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73% (00:41) correct
26% (00:57) wrong based on 262 sessions

\(x > 0\)

Quantity A

Quantity B

\(\frac{1}{x}\)

\(\frac{(x+1)}{x^2}\)

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.

Re: Compare for x > 0 [#permalink]
20 Jan 2017, 15:38

3

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Quantity A Quantity B 1/X (1+X)/X^2 Multiply both by X 1 (1+X)/X 1 1/X + X/X 1 1/X + 1 Since X Always >0 , Then Quantity B is always greater. Answer is B.

Re: Compare for x > 0 [#permalink]
25 Jan 2017, 11:10

4

This post received KUDOS

Expert's post

sandy wrote:

\(x > 0\)

Quantity A

Quantity B

\(\frac{1}{x}\)

\(\frac{(1 + x)}{x^2}\)

Explanation

Another approach is to use Matching Operations

Given: Quantity A: 1/x Quantity B: (1 + x)

Since x ≠ 0, we can be certain that x² is POSITIVE So, we can safely multiply both quantities by x² to get: Quantity A: x²/x Quantity B: (1 + x)

Simplify to get: Quantity A: x Quantity B: 1 + x

Subtract x from both sides to get: Quantity A: 0 Quantity B: 1

Answer: B

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Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Subtract 1/x from both quantities to get: Quantity A: 0 Quantity B: 1/x²

Since x > 0, we know that x² > 0, which means 1/x² > 0

Answer: B

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_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: Compare for x > 0 [#permalink]
14 Dec 2018, 06:48

1

This post received KUDOS

Expert's post

sandy wrote:

\(x > 0\)

Quantity A

Quantity B

\(\frac{1}{x}\)

\(\frac{(1 + x)}{x^2}\)

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.

If we're not sure how to proceed, we can always test some values to at least eliminate some answer choices.

We're told that x > 0

So, let's first test x = 1 We get: QUANTITY A: 1/1 = 1 QUANTITY B: (1 + 1)/1² = 2/1 = B In this case, Quantity B is greater This means we can ELIMINATE A and C. So, if we must guess, we're down to a 50-50 proposition!

Let's test some more values.

Test x = 0.1 QUANTITY A: 1/0.1 = 10 QUANTITY B: (1 + 0.1)/0.1² = 1.1/0.01 = 110 In this case, Quantity B is greater

Test x = 3 QUANTITY A: 1/3 = 1/3 QUANTITY B: (1 + 3)/3² = 4/9 In this case, Quantity B is greater

Test x = 10 QUANTITY A: 1/3 = 1/10 QUANTITY B: (1 + 10)/10² = 11/100 In this case, Quantity B is greater

At this point, it SEEMS like Quantity B will always be greater? Can we be 100% sure that the answer B? No, but B would be a reasonable guess, and guess what? The correct answer IS B.

Cheers, Brent

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_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

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Re: Compare for x > 0
[#permalink]
14 Dec 2018, 06:48