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Which is greater (2x-11)(2x+11)/4

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Carcass
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Which is greater (2x-11)(2x+11)/4 [#permalink] New post   22 Apr 2019, 08:56
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Quantity A
Quantity B
\(\frac{(2x-11)(2x+11)}{4}\)
\((x-11)(x+11)\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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A
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LT2018
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Re: Which is greater (2x-11)(2x+11)/4 [#permalink] New post   22 Apr 2019, 13:48
Solution please?
Thanks so much
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GreenlightTestPrep
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Which is greater (2x-11)(2x+11)/4 [#permalink] New post   22 Apr 2019, 14:38
2
Carcass wrote:
Quantity A
Quantity B
\(\frac{(2x-11<}{div>
2x+11)/4}\))(\((x-11)(x+11)\)



We can solve this question using matching operations

Given:
Quantity A: \(\frac{(2x-11)(2x+11)}{4}\)

Quantity B: \((x-11)(x+11)\)

Multiply both quantities by 4 to get:
Quantity A: \((2x-11)(2x+11)\)
Quantity B: \((4)(x-11)(x+11)\)

Expand and simplify both quantities to get:
Quantity A: \(4x^2 - 121\)
Quantity B: \(4x^2 - 484\)

Subtract \(4x^2\) from both quantities to get:
Quantity A: \(-121\)
Quantity B: \(-484\)

Answer: A

Cheers,
Brent

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Re: Which is greater (2x-11)(2x+11)/4 [#permalink] New post   23 Apr 2019, 04:17
Thank you so much for the explanation, Brent! :)
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Re: Which is greater (2x-11)(2x+11)/4 [#permalink] New post   10 Aug 2019, 12:45
Should we not consider different values of x, say x=0 and such?
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Re: Which is greater (2x-11)(2x+11)/4 [#permalink] New post   10 Aug 2019, 12:48
almondspeeing wrote:
Should we not consider different values of x, say x=0 and such?


Sure, you can test all sorts of x-values (including x = 0).
When you do that, you'll find that Quantity A is always greater.
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Re: Which is greater (2x-11)(2x+11)/4 [#permalink]
10 Aug 2019, 12:48
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