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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: 58364
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
1
9
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Difficulty:

75% (hard)

Question Stats:

55% (02:10) correct 45% (02:03) wrong based on 262 sessions

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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

_________________
Retired Moderator
Joined: 28 Mar 2017
Posts: 1195
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
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

IMO answer should be "E"
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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.
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Joined: 11 Feb 2017
Posts: 182
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

IMO answer should be "E"

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?
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Joined: 14 Dec 2016
Posts: 11
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
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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

IMO answer should be "E"

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
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Posts: 58364
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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24 Dec 2018, 02:41
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

_________________
Manager
Joined: 24 Dec 2018
Posts: 107
Concentration: Entrepreneurship, Finance
GMAT 1: 710 Q47 V40
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 Jan 2019, 04:51
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

Hi EgmatQuantExpert

Many thanks
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Joined: 04 Jan 2015
Posts: 3074
What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15  [#permalink]

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04 Jan 2019, 05:20
1
GMATin 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

Hi EgmatQuantExpert

Many thanks

Hi GMATin,

We are asked to find out the value of |a - b|

Statement 1:

$$"a^2 - b^2 = 9"$$
(a - b) * (a + b) = 1 * 9 = -1 * -9 = 3 * 3 = -3 * -3 and many more
So, |a - b| can be either 1 or 3 or 9 and many more

Hence, Statement 1 is not sufficient

Statement 2:

$$"a^2 + b^2 = 15"$$
$$(a - b)^2 + 2ab = 15$$
$$(a - b)^2 = 15 - 2ab$$
Taking square root on both sides, we get, |a - b| = √(15 - 2ab)

So, the value of |a - b| depends on the value of ab

Hence, Statement 2 is not sufficient

Combining both statements:

From statement 1, we have, |a - b| = 1 or 3 or 9 and many more
From statement 2, we have, |a - b| = √(15 - 2ab)

Combining both still we do not know the values of a and b

Hence, both statements together are also not sufficient.

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Joined: 07 Apr 2018
Posts: 19
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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12 Jul 2019, 10:57
Need to find |a - b|
so need value of a & b
1) a^2 - b^2 = 9
5^2-3^2 =9 or 3^2-0=9 NS
2) a^2 + b^2 = 15
a^2 = 12 b^2= 3 or a^2 = 10 b^2 =5 NS
1+2
a^2= 12.5 a=+/- 12.5
b= +/- 2.5 NS
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Location: India
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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08 Oct 2019, 04:08
Bunuel wrote:

GMAT Club's Fresh Question

What is the value of |a - b| ?

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

Asked: What is the value of |a - b| ?

(1) a^2 - b^2 = 9
1 equation 2 unknowns
NOT SUFFICIENT

(2) a^2 + b^2 = 15
1 equation 2 unknowns
NOT SUFFICIENT

(1) + (2)
(1) a^2 - b^2 = 9
(2) a^2 + b^2 = 15
a^2 = 12; b^2 = 3
Still signs of a & b are unknown
NOT SUFFICIENT

IMO E
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Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15   [#permalink] 08 Oct 2019, 04:08
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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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