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

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What is the value of |a - b| ?

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

M36-126

Bunuel · Accepted Answer

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

gmatexam439 · Answer

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"

bobnil · Answer

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.

rocko911 · Answer

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?

qazi11 · Answer

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

gmatexam439 · Answer

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

Bunuel · Answer

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

GMATin · Answer

Hi  EgmatQuantExpert

Can you please help with this question?

Many thanks

EgmatQuantExpert · Answer

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

rahul12988 · Answer

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

Kinshook · Answer

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

exc4libur · Answer

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

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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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