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06 Jun 2017, 01:39
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Difficulty:
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Question Stats:
90% (01:04) correct
10%
(01:38)
wrong
based on 1156
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Which of the following is equivalent to \(\frac{2x+4}{2x^2+8x+8}\) for all values of x for which both expressions are defined?
(A) 1/(2x^2+6)
(B) 1/(9x+2)
(C) 2/(x+6)
(D) 1/(x+4)
(E) 1/(x+2)
(A) 1/(2x^2+6)
(B) 1/(9x+2)
(C) 2/(x+6)
(D) 1/(x+4)
(E) 1/(x+2)
sashiim20
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Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 609
06 Jun 2017, 02:28
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GMATinsight
\(\frac{(2x+4)}{[2x^2+8x+8]}\) = \(\frac{2(x+2)}{2[x^2+4x+4]}\) = \(\frac{2(x+2)}{2(x+2)^2}\) = \(\frac{1}{(x+2)}\) . Answer E...
06 Jun 2017, 10:02
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GMATinsight
sashiim20 has demonstrated the best/faster approach, BUT if you didn't think of that technique, you can still solve the question.
We're looking for an expression that is EQUIVALENT to (2x + 4)/(2x² + 8x + 8)
So, for ANY value of x, the correct answer must evaluate to have the same value as (2x + 4)/(2x² + 8x + 8) does
So, let's plug in a value for x
Let's try x = 1
First plug this value into the GIVEN expression.
We get: (2x + 4)/(2x² + 8x + 8) = [2(1) + 4]/[2(1²) + 8(1) + 8]
= 6/18
= 1/3
So, the correct answer choice will be the one that evaluates to 1/3 when we plug in x = 1
A) 1/(2x² + 6) = 1/[2(1²) + 6] = 1/8. We want 1/3, so ELIMINATE A
B) 1/(9x + 2) = 1/[9(1) + 2] = 1/11. We want 1/3, so ELIMINATE B
C) 2/(x + 6) = 2/(1 + 6) = 2/7. We want 1/3, so ELIMINATE C
D) 1/(x + 4) = 1/(1 + 4) = 1/5. We want 1/3, so ELIMINATE D
E) 1/(x + 2) = 1/(1 + 2) = 1/3. BINGO!!
By the process of elimination, the correct answer is
Cheers,
Brent
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