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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, 20:46
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Difficulty:

75% (hard)

Question Stats:

43% (01:59) correct 57% (01:41) wrong based on 61 sessions

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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

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Originally posted by gmatbusters on 17 Jul 2018, 09:33.
Last edited by Bunuel on 17 Jul 2018, 20:46, 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, 09:43
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, 12:09
1
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, 12:15
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, 06:40
1
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, 07:04
3
Another Approach:
Attachments

IMG-20180722-WA0000_1532201863144.jpg [ 62.51 KiB | Viewed 303 times ]

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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, 03:37
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? &nbs [#permalink] 23 Jul 2018, 03:37
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