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# What is the value of a – b?

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What is the value of a – b?  [#permalink]

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05 Jun 2016, 14:02
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Difficulty:

55% (hard)

Question Stats:

54% (01:22) correct 46% (01:22) wrong based on 127 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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Md. Abdur Rakib

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Re: What is the value of a – b?  [#permalink]

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05 Jun 2016, 14:07
1
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

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Re: What is the value of a – b?  [#permalink]

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05 Jun 2016, 14:09
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.

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Re: What is the value of a – b?  [#permalink]

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05 Jun 2016, 14:10
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

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]

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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?
Re: What is the value of a – b?   [#permalink] 12 Dec 2018, 06:36
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