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awilhelm: Master | Next Rank: 500 Posts; Posts: 117; Joined: Fri Oct 17, 2008 7:41 am

by awilhelm » Mon Jan 26, 2009 10:18 pm

If x is positive, which of the following could be the correct ordering of 1/x, 2x, and x^2?

I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x

a) none
b) I only
c) I & III only
d) I & II only
e) I, II & III

Is there a fast way to solve this?

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Source: Beat The GMAT — Problem Solving | Mon Jan 26, 2009 10:18 pm

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Mon Jan 26, 2009 10:35 pm

This can be easily solved by picking numbers.
Choosing integers will give a relation that is not mentioned in the choices.
So choose a fraction. say 0.2

I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x

x = 0.2

x^2 = 0.04
2x = 0.4
1/x = 1/0.2 = 10/2 = 5

x^2 < 2x < 1/x

ie. Stmt I

HT helps

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awesomeusername: Master | Next Rank: 500 Posts; Posts: 226; Joined: Tue Jan 13, 2009 1:27 pmFollowed by: 1 member; Thanked: 23 times

by awesomeusername » Mon Jan 26, 2009 11:29 pm

Actually both I and II are true. To show this, you can use 0.99 for statement II and it will hold true.

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sjd00d: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Jan 05, 2009 11:04 pm; Thanked: 2 times

by sjd00d » Mon Jan 26, 2009 11:31 pm

OA should be D. Stmt 2 is correct as well. Take 0.9 as an example..no easy method that i could think of, just trial and error knowing that you should move from 0 to 1

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awesomeusername: Master | Next Rank: 500 Posts; Posts: 226; Joined: Tue Jan 13, 2009 1:27 pmFollowed by: 1 member; Thanked: 23 times

by awesomeusername » Mon Jan 26, 2009 11:34 pm

https://www.beatthegmat.com/number-prope ... 13538.html

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bsandhyav: Master | Next Rank: 500 Posts; Posts: 116; Joined: Fri Aug 29, 2008 10:22 am; Location: Mumbai,India; Thanked: 1 times

by bsandhyav » Tue Jan 27, 2009 1:44 am

Why did you not substitute any natural(non decimal) nos. ?How did you guess that the number to be substituted was decimal?

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awesomeusername: Master | Next Rank: 500 Posts; Posts: 226; Joined: Tue Jan 13, 2009 1:27 pmFollowed by: 1 member; Thanked: 23 times

by awesomeusername » Tue Jan 27, 2009 10:17 am

You want to try different combinations of positive numbers. With positive numbers, you'll generally want to try a fraction (decimal) and a non-fraction. Since we see squares, fractions and multiples of numbers, you'll want to use fractions and non-fractions when testing because they act differently in these situations.

For instance:

1/x > x^2

If x is 1/2, then the inequality is true
If x is 2, it is false.

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