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x^2 +6x=7 (x+3) ^2

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x^2 +6x=7 (x+3) ^2 [#permalink] New post 05 Dec 2017, 12:45
Expert's post
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Question Stats:

76% (00:34) correct 23% (01:50) wrong based on 13 sessions
\(x^2 +6x=7\)
Quantity A
Quantity B
\((x+3)^2\)
\(16\)



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.
[Reveal] Spoiler: OA

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Re: x^2 +6x=7 (x+3) ^2 [#permalink] New post 06 Dec 2017, 09:40
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Expert's post
Carcass wrote:
\(x^2 +6x=7\)
Quantity A
Quantity B
\((x+3)^2\)
\(16\)


[Reveal] Spoiler: OA
OA in 24h


APPROACH #1:

GIVEN: x² + 6x = 7

Quantity A: (x + 3)²
Quantity B: 16

Use FOIL to expand and simplify Quantity A:
Quantity A: x² + 6x + 9
Quantity B: 16

Notice the following:
Quantity A: x² + 6x + 9
Quantity B: 16

Replace x² + 6x with 7 to get:
Quantity A: 7 + 9
Quantity B: 16

Answer: C

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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2 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1177
Followers: 44

Kudos [?]: 1053 [2] , given: 6

CAT Tests
Re: x^2 +6x=7 (x+3) ^2 [#permalink] New post 06 Dec 2017, 09:43
2
This post received
KUDOS
Expert's post
Carcass wrote:
\(x^2 +6x=7\)
Quantity A
Quantity B
\((x+3)^2\)
\(16\)



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.

[Reveal] Spoiler: OA
OA in 24h


APPROACH #2:

GIVEN: x² + 6x = 7
Notice that the left side can be turned into a PERFECT SQUARE if we add 9 to both sides of the equation to get:
x² + 6x + 9 = 7 + 9

Factor left side and evaluate right side to get: (x + 3)² = 16

NOW ONTO THE QUESTION....

Quantity A: (x + 3)²
Quantity B: 16

Replace (x + 3)² with 16 to get:
Quantity A: 16
Quantity B: 16

Answer: C

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
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Re: x^2 +6x=7 (x+3) ^2   [#permalink] 06 Dec 2017, 09:43
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