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Master | Next Rank: 500 Posts
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by Needgmat » Sat Oct 08, 2016 8:46 am
If 0<x<2, which of the following must be greatest?

A) x

B) x^2

C) 2x

D) x+2

E) 2^x

OAD

Please explain
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by [email protected] » Sat Oct 08, 2016 9:26 am
Hi Needgmat,

This question is more about the mathematical concepts involved than about actually doing calculations. I'm going to give you some hints so that you can reattempt this question on your own.

Given the range 0 < X < 2, we know that X can get really, really close to 2, but not 2 exactly...

[spoiler] Consider X^2 vs. 2X. If you maximize the value of X, which of those outcomes would be BIGGER? As a simple example, consider X = 1.9.....

(1.9)^2 = (1.9)(1.9)
2(1.9) = (2)(1.9)

Without multiplying those out, can you determine which one is bigger? How do you know? Now use THAT understanding to assess the remaining answer choices.[/spoiler]

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by Needgmat » Sat Oct 08, 2016 9:15 pm
This question is more about the mathematical concepts involved than about actually doing calculations. I'm going to give you some hints so that you can reattempt this question on your own.

Given the range 0 < X < 2, we know that X can get really, really close to 2, but not 2 exactly...

[spoiler] Consider X^2 vs. 2X. If you maximize the value of X, which of those outcomes would be BIGGER? As a simple example, consider X = 1.9.....

(1.9)^2 = (1.9)(1.9)
2(1.9) = (2)(1.9)

Without multiplying those out, can you determine which one is bigger? How do you know? Now use THAT understanding to assess the remaining answer choices.

Hi Rich ,

Thanks for your reply.

Can you please advise why E is wrong and D is right?

Many thanks in advance.

Kavin
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by GMATGuruNY » Sun Oct 09, 2016 3:35 am
Needgmat wrote:If 0<x<2, which of the following must be greatest?

A) x

B) x^2

C) 2x

D) x+2

E) 2^x
Test x=1 in the answer choices:

A) x = 1
B) x² = 1² = 1
C) 2x = 2*1 = 2
D) x+2 = 1+2 = 3
E) 2^x = 2¹ = 2

Since A, B, C and E do NOT have to be the greatest, eliminate A, B, C and E.

The correct answer is D.
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