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# x2 – 49 = 0

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Retired Moderator
Joined: 07 Jun 2014
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x2 – 49 = 0 [#permalink]  15 Apr 2018, 04:07
Expert's post
00:00

Question Stats:

75% (00:33) correct 25% (01:06) wrong based on 20 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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Sandy
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Kudos [?]: 770 [1] , given: 88

Re: x2 – 49 = 0 [#permalink]  17 Apr 2018, 02:12
1
KUDOS
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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Manager
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Re: x2 – 49 = 0 [#permalink]  17 Apr 2018, 02:59
1
KUDOS
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.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2918 [0], given: 394

Re: x2 – 49 = 0 [#permalink]  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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Sandy
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Re: x2 – 49 = 0 [#permalink]  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]  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

Intern
Joined: 04 May 2017
Posts: 36
Followers: 0

Kudos [?]: 29 [0], given: 6

Re: x2 – 49 = 0 [#permalink]  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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