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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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if x<1 and x ≠ 0 [#permalink]
Expert's post 00:00

Question Stats: 77% (00:31) correct 22% (00:17) wrong based on 53 sessions
x<1 and x ≠ 0

 Quantity A Quantity B $$x^2 + 1$$ $$x^3 + 1$$

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.

Practice Questions
Question: 2
Page: 457
Difficulty: medium
[Reveal] Spoiler: OA

_________________

Sandy
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Re: if x<1 and x ≠ 0 [#permalink]
1
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Expert's post
Solution

A conceptual approach is the better way here to attack the question

$$x^2$$ no matter what is always positive

on the other hand $$x^3$$ no. could be positive or negative: it depends on the sign of the number

We do know that$$x<1$$ so X could be positive or negative as well. But the $$A$$ quantity is always positive and $$>$$ than quantity $$B$$ that could be positive or negative

The answer is $$A$$
_________________ GRE Instructor Joined: 10 Apr 2015
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Kudos [?]: 1456  , given: 8

Re: if x<1 and x ≠ 0 [#permalink]
2
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Expert's post
sandy wrote:
x<1 and x ≠ 0

 Quantity A Quantity B $$x^2 + 1$$ $$x^3 + 1$$

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.

Given:
Quantity A: x² + 1
Quantity B: x³ + 1

Subtract 1 from both quantities ...
Quantity A: x²
Quantity B: x³

NOTE: Since x ≠ 0, we know that x² MUST be POSITIVE.
This allows us to divide both quantities by x² to get....
Quantity A: 1
Quantity B: x

Since it is given that x < 1, we can be certain that quantity A is greater.

For more on this technique see...

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Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Intern Joined: 27 Jun 2018
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Re: if x<1 and x ≠ 0 [#permalink]
1
KUDOS
This problem was a good candidate for a picking numbers strategy. Because x<1 and x not equal to zero, I picked the numbers 1/2, -1/2 and -1. In each of those cases, A was the largest quantity, so I was pretty confident in choosing A as the correct answer. GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1776  , given: 397

Re: if x<1 and x ≠ 0 [#permalink]
1
KUDOS
Expert's post
This problem was a good candidate for a picking numbers strategy. Because x<1 and x not equal to zero, I picked the numbers 1/2, -1/2 and -1. In each of those cases, A was the largest quantity, so I was pretty confident in choosing A as the correct answer.

Nice! Correct strategy.

Usually we might even pick a an integer other than +/- 1 in such cases. Such as -2 in this case.

The idea is to validate if the hypothesis holdds for both integers and fractions alike.
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Sandy
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Intern Joined: 15 May 2018
Posts: 38
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Re: if x<1 and x ≠ 0 [#permalink]
sandy wrote:
x<1 and x ≠ 0

 Quantity A Quantity B $$x^2 + 1$$ $$x^3 + 1$$

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.

Practice Questions
Question: 2
Page: 457
My Answer is A
Difficulty: medium
Manager Joined: 27 Feb 2017
Posts: 189
Followers: 0

Kudos [?]: 49 , given: 15

Re: if x<1 and x ≠ 0 [#permalink]
I did substitution for this. But we have to be careful. I picked -1, -0.5 and +0.5. We have to make sure we cover all bases. In all cases, here, A was larger. It is also important to remember that during exam, because of time crunch and panic we might miss certain numbers. Re: if x<1 and x ≠ 0   [#permalink] 05 Aug 2018, 16:18
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