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# a is directly proportional to b. If a = 8 when b = 2, what

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a is directly proportional to b. If a = 8 when b = 2, what [#permalink]  17 Jul 2018, 12:01
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Question Stats:

90% (00:34) correct 9% (00:40) wrong based on 11 sessions
a is directly proportional to b. If a = 8 when b = 2, what is a when b = 4?

(A) 10
(B) 16
(C) 32
(D) 64
(E) 128
[Reveal] Spoiler: OA

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Re: a is directly proportional to b. If a = 8 when b = 2, what [#permalink]  17 Jul 2018, 12:51
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The question can be restated as ax=b, so subbing in a=8 and b=2, we solve 8x=2 for x, giving us x=1/4. We then solve for the new a value given by a*0.25=4 from which we get a=16.
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Re: a is directly proportional to b. If a = 8 when b = 2, what [#permalink]  17 Jul 2018, 14:19
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sandy wrote:
a is directly proportional to b. If a = 8 when b = 2, what is a when b = 4?

(A) 10
(B) 16
(C) 32
(D) 64
(E) 128

when b is 2, a is 8

when b is (2*2) =4, a is (8*2) = 16.

GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: a is directly proportional to b. If a = 8 when b = 2, what [#permalink]  28 Jul 2018, 16:18
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Explanation

To answer this question, it is important to understand what is meant by the phrase “directly proportional.”

It means that $$a = kb$$, where k is a constant.

In alternative form: = k, where k is a constant.

So, because they both equal the constant, $$\frac{a_{old}}{b_{old}}=\frac{a_{new}}{b_{new}}$$. Plugging in values: $$\frac{8}{2}=\frac{a_{new}}{4}$$.
Crossmultiply and solve:
$$32 = 2a_{new}$$
$$a_{new} = 16$$
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Re: a is directly proportional to b. If a = 8 when b = 2, what   [#permalink] 28 Jul 2018, 16:18
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