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a ≠ –b

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sandy
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a ≠ –b [#permalink] New post   15 Apr 2018, 04:34
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A
B
C
D

Question Stats:

79% (00:46) correct 20% (01:14) wrong based on 44 sessions

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a ≠ –b

Quantity A
Quantity B
6a2+12ab+6b2(a+b)
6(a+b)


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 1
Question: 5
Page: 511
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Official Answer
C
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sandy
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Re: a ≠ –b [#permalink] New post   18 Apr 2018, 15:44
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Explanation

Whenever you see exponents, think common quadratics.

If you factor the 6 out of the numerator in Quantity A, you get 6(a2+2ab+b2), which includes a common quadratic (a+b)2.

Then you can cancel (a + b) from both the numerator and the denominator; Quantity A is really just 6(a + b). The quantities are equal.
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Re: a ≠ –b [#permalink] New post   06 Sep 2021, 10:16
2
sandy wrote:
a ≠ –b

Quantity A
Quantity B
6a2+12ab+6b2(a+b)
6(a+b)


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 1
Question: 5
Page: 511


Given:
QUANTITY A: 6a2+12ab+6b2(a+b)

QUANTITY B: 6(a+b)


First factor out the 6 from numerator in Quantity A to get:
QUANTITY A: 6(a2+2ab+b2)(a+b)

QUANTITY B: 6(a+b)


Now factor quadratic in Quantity A to get:
QUANTITY A: 6(a+b)(a+b)(a+b)

QUANTITY B: 6(a+b)


The (a+b) terms cancel out in the denominator and numerator in Quantity A to get:
QUANTITY A: 6(a+b)
QUANTITY B: 6(a+b)

Answer: C
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Re: a b [#permalink] New post   22 Jan 2024, 13:56
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Re: a b [#permalink]
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