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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

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

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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

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

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.

Answer: A

For more on this technique see...

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

1

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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

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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.
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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