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

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DS Forum Moderator
Joined: 22 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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23 Jul 2018, 21:24
2
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Difficulty:

35% (medium)

Question Stats:

69% (02:20) correct 31% (02:37) wrong based on 42 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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Re: If a, b, c are positive numbers, is c equal to b percent more than a?  [#permalink]

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23 Jul 2018, 22:34
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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23 Jul 2018, 22:48
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, 22:48
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