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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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08 Jun 2014, 23:48
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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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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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24 Jun 2014, 03:06
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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) $$2^x = 2^1 = 2$$

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

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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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14 Sep 2016, 00:38
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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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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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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05 Apr 2017, 21:36
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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05 Apr 2017, 22:20
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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.

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

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29 Nov 2017, 09:26
Expert's post
Top Contributor
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

Cheers,
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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