It is currently 06 Jul 2020, 19:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# if x<1 and x ≠ 0

Author Message
TAGS:
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 163

Kudos [?]: 2753 [0], given: 394

if x<1 and x ≠ 0 [#permalink]  20 Jan 2016, 18:21
Expert's post
00:00

Question Stats:

73% (00:32) correct 26% (00:23) wrong based on 121 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
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Founder
Joined: 18 Apr 2015
Posts: 11958
Followers: 252

Kudos [?]: 2983 [2] , given: 11204

Re: if x<1 and x ≠ 0 [#permalink]  21 Jan 2016, 08:39
2
KUDOS
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 $$A$$
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3523
Followers: 133

Kudos [?]: 3964 [2] , given: 65

Re: if x<1 and x ≠ 0 [#permalink]  09 Jun 2016, 09:26
2
KUDOS
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...

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Intern
Joined: 27 Jun 2018
Posts: 2
Followers: 0

Kudos [?]: 2 [2] , given: 0

Re: if x<1 and x ≠ 0 [#permalink]  30 Jun 2018, 09:48
2
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.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 163

Kudos [?]: 2753 [1] , given: 394

Re: if x<1 and x ≠ 0 [#permalink]  30 Jun 2018, 15:35
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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 15 May 2018
Posts: 38
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: if x<1 and x ≠ 0 [#permalink]  09 Jul 2018, 18:40
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
Difficulty: medium
Manager
Joined: 27 Feb 2017
Posts: 188
Followers: 1

Kudos [?]: 75 [0], given: 15

Re: if x<1 and x ≠ 0 [#permalink]  05 Aug 2018, 16:18
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
Display posts from previous: Sort by

# if x<1 and x ≠ 0

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.