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

Question

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

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)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards