If X is positive, which one of the following could be the correct order 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) III only
(D) I and II
(E) I, II, and III
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Positive X
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nakul_anand
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papgust
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IMO B
Consider three cases here to test the order - Integer, Proper fraction and Improper fraction.
If x=1/2,
x^2 < 2x < 1/x (Satisfies I)
If x=3,
1/x < 2x < x^2 (No options to satisfy)
If x=3/2,
1/x < x^2 < 2x ( " )
Hence B.
Consider three cases here to test the order - Integer, Proper fraction and Improper fraction.
If x=1/2,
x^2 < 2x < 1/x (Satisfies I)
If x=3,
1/x < 2x < x^2 (No options to satisfy)
If x=3/2,
1/x < x^2 < 2x ( " )
Hence B.
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nakul_anand
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Hello Papgust....
I did pretty much the same thing and got the same answer (which is B).
But the OA is D.
Wasn't able to figure out why II could be correct.
I did pretty much the same thing and got the same answer (which is B).
But the OA is D.
Wasn't able to figure out why II could be correct.
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raghavakumar85
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you must consider all the possible values of x ie., if x is 1, >1 and is a fraction (0<x<1). then you will get the right option D. this question tests the knowledge of number properties.
consider x = 3 then I holds good
consider x = 3/4; then 4/3;6/4;(3/4)^2 => x^2 < 1/x < 2x
thanks!
consider x = 3 then I holds good
consider x = 3/4; then 4/3;6/4;(3/4)^2 => x^2 < 1/x < 2x
thanks!
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Testluv
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x = 1/2 satisfies I
x = 3/4 satisfies II
If x = 3/4, then x^2 = 9/16, and 1/x = 4/3, and 2x = 3/2
9/16 < 4/3 < 3/2
So, both I and II are possible orders. If x is positive, however, it is impossible that x^2 < 1/x while simultaneously 2x < x^2.
Choose D.
x = 3/4 satisfies II
If x = 3/4, then x^2 = 9/16, and 1/x = 4/3, and 2x = 3/2
9/16 < 4/3 < 3/2
So, both I and II are possible orders. If x is positive, however, it is impossible that x^2 < 1/x while simultaneously 2x < x^2.
Choose D.
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[email protected]
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Testluv,
how do I know that I have to choose 3/4? I tested numbers and I chose 2 (Integer) and 1/2 ( Non-Integer) and I got therefore B. So what is your key to pick the right numbers?
Thanks!
how do I know that I have to choose 3/4? I tested numbers and I chose 2 (Integer) and 1/2 ( Non-Integer) and I got therefore B. So what is your key to pick the right numbers?
Thanks!
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GMATGuruNY
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Check my post here:[email protected] wrote:Testluv,
how do I know that I have to choose 3/4? I tested numbers and I chose 2 (Integer) and 1/2 ( Non-Integer) and I got therefore B. So what is your key to pick the right numbers?
Thanks!
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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