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If 0 < x < 2, which of the following must be greatest?

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If 0 < x < 2, which of the following must be greatest? [#permalink]

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If 0 < x < 2, which of the following must be greatest?

(A) x
(B) x^2
(C) 2x
(D) x + 2
(E) 2^x
[Reveal] Spoiler: OA

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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 08 Jun 2014, 23:52
A graphical solution is the best in this case.


At \(x = 0\) , try to compare values of all functions, only two functions have non zero values \(x+2 = 2, 2^x = 1\).
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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For x = 1, try the options given

(A) x = 1
(B) \(x^2 = 1^2 = 1\)
(C) 2x = 2
(D) x + 2 = 1 + 2 = 3
(E) \(2^x = 2^1 = 2\)

Answer = D
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 13 Sep 2016, 20:19
why can it not be 1.5? are they looking for integers specifically
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 14 Sep 2016, 00:38
Expert's post
Joshuad25 wrote:
why can it not be 1.5? are they looking for integers specifically


x can be any number satisfying 0 < x < 2, including fractions. For any x from that range options D is the greatest.
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 02 Jan 2017, 16:57
0 < x < 2
x > 0 , x < 2
x = 1
D
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 05 Apr 2017, 19:56
If x has to be less than 2 then how option D is the answer ? since D says x=2.
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 05 Apr 2017, 21:36
Expert's post
Shekhar44 wrote:
If x has to be less than 2 then how option D is the answer ? since D says x=2.


Option D is x + 2, not x = 2.
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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Hi,

The best way to solve any MUST-BE/COULD –BE question in GMAT is plugging in,

Just plug values based out of the range given in the question,

Let’s pick x= 1

(A) x --> 1

(B) x^2 -->1

(C) 2x -->2

(D) x + 2 -->3

(E) 2^x -->2

So answer has to be D.

Here we are little lucky, because we plugged in value, we got the answer.

But sometime we might have to Plug more than once to get to a final answer.

Some students might think, we have plugged in only one value, what if we try other values and we might get more options,

Just remember this in GMAT, MUST BE means “Always”. So here all the other four options were not greater than D for x = 1. So we can eliminate.

So answer is D.

Hope this helps.
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Re: If 0 < x < 2, which of the following must be greatest? [#permalink]

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New post 29 Nov 2017, 09:26
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NoHalfMeasures 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


The key word here is MUST.
That is, the correct answer must yield the biggest value for ALL values of x between 0 and 2
So, we need only test ONE of the possible x-values.

Let's test x = 1

We get....
(A) x = 1
(B) x^2 = 1^2 = 1
(C) 2x = (2)(1) = 2
(D) x + 2 = 1 + 2 = 3
(E) 2^x = 2^1 = 2

Since D yields the biggest value, then the correct answer MUST be D

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Brent
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Re: If 0 < x < 2, which of the following must be greatest?   [#permalink] 29 Nov 2017, 09:26
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