what is the value of a - b?

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

ST 2:
(a-b) ^2 =1
---> (a-b)= +1 or -1

Not sufficient to tell the value of (a-b) distinctly

Same with st 1 also.

SO E

rahul.s wrote:what is the value of a - b?

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

OA: E
Source: Kaplan 800

my solution:
i opted for B. for statement 2, in the OE, it is mentioned that (a - b)^2 = 1, so (a - b) = sqrt1, and (a - b) = +1 or -1
but aren't square roots of a number considered only positive on the GMAT? i'm confused.

Here you are not using sqrt(x) function - Square root function as you have rightly pointed out refers to positive roots only. but while solving an equation we are not using square root function.

(a - b)^2 = 1
(a - b) = sqrt1
so a - b = 1, right?

where am i going wrong?

rahul.s wrote:(a - b)^2 = 1
(a - b) = sqrt1
so a - b = 1, right?

where am i going wrong?

Rahul, value of (a-b) can either be 1 or -1

okay, but sqrt9 will be 3, right?

gmatmachoman wrote:

rahul.s wrote:(a - b)^2 = 1
(a - b) = sqrt1
so a - b = 1, right?

where am i going wrong?

Rahul, value of (a-b) can either be 1 or -1

Indeed,

In the rush of things I completely ignored that. a-b= 1 or -1

(a-b)(a-b)=1

-1 X -1 = 1

1 X 1= 1


I would have WRONGFULLY chose B as well, The correct answer is indeed E.

rahul.s wrote:okay, but sqrt9 will be 3, right?

I donot think you shift sq from LHS and put it on to RHS in this way as we are not sure regarding the sign of number that is squared.

(5)^2 = 25

(-5)^2 = 25

But, if we shift the sq and make it a sqrt of 25 then we will get only (5).

I too did this one wrong on running timer.

You're correct that, by convention, if we say "sqrt25", we mean +5 only.

So, if you ever see the statement:

x = sqrt25

or

x = √25

on the GMAT, you know that x = +5 only.

However, if you saw:

x^2 = 25

we would actually solve this as:

x^2 - 25 = 0
(x+5)(x-5) = 0

so x could be -5 or +5.

Similarly, when we see:

(a-b)^2 = 1

the way to solve is:


(a-b)^2 - 1 = 0

((a-b) + 1) ((a-b) - 1) = 0

So we have:

a-b = -1
or
a-b = +1

Just because you say "sqrt1" in your own scratchwork, that doesn't mean you only consider the positive root. It's only when we see that term (or the √ symbol) in the actual question that we use the conventional definition.

rahul.s wrote:(a - b)^2 = 1
(a - b) = sqrt1
so a - b = 1, right?

where am i going wrong?

you r wrng bcoz
when u take sqrt root bth side then
LHS will be +/- (a-b) {bcoz its a variable}
and RHS=1

so +/-(a-b)=1-------->a-b=+/-1
HTH

now i get it. thanks a lot for your explanation Stuart.