a)$$

$$b/a = 5/8$$

Hence (1) Sufficient

(2) gives us
$$a+b=2k$$
$$k= (a+b)/2$$

Not sufficient

Hence A
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What is the value of k?  [#permalink]

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05 Jul 2017, 06:41
1
Bunuel wrote:
What is the value of k?

(1) $$\frac{a}{4} = \frac{2b}{5} = \frac{(3a − 4b)}{k}$$

(2) $$a + b = 2k$$

(1) $$\frac{a}{4} = \frac{2b}{5} = \frac{(3a − 4b)}{k}$$

$$\frac{a}{4} = \frac{(3a − 4b)}{k}$$

$$k = \frac{(3a − 4b) * 4}{a}$$ $$=> k = \frac{12a - 16b}{a}$$

$$k = \frac{12a}{a} - \frac{16b}{a}$$

$$k = 12 - \frac{16b}{a}$$ ------- (i)

$$\frac{a}{4} = \frac{2b}{5}$$

$$\frac{b}{a}= \frac{5}{8}$$ --------- (ii)

Substituting (i) in (ii), we get;

$$k = 12 - 16(\frac{5}{8}) = > 12 - 10 => 2$$

Hence I is Sufficient.

(2) $$a + b = 2k$$

$$k = \frac{(a + b)}{2}$$

We do not have value of $$a$$ or $$b$$ or $$(a+b)$$. Hence II is Not Sufficient.

What is the value of k?   [#permalink] 05 Jul 2017, 06:41
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