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x2 – 49 = 0

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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x2 – 49 = 0 [#permalink] New post 15 Apr 2018, 04:07
Expert's post
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Question Stats:

76% (00:30) correct 23% (00:41) wrong based on 13 sessions
\(x^2 - 49 = 0\)
Quantity A
Quantity B
\(x^2 - 7x\)
\(-7x+49\)


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 2
Question: 3
Page: 510
[Reveal] Spoiler: OA

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Re: x2 – 49 = 0 [#permalink] New post 17 Apr 2018, 02:12
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From the eqn \(x^2 = 49\)
therefore, \(x = 7, -7\)

when \(x\) is replaced by either \(7\) or \(-7\) the two quantities are equal
When \(x = 7\) both quantities are \(0\)
when \(x = -7\) both quantities are \(98\)
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Re: x2 – 49 = 0 [#permalink] New post 17 Apr 2018, 02:59
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x can be eithr +7 or -7. In options A and B, the term including x are both -7x, and the other term has same value.

x^2 or 49, both are same.

Hence both A and B are equal.
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Re: x2 – 49 = 0 [#permalink] New post 18 Apr 2018, 15:43
Expert's post
Explanation

Remember that when a variable is squared, it yields a positive and a negative solution; hence, \(x^2 - 49 = 0\) means that \(x^2 = 49\) and x = ± 7.

If x = 7, then both quantities are equal to zero. If x = –7, then both quantities are equal to 98. The answer is choice (C).
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Re: x2 – 49 = 0 [#permalink] New post 18 Apr 2018, 19:31
We get x^2 = 49 from the given condition.

Qty A is x^2 - 7x which is nothing but 49 -7x
Qty B is -7x + 49 which I can write as 49 -7x

Observe both the quantities now!

What do you see??

Both are same!!!
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Re: x2 – 49 = 0 [#permalink] New post 09 Jul 2018, 18:43
sandy wrote:
\(x^2 - 49 = 0\)
Quantity A
Quantity B
\(x^2 - 7x\)
\(-7x+49\)


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 2
Question: 3
Page: 510

My Answer is C
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Re: x2 – 49 = 0 [#permalink] New post 10 Jul 2018, 08:32
x^2=49 -> x=7 or x=-7. In either case, QA=QB -> C.
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Re: x2 – 49 = 0   [#permalink] 10 Jul 2018, 08:32
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