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What is a% of b?

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What is a% of b?  [#permalink]

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New post 07 Oct 2019, 19:59
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A
B
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EMPOWERgmat DS Series:
Pack 2, Question 5

What is a% of b?

(1) 200% of a% of b = 360
(2) b% of a = 180



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Re: What is a% of b?  [#permalink]

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New post 07 Oct 2019, 20:30
1
a% of b = a/100*b or, ab /100. So, basically the question is asking whether we can derive the value of ab/100 from the given information.

Statement 1 :

200% of a% of b = 360
or, 2a% of b =360
or, 2a/100* b = 360
or, 2ab/100 =360
So, ab/100 = 180. SUFFICIENT

Statement 2 :

b% of a = 180
or, b/100* a = 180
So, ab/100 = 180. SUFFICIENT

Answer: D
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New post 07 Oct 2019, 20:35
1
1) 200% of a% of b=360

i.e 2a% X b =360
2ab/100=360
ab/100=180
suff

2) b% of a = 180

as we know a% of b = b% of A
sufficient


IMO D

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What is a% of b?  [#permalink]

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New post Updated on: 10 Oct 2019, 22:53
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a% of b = \(\frac{ab}{100}\)

Statement 1) 200% of a% of b =360
\(\frac{200}{100}\) * \(\frac{ab}{100}\) =360
\(\frac{ab}{100}\)= 180 SUFFICIENT. Cross off B,C and E

Statement 2 b% of a =180
\(\frac{ab}{100}\)=180 SUFFICIENT. Cross off A.

Hence D is correct

Originally posted by saukrit on 09 Oct 2019, 09:58.
Last edited by saukrit on 10 Oct 2019, 22:53, edited 1 time in total.
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Re: What is a% of b?  [#permalink]

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New post 10 Oct 2019, 21:57
OFFICIAL EXPLANATION

Hi All,

We're asked what is A% of B. This question can be solved with Arithmetic or by TESTing VALUES.

(1) 200% of A% of B = 360

IF....
A = 100, then 200% of 100% of B = 360.... Since 100% of B would be "all" of B, taking 200% of that number would mean DOUBLING the value of B and getting 360. This means that B would equal 180. The answer to the question is... 100% of 180 = 180

A = 10, then 200% of 10% of B = 360. From our prior example, we know that taking 200% of a number means DOUBLING the number. Here, we would have 20% of B equaling 360...
(.2)(B) = 360
B = 1800.... The answer to the question is... 10% of 1800 = 180

No matter what values you TEST, the answer to the question will ALWAYS equal 180.
Fact 1 is SUFFICIENT

(2) B% of A = 180

IF....
B = 100, A = 180... The answer to the question is 180% of 100 = (1.8)(100) = 180
B = 50, A = 360... The answer to the question is 360% of 50 = (3.6)(50) = 180

No matter what values you TEST, the answer to the question will ALWAYS equal 180.
Fact 2 is SUFFICIENT

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Re: What is a% of b?   [#permalink] 10 Oct 2019, 21:57
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