value of X

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lukaswelker: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Mar 26, 2014 6:56 am; Followed by:1 members

value of X

by lukaswelker » Tue Apr 08, 2014 9:59 am

Here's the question;

If X is positive, which of the following could be the correct ordering of; 1/x; 2x and x2(exponent)

I. x2(exponent) < 2x < 1/x
II. x2(exponent) < 1/x < 2x
III. 2x < x2(exponent) < 1/x

"¢ NONE
"¢ 1 only
"¢ 3 only
"¢ 1 and 2 only
"¢ 1, 2, and 3

I tried to substitute with 1 but it didn't give me the correct answer. Any useful tip?
Cheers
Lukas

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Source: Beat The GMAT — Problem Solving | Tue Apr 08, 2014 9:59 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 08, 2014 10:02 am

If x is positive, which of the following could be the correct ordering of 1/x, 2x and xÂ²?
I. xÂ² < 2x < 1/x
II. xÂ² < 1/x < 2x
III. 2x < xÂ² < 1/x

(A) None
(B) I only
(C) III only
(D) I and II only
(E) I II and III

Let's start by PLUGGING IN some positive values of x and see what we get.

x = 1/2
1/x = 2
2x = 1
xÂ² = 1/4
So, we get xÂ² < 2x < 1/x
This matches statement I.

x = 3/4
1/x = 4/3
2x = 3/2
xÂ² = 9/16
So, we get xÂ² < 1/x < 2x
This matches statement II

x = 3
1/x = 1/3
2x = 6
xÂ² = 9
So, we get 1/x < 2x < xÂ²
NO MATCHES

At this point, the correct answer is either D or E.
If you're pressed for time, you might have to guess.

Alternatively, you can use some algebra to examine statement III (2x < xÂ² < 1/x)
Notice that there are 2 inequalities here (2x < xÂ² and xÂ² < 1/x)
Take 2x < xÂ² and divide both sides by x to get 2 < x
Take xÂ² < 1/x and multiply both sides by x to get x^3 < 1, which means x < 1
Hmmm, so x is greater than 2 AND less than 1. This is IMPOSSIBLE, so statement III cannot be true.

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com