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

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Joined: 18 Apr 2015
Posts: 5538
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Kudos [?]: 1115 [0], given: 5143

x^2 +6x=7 (x+3) ^2 [#permalink]  05 Dec 2017, 12:45
Expert's post
00:00

Question Stats:

73% (00:37) correct 26% (01:29) wrong based on 15 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

_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 1410
Followers: 54

Kudos [?]: 1352 [3] , given: 8

Re: x^2 +6x=7 (x+3) ^2 [#permalink]  06 Dec 2017, 09:40
3
KUDOS
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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 1410
Followers: 54

Kudos [?]: 1352 [2] , given: 8

Re: x^2 +6x=7 (x+3) ^2 [#permalink]  06 Dec 2017, 09:43
2
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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: x^2 +6x=7 (x+3) ^2   [#permalink] 06 Dec 2017, 09:43
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# x^2 +6x=7 (x+3) ^2

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