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# What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1

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Intern
Joined: 25 Aug 2010
Posts: 2
What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1 [#permalink]

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30 Aug 2010, 14:52
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So I ran across this question in the GMAT paper exams:

What is the value of a - b?

(1) a = b + 4
(2) (a - b)^2 = 16

I marked D since I thought that the GMAT only considers square roots of numbers to equal the positive root only and not the negative root. Thus, wouldn't (2) above be equivalent to a - b = 4? Can someone please explain to me how the GMAT treats square roots of numbers? Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 45244
Re: What is the value of a-b? [#permalink]

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30 Aug 2010, 15:06
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rk9 wrote:
So I ran across this question in the GMAT paper exams:

What is the value of a - b?

(1) a = b + 4
(2) (a - b)^2 = 16

I marked D since I thought that the GMAT only considers square roots of numbers to equal the positive root only and not the negative root. Thus, wouldn't (2) above be equivalent to a - b = 4? Can someone please explain to me how the GMAT treats square roots of numbers? Thanks!

Hi, and welcome to Gmat Club!

It seems that you are mixing square roots ($$\sqrt{x}$$) with quadratics ($$x^2$$).

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root. That is, $$\sqrt{25}=5$$, NOT +5 or -5. Even roots have only non-negative value on the GMAT. Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5.

Hope it helps.
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Re: What is the value of a-b? [#permalink]

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30 Aug 2010, 15:08
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rk9 wrote:
So I ran across this question in the GMAT paper exams:

What is the value of a - b?

(1) a = b + 4
(2) (a - b)^2 = 16

I marked D since I thought that the GMAT only considers square roots of numbers to equal the positive root only and not the negative root. Thus, wouldn't (2) above be equivalent to a - b = 4? Can someone please explain to me how the GMAT treats square roots of numbers? Thanks!

You are right +ve square roots are there. But when you will take square root on both the sides, how you will come to know whether a>b or b>a

(a - b)^2 = 16 take square root on both the sides

=> |a-b| = 4 , see both the square roots are positive. Now when you will open the modulus you will have to consider two cases.
a>b and b>a

if a>b then a - b = 4
if b>a then a - b = -4.

Hope this helps
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Intern
Joined: 25 Aug 2010
Posts: 2
Re: What is the value of a-b? [#permalink]

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30 Aug 2010, 16:25
Thank you both! This helps!
Senior Manager
Joined: 23 May 2010
Posts: 314
Re: What is the value of a-b? [#permalink]

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21 Sep 2010, 11:00
hey Gurpreet Bunuel ....thanx so much I was struggling at this.. even I was mixing quadratic and roots ..... ( in what proportion it does not matter )...cheers

By the way why dont guys open an academy ...with the name as
" We make duds - STUDS in no time.. example gauravnagpal."

LOL !!!
lets keep enjoying the journey ..

cheers
Manager
Joined: 20 Jul 2010
Posts: 231
Re: What is the value of a-b? [#permalink]

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21 Sep 2010, 11:44
1) Sufficient
2) a-b = 4 or -4 ----> insufficient
Ans is A
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Re: What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1 [#permalink]

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01 Dec 2014, 08:07
Algebra DS problem
Asking a-b =? Value based !!
1, Easy to get a-b = 4
2, Formula ( a-b)^2 = 16
Even after solving this we cannot get a-b? So No answer

A
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Intern
Joined: 20 Oct 2015
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Re: What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1 [#permalink]

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05 Jul 2016, 01:13
[quote="rk9"]So I ran across this question in the GMAT paper exams:

What is the value of a - b?

(1) a = b + 4
(2) (a - b)^2 = 16

I marked D since I thought that the GMAT only considers square roots of numbers to equal the positive root only and not the negative root. Thus, wouldn't (2) above be equivalent to a - b = 4? Can someone please explain to me how the GMAT treats square roots of numbers? Thanks![/quot
a=b+4 ===> a-b=4 A is ok

(a-b)^2=16 ====> a-b= +4 and a-b= -4 so we got two answer not ok

when B is not ok then D obviously is not ok

we go with A then between A and D
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Re: What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1 [#permalink]

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16 Sep 2016, 16:07
a-b = ?

(1) a = b+4 --> a-b =4

(2) (a-b)^2 = 16 --> a-b = +/- (4)

(1) gives us a definitive answer where (2) is ambiguous --> hence A is the correct answer
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Joined: 13 Jun 2016
Posts: 19
Re: What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1 [#permalink]

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09 Dec 2016, 07:59
Could someone please help me explain this very basic concept? or give an example of how b might be larger than a, and a larger than b

On the other hand, if the expression would be (a+b)^2 = 16 , would this only yield one possible answer, 4?
thank you
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Re: What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1 [#permalink]

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29 Jan 2018, 13:20
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Re: What is the value of a - b? (1) a = b + 4 (2) (a - b)^2 = 1   [#permalink] 29 Jan 2018, 13:20
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