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# If a, b, and c are positive, is a > b?

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If a, b, and c are positive, is a > b?  [#permalink]

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20 Oct 2018, 14:13
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Difficulty:

85% (hard)

Question Stats:

47% (01:10) correct 53% (01:22) wrong based on 109 sessions

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If a, b, and c are positive, is a > b?

(1) $$\frac{a}{(b+c)}>\frac{b}{(a+c)}$$

(2) $$b+c < a$$

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Re: If a, b, and c are positive, is a > b?  [#permalink]

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20 Oct 2018, 18:31
1
If a, b, and c are positive, is a>b?

(1) $$\frac{a}{(b+c)}>\frac{b}{(a+c)}$$
Since you have one term in numerator and the other two terms in denominator, add 1 to both sides to get all three on top...
$$\frac{a}{(b+c)}+1>\frac{b}{(a+c)}+1$$...
$$\frac{a+b+c}{(b+c)}>\frac{b+a+c}{(a+c)}$$
Now numerators are equal, so LHS >RHS when the denominator is lesser..
So b+c<a+c......or b<a
Sufficient

(2) $$b+c < a$$
All three a,b and c are positive, and a is GREATER than sum of other two , a has to be the largest..
So a>b
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If a, b, and c are positive, is a > b?  [#permalink]

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20 Oct 2018, 20:58
dimmak wrote:
If a, b, and c are positive, is a>b?

(1) $$\frac{a}{(b+c)}>\frac{b}{(a+c)}$$
(2) $$b+c < a$$

Statement 1: $$\frac{a}{(b+c)}>\frac{b}{(a+c)}$$

Cross multiplying
$$a*(a+c) > b*(b+c)$$
i.e. $$a^2 + ac > b^2 + bc$$

Since a, b and c are positive so if a^2 > b^2 then ac will also be greater than bc and vice-versa
i.e. for the condition to be true

a > b

SUFFICIENT

Statement 2: $$b+c < a$$

i.e. since b + another positive number is less than a then b is definitely less than a hence

SUFFICIENT

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Re: If a, b, and c are positive, is a > b?  [#permalink]

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20 Oct 2018, 22:09
If a, b, and c are positive, is a>b?

(1) a(b+c)>b(a+c)a(b+c)>b(a+c)
(2) b+c<a

From statement 1:
a^2+ac>b^2+bc
a(a+c)>b(b+c)
a/b>{(b+c)/(a+c)}---(1)

Since given that all are + ve and from (1) it can be deduced that a>b , hence true..

For statement 2

given a>b+c

since all are + ve numbers so from the given the expression it can be concluded that a>b ...

Hence D is right option..
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Re: If a, b, and c are positive, is a > b?  [#permalink]

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08 Nov 2018, 06:35
chetan2u Is there any other way to solve Statement 2?

Can plugging in numbers help in solving such questions?
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Re: If a, b, and c are positive, is a > b?  [#permalink]

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08 Nov 2018, 17:49
topper97 wrote:
chetan2u Is there any other way to solve Statement 2?

Can plugging in numbers help in solving such questions?

You can plug any numbers you will get your number ...
But statement II is a very straight forward choice to infer a>b..

Since all three are positive and a is GREATER than SUM of other two , a has to be greater than each one of them too...
If B is 4 and c is 7, a>4+7 or a>11, so a>4 hence a>b
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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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Re: If a, b, and c are positive, is a > b?  [#permalink]

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08 Nov 2018, 23:39
dimmak wrote:
If a, b, and c are positive, is a > b?

(1) $$\frac{a}{(b+c)}>\frac{b}{(a+c)}$$

(2) $$b+c < a$$

Knowing they’re all positive we can cross multiply the first statement.

It becomes a (a+c) > b (b+c)

Given that we are adding the same constant c to both sides. We know a is larger than b

The second statement 2)

a > b + c

If a is larger than the sum of both and the numbers are positive then a > b

Sufficient

D

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Re: If a, b, and c are positive, is a > b? &nbs [#permalink] 08 Nov 2018, 23:39
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