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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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Bunuel
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What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink] New post   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


M36-126

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Bunuel
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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] New post   16 Nov 2021, 04:51
Expert Reply
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


M36-126


Official Solution:


What is the value of \(|a - b|\) ?

(1) \(a^2 - b^2 = 9\)

This equation has infinitely many solutions (notice that we are NOT told that \(a\) and \(b\) are integers). Not sufficient.

(2) \(a^2 + b^2 = 15\)

This equation also has infinitely many solutions. Not sufficient.

(1)+(2) Sum (1) and (2): \(2a^2=24\);

\(a=\sqrt{12}\) or \(a=-\sqrt{12}\);

So, \(b=\sqrt{3}\) or \(a=-\sqrt{3}\).

\(|a - b|=|\sqrt{12}-\sqrt{3}|\) or \(|a - b|=|\sqrt{12}+\sqrt{3}|\). Not sufficient.


Answer: 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] New post   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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Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink] New post   02 Mar 2018, 06:24
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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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Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink] New post   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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Re: What is the value of |a - b| ? (1) a^2 - b^2 = 9 (1) a^2 + b^2 = 15 [#permalink] New post   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] New post   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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Bunuel
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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] New post   24 Dec 2018, 02:41
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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


Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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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] New post   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

Can you please help with this question?

Many thanks
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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] New post   04 Jan 2019, 05:20
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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

Can you please help with this question?

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.

Correct Answer: 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] New post   Updated on: 17 Oct 2019, 07:13
Need to find |a - b|
so need value of a & b
1) a^2 - b^2 = 9
5^2-4^2 =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
Answer = E

Originally posted by rahul12988 on 12 Jul 2019, 10:57.
Last edited by rahul12988 on 17 Oct 2019, 07:13, edited 2 times in total.
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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] New post   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] New post   17 Oct 2019, 06:05
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


(1) a^2 - b^2 = 9: insufic.

\(a^2 - b^2 = 9…(a+b)(a-b)=9\)
\(a+b=9…a=9-b…a-b=1…9-b-b=1…-2b=-9…b=4…a=5…|a-b|=5-4=1\)
\(a+b=3…a=3-b…a-b=3…3-b-b=3…-2b=0…b=0…a=3…|a-b|=3-0=3\)

(2) a^2 + b^2 = 15: insufic.

\(a^2 + b^2 = 15…|a|=√12…|b|=√3\)
\(|a-b|=√12-√3…or…|a-b|=√12+√3\)

(1&2): insufic.

\(a^2 + b^2 = 15…a^2 - b^2 = 9\)
\(a^2 + b^2 + (a^2 - b^2) = 15+9…2a^2=24…a^2=12…|a|=√12…|b|=√3\)
\(|a-b|=√12-√3…or…|a-b|=√12+√3\)

Answer (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] New post   17 Jun 2023, 04:02
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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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