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# What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15

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Math Expert
Joined: 02 Sep 2009
Posts: 44285
What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink]

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02 Mar 2018, 01:06
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GMAT Club's Fresh Question

What is the value of |a - b| ?

(1) a^2 - b^2 = 9
(1) a^2 + b^2 = 15
[Reveal] Spoiler: OA

_________________
Director
Joined: 28 Mar 2017
Posts: 962
Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink]

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02 Mar 2018, 06:03
Bunuel wrote:

GMAT Club's Fresh Question

What is the value of |a - b| ?

(1) a^2 - b^2 = 9
(1) a^2 + b^2 = 15

Statement 1:
(a+b)(a-b)=9 --Insufficient

Statement 2:
$$a^2$$+$$b^2$$=15 --Insufficient

Statement 1 & 2:
$$a^2$$=12 and $$b^2$$=3 --Still we don't know the sign of a and b. Insufficient

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Intern
Joined: 28 May 2017
Posts: 6
What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink]

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02 Mar 2018, 06:24
Statement 1 : Insufficient as we couldn't find the values & signs of both a & b
Statement 2 : Also, Insufficient as we couldn't find the values & signs of both a & b
St 1 & 2: we will be able to find the values of a^2 & b^2 , thus a & b , but unable to find out the signs, hence insuff.
Ans in E.
Manager
Joined: 11 Feb 2017
Posts: 204
Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink]

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07 Mar 2018, 11:39
gmatexam439 wrote:
Bunuel wrote:

GMAT Club's Fresh Question

What is the value of |a - b| ?

(1) a^2 - b^2 = 9
(1) a^2 + b^2 = 15

Statement 1:
(a+b)(a-b)=9 --Insufficient

Statement 2:
$$a^2$$+$$b^2$$=15 --Insufficient

Statement 1 & 2:
$$a^2$$=12 and $$b^2$$=3 --Still we don't know the sign of a and b. Insufficient

why can't we say that Statement 1 is sufficient?

(a+b) * (a-b) = 9

2 numbers can only be a=5 and b= 4

why can't we consider this?
Intern
Joined: 14 Dec 2016
Posts: 7
Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink]

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07 Mar 2018, 12:06
statement 1:- a^2 -b^2 =9
(a+b) (a-b)=9 => either both the terms (a+b) and (a-b) are positive or both are negative.
so if (a+b) is negative , a=-5 and b=-4 i.e (a+b)= -9 and (a-b)=-1 or a&b both can be positive 5,4.
in either case |a-b|=|5-4| (a&b both positive) or |-5 -(-4)| |a-b|=1 +ve, as it has to be absolute value.

IMO-A
Director
Joined: 28 Mar 2017
Posts: 962
Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink]

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07 Mar 2018, 12:55
rocko911 wrote:
gmatexam439 wrote:
Bunuel wrote:

GMAT Club's Fresh Question

What is the value of |a - b| ?

(1) a^2 - b^2 = 9
(1) a^2 + b^2 = 15

Statement 1:
(a+b)(a-b)=9 --Insufficient

Statement 2:
$$a^2$$+$$b^2$$=15 --Insufficient

Statement 1 & 2:
$$a^2$$=12 and $$b^2$$=3 --Still we don't know the sign of a and b. Insufficient

why can't we say that Statement 1 is sufficient?

(a+b) * (a-b) = 9

2 numbers can only be a=5 and b= 4

why can't we consider this?

Hi rocko911,

The question doesn't state that a and b are integers. So they can be any real number consisting of decimals. Thus there will be infinitely many such possible pairs.

I hope that helps
_________________
Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15   [#permalink] 07 Mar 2018, 12:55
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