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# If p > 0 and a is 2p percent of b, then, in terms of p, b is what perc

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Math Expert
Joined: 02 Sep 2009
Posts: 48117
If p > 0 and a is 2p percent of b, then, in terms of p, b is what perc  [#permalink]

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13 Dec 2017, 00:57
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Difficulty:

45% (medium)

Question Stats:

59% (01:22) correct 41% (01:40) wrong based on 36 sessions

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If p > 0 and a is 2p percent of b, then, in terms of p, b is what percent of a ?

A. 50p
B. 1/(500p)
C. 5/p
D. 50/p
E. 5000/p

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Senior Manager
Joined: 15 Jan 2017
Posts: 367
Re: If p > 0 and a is 2p percent of b, then, in terms of p, b is what perc  [#permalink]

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13 Dec 2017, 02:08
a/ 2 is 1/4 b
a is 1/2 b

hence b is 2a. Option A fits best.

Looking for more detailed options on OA
Math Expert
Joined: 02 Aug 2009
Posts: 6564
If p > 0 and a is 2p percent of b, then, in terms of p, b is what perc  [#permalink]

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13 Dec 2017, 04:26
Bunuel wrote:
If p > 0 and a is 2p percent of b, then, in terms of p, b is what percent of a ?

A. 50p
B. 1/(500p)
C. 5/p
D. 50/p
E. 5000/p

Solve the Q for answer or substitute..
Solution..
$$a=\frac{2p}{100}*b.........b=\frac{50a}{p}$$
Now, in terms of % of a...$$b=\frac{50a}{ap}*100=5000/p$$

Substitute..
Take a as 50 and b as 100, so 2p=50% or p=25
So b in % of a = 100*100/50=200%
Substitute in Choices
Only E gives 200%
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 02 Mar 2017
Posts: 9
If p > 0 and a is 2p percent of b, then, in terms of p, b is what perc  [#permalink]

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13 Dec 2017, 04:47
a= 2p% of b --> 2pb/100
Now b is what percentage of a
2pb/100 -->100%
then b --> (100*b) / (2pb/100)

After cancelling b and dividing 100 by 2 -- > (50*100)/p ==> 5000/p

Ans: E
If p > 0 and a is 2p percent of b, then, in terms of p, b is what perc &nbs [#permalink] 13 Dec 2017, 04:47
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