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# Percentage of a Number compared with Fraction of a Number

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Manager
Joined: 13 Aug 2016
Posts: 77
GRE 1: Q158 V154
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Kudos [?]: 41 [1] , given: 21

Percentage of a Number compared with Fraction of a Number [#permalink]  09 Oct 2016, 05:33
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Question Stats:

50% (00:34) correct 49% (00:27) wrong based on 83 sessions
 Quantity A Quantity B 30 percent of x (4/13) of x

A : Quantity A is greater
B : Quantity B is greater
C : Both quantities are equal
D : Answer Cannot be determined
[Reveal] Spoiler: OA
Retired Moderator
Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2776 [2] , given: 394

Re: Percentage of a Number compared with Fraction of a Number [#permalink]  09 Oct 2016, 05:45
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Expert's post
yasir9909 wrote:
 Quantity A Quantity B 30 percent of x (4/13) of x

A : Quantity A is greater
B : Quantity B is greater
C : Both quantities are equal
D : Answer Cannot be determined

Now rewriting 30 percent of x as $$\frac{30}{100}x$$=$$\frac{3}{10}x$$=$$0.3x$$.

Re writing Quantity B can be rewritten as $$0.3076x$$.

Now x is a positive number say 5. Then Quantity B is greater than Quantity A.

If x = 0. Then Quantity A is equal to Quantity B.

If x is a negative number say -5. Then Quantity A is greater than Quantity B.

Hence Option D is the correct.
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Manager
Joined: 13 Aug 2016
Posts: 77
GRE 1: Q158 V154
Followers: 0

Kudos [?]: 41 [0], given: 21

Re: Percentage of a Number compared with Fraction of a Number [#permalink]  09 Oct 2016, 06:37
Since no information has been given about x so it could be integer,decimal,rational,irrational number or even 0.So we have three cases to test values of Quantity A & B

Case 1: if x>0 => let x = 2
 Quantity A Quantity B 0.3*2=0.6 0.3077*2~0.6164

=> Quantity A < Quantity B

Case 2: if x=0 => let x = 2
 Quantity A Quantity B 0.3*0=0.6 0.3077*0=0

=> Quantity A = Quantity B

Case 3: if x<0 => let x = -2
 Quantity A Quantity B -0.3*2=-0.6 -0.3077*2~-0.6164

=> Quantity A > Quantity B

Therefore answer is D and answer cannot be determined from given information
GRE Instructor
Joined: 10 Apr 2015
Posts: 3535
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Kudos [?]: 4020 [3] , given: 65

Re: Percentage of a Number compared with Fraction of a Number [#permalink]  12 Nov 2016, 08:03
3
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Expert's post
yasir9909 wrote:
 Quantity A Quantity B 30 percent of x (4/13) of x

Whenever I have the option of plugging in values, I first look for equality
That is, I look for a value that will make the two quantities equal.
Right away, I see that if x = 0, then Quantities A and B are equal.
So, EITHER the two quantities are always equal (which means the answer is A) OR the two quantities are not always equal (which means the answer is D)
So, in a matter of seconds, I know the correct answer is A or D

Now plug in a different value for x. How about x = 1
We get...
Quantity A: 30 percent of 1 = 3/10 of 1 = 3/10
Quantity B: (4/13) of 1 = 4/13
These two values are clearly NOT equal.

So, the answer must be D

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GRE Instructor
Joined: 10 Apr 2015
Posts: 3535
Followers: 134

Kudos [?]: 4020 [2] , given: 65

Re: Percentage of a Number compared with Fraction of a Number [#permalink]  12 Nov 2016, 08:09
2
KUDOS
Expert's post
yasir9909 wrote:
 Quantity A Quantity B 30 percent of x (4/13) of x

Another approach is matching operations

Given:
Quantity A: 30 percent of x
Quantity B: 4/13 of x

Rewrite Quantity A as follows....
Quantity A: 3/10 of x
Quantity B: 4/13 of x

This is the same as ....
Quantity A: (3/10)x
Quantity B: (4/13)x

Rewrite fractions with common denominators
Quantity A: (39/130)x
Quantity B: (40/130)x

Subtract (39/130)x from both quantities
Quantity A: 0
Quantity B: (1/130)x

Divide both quantities by 1/130
Quantity A: 0
Quantity B: x

Since we're told nothing about x, we can see that Quantity B can be less than, equal to, or greater than Quantity A
[Reveal] Spoiler:
D

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Re: Percentage of a Number compared with Fraction of a Number   [#permalink] 12 Nov 2016, 08:09
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# Percentage of a Number compared with Fraction of a Number

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