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If a, b, c are positive numbers, is c equal to b percent more than a?

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Joined: 21 Aug 2013
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If a, b, c are positive numbers, is c equal to b percent more than a?  [#permalink]

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New post 23 Jul 2018, 20:24
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (02:15) correct 36% (02:34) wrong based on 53 sessions

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If a, b, c are positive numbers, is c equal to b percent more than a?

(1) a is ab/c % less than c.

(2) ab/(c-a) = 100
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Posts: 995
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
Re: If a, b, c are positive numbers, is c equal to b percent more than a?  [#permalink]

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New post 23 Jul 2018, 21:34
1
To find whether c is equal to b percent more than a

=> To find c = \(a * (\frac{b}{100} + 1)\)

=> To find c = \(\frac{ab + 100a}{100}\)

=> To find 100c = ab + 100a

Statement 1

a is \(\frac{ab}{c}\) % less than c

=> a = c * \((1 - \frac{ab}{c} * \frac{1}{100})\)

=>a = \(\frac{100c^2 - abc}{100c}\)

=> 100ac = \(100c^2 - abc\)

=> 100a = 100c - ab

=> 100c = ab + 100a

Statement 1 is sufficient

Statement 2

\(\frac{ab}{c - a}\) = 100

=> 100(c - a) = ab

=> 100c - 100a = ab

=> 100c = ab + 100a

Statement 2 is sufficient

Hence option D
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If a, b, c are positive numbers, is c equal to b percent more than a?  [#permalink]

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New post 23 Jul 2018, 21:48
amanvermagmat wrote:
If a, b, c are positive numbers, is c equal to b percent more than a?

(1) a is ab/c % less than c.

(2) ab/(c-a) = 100



It is all about forming equations and getting them in a form similar to given in the statements..
is c equal to b percent more than a?
means
\(c=\frac{100+b}{100}*a=a+\frac{ab}{100}\)

let us see the statements:-

(1) a is ab/c % less than c.
\(a=(1-\frac{ab}{100c})*c=c-\frac{ab}{100}...........c=a+\frac{b}{100}\)
same as main statement
sufficient

(2) ab/(c-a) = 100
\(\frac{ab}{(c-a)} = 100....................ab=100(c-a)..............c-a=\frac{ab}{100}.............c=a+\frac{ab}{100}\)
sufficient

D
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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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If a, b, c are positive numbers, is c equal to b percent more than a? &nbs [#permalink] 23 Jul 2018, 21:48
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If a, b, c are positive numbers, is c equal to b percent more than a?

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