If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? : Problem Solving (PS)

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If a - b > ((b+c-a)^2)^(1/2) which of the following must be true?

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If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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Updated on: 17 Jul 2018, 19:46

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Question Stats:

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51% (02:07) wrong

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If $a-b > \sqrt{(b+c-a)^2}$ which of the following must be true?

A. a>0

B. a<b

C. b=0

D. c>0

E. c<0

Spoiler: OA

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Originally posted by GMATBusters on 17 Jul 2018, 08:33.
Last edited by Bunuel on 17 Jul 2018, 19:46, edited 1 time in total.

Renamed the topic and edited the question.

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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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17 Jul 2018, 08:43

I was testing different numbers and came to the conclusion that B always has to be true.

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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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17 Jul 2018, 11:09

D.

a-b > sq. root[(b+c-a)^2 ]

sq. root[(b+c-a)^2 ] = sq. root[(-(b+c-a))^2 ] =sq. root[(a-b-c)^2 ]
Since, a-b > sq. root[(a-b-c)^2 ]

a-b-c should be less than a-b
So c must be positive.

Don't know whether it is right.

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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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17 Jul 2018, 11:15

Gemelo90 wrote:

I was testing different numbers and came to the conclusion that B always has to be true.

a-b is always greater than 0. Since it involves a square root of a square which is always a positive or a zero.
So a-b > 0
a>b.

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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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19 Jul 2018, 05:40

gmatbusters wrote:

If $a-b > \sqrt{(b+c-a)^2}$ which of the following must be true?

A. a>0

B. a<b

C. b=0

D. c>0

E. c<0

Given : $a-b > \sqrt{(b+c-a)^2}$

We know that $\sqrt{(x)^2}$ = $|x|$

So, $a - b > |b+c-a|$

Therefore we have 2 cases :

Case 1 :

$a - b > b + c - a$

$2a - 2b > c$

$a - b > \frac{c}{2}$ (No match)

Case 2:

$a - b > -(b + c - a)$

$a - b > - b - c + a$

$a - a - b + b > - c$

$0 > - c$

$c > 0$

(D)
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If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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19 Jul 2018, 06:04

Another Approach:

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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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23 Jul 2018, 02:37

Another approach:
(a-b) > 0 because square root is always non negative.
therefore, (b-a) < 0
hence c must be >0, so that (b+c-a) is non negative.
(If (b+c-a) is negative, square root is not defined)

Hence, c > 0
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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink]

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Re: If a - b > ((b+c-a)^2)^(1/2) which of the following must be true? [#permalink] 28 Nov 2019, 08:50

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