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# For all numbers x, the function h is defined by h(x) = 2x − 1, and the

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
For all numbers x, the function h is defined by h(x) = 2x − 1, and the  [#permalink]

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24 Oct 2018, 04:07
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Question Stats:

86% (01:27) correct 14% (01:23) wrong based on 43 sessions

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For all numbers x, the function h is defined by h(x) = 2x − 1, and the function g is defined by g(x) = (2x − 3)/5. If k is a positive number, what is the value of g(k)?

(1) h(k) = 7

(2) h(1) = k/4

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Re: For all numbers x, the function h is defined by h(x) = 2x − 1, and the  [#permalink]

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24 Oct 2018, 04:43
Bunuel wrote:
For all numbers x, the function h is defined by h(x) = 2x − 1, and the function g is defined by g(x) = (2x − 3)/5. If k is a positive number, what is the value of g(k)?

(1) h(k) = 7

(2) h(1) = k/4

Statement 1) tells us the h(k) = 7 from this we can find the value of k and can then substitute it in g(k) to find the value of g(k) so it is sufficient.

For the sake of showing how we get the value h(k) = 7 so this means $$2k - 1 = 7$$ so $$2k = 8$$ and k = 4

substitute k = 4 into g(4) = $$\frac{(2*4 - 3)}{5} = \frac{(8-3)}{5} = \frac{5}{5} = 1$$

Statement 2)

$$2-1 = \frac{k}{4}$$ so k = 4 now substitute in g(4) we get the answer.

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Re: For all numbers x, the function h is defined by h(x) = 2x − 1, and the  [#permalink]

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24 Oct 2018, 07:28
Question asks us to find g(k) = (2*k-3)/5. Hence, a statement is sufficient if you can find the value of k.

Stmt 1: h(k) = 2*k - 1 = 7 => k can be found, Hence sufficient, Eliminate B, C, E

Stmt 2: h(1) = 2*1 - 1 = k/4 => k can be found, Hence sufficient.

No Need to solve, since it a DS question. Answer is Option D.
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Re: For all numbers x, the function h is defined by h(x) = 2x − 1, and the   [#permalink] 24 Oct 2018, 07:28
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