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What is the value of a – b?

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AbdurRakib
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What is the value of a – b? [#permalink] New post   05 Jun 2016, 14:02
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59% (01:29) correct 41% (01:28) wrong based on 220 sessions
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What is the value of a – b?

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

(2) a^2 - 2ab + b^2 = 1
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E
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Divyadisha
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Re: What is the value of a – b? [#permalink] New post   05 Jun 2016, 14:07
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AbdurRakib wrote:
What is the value of a – b?

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

(2) a^2 - 2ab + b^2 = 1


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

Four possibilities= 1*9, 9*1, -1*-9, -9*-1

Not sufficient.

(2) a^2 - 2ab + b^2 = 1

(a-b)^2= 1

two possibilities for (a-b)= +1, -1

Combining both statements (a-b) can be +1 or -1. Not sufficient

E is the answer
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Re: What is the value of a – b? [#permalink] New post   05 Jun 2016, 14:09
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What is the value of a – b?

(1) a^2 - b^2 = 9 --> (a - b)(a + b) = 9. Not sufficient.

(2) a^2 - 2ab + b^2 = 1 --> (a - b)^2 = 1 --> a - b = 1 or a - b = -1. Not sufficient.

(1)+(2) Still not sufficient:
Case 1: a - b = 1 and a + b = 9.
Case 1: a - b = -1 and a + b = -9.

Answer: E.
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Re: What is the value of a – b? [#permalink] New post   05 Jun 2016, 14:10
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Divyadisha wrote:
AbdurRakib wrote:
What is the value of a – b?

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

(2) a^2 - 2ab + b^2 = 1


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

Four possibilities= 1*9, 9*1, -1*-9, -9*-1
Not sufficient.

(2) a^2 - 2ab + b^2 = 1

(a-b)^2= 1

two possibilities for (a-b)= +1, -1

Combining both statements (a-b) can be +1 or -1. Not sufficient

E is the answer


The highlighted part is not correct. We are not told that a and b are integers, thus a^2 - b^2 = 9 has infinitely many solutions for a and b.
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Re: What is the value of a – b? [#permalink] New post   12 Dec 2018, 06:36
Can anyone help me with 1st option? generally in algebra this is how we write a2-b2=9 mean (a-b)*(a+b)=3*3
a-b=3 & a+b=3

Can anyone help me where I am going wrong?
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Re: What is the value of a – b? [#permalink] New post   28 Aug 2020, 02:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the value of a – b? [#permalink]
28 Aug 2020, 02:06
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