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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

80% (00:31) correct
20% (00:18) wrong based on 45 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

Re: if x<1 and x ≠ 0 [#permalink]
21 Jan 2016, 08:39

1

This post received 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

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

2

This post received 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.

Answer: A

For more on this technique see...

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Dayemails

Re: if x<1 and x ≠ 0 [#permalink]
30 Jun 2018, 09:48

1

This post received 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.

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

1

This post received KUDOS

Expert's post

Roadrunner wrote:

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

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 My Answer is A Difficulty: medium

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.

greprepclubot

Re: if x<1 and x ≠ 0
[#permalink]
05 Aug 2018, 16:18