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(Please solve this problem, anyone!) PS Problem #4. Thx!!

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Intern
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Joined: 23 Jun 2009
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Kudos [?]: 26 [0], given: 6

(Please solve this problem, anyone!) PS Problem #4. Thx!! [#permalink]

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New post 24 Jul 2009, 13:42
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E

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If 0<x<1, which of the following inequalities must be true?
I. x^5 < x^3
II. x^4 + x^5 < x^3 + x^2
III. x^4 - x^5 < x^2 - x^3

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


Thanks in advance! I would appreciate this help, especially if I can understand a very structured way to reason it out. I think I got the answer by intelligent guessing, but a better approach would help.

Kudos [?]: 26 [0], given: 6

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Joined: 18 Jul 2009
Posts: 168

Kudos [?]: 113 [0], given: 37

Location: India
Schools: South Asian B-schools
Re: (Please solve this problem, anyone!) PS Problem #4. Thx!! [#permalink]

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New post 24 Jul 2009, 14:43
U must have got ur ans from Prep Software ----

Ans is E >> I,II and III (plz refer JPG i have attached ...i have made this JPG so that all indices variation wrto number line can be seen in one shot...i hope this will help you...

I) its very clear from the image attached that between 0<x<1

x^5 < x^3

II) x^4 + x^5 < x^3 + x^2 (since x is +ve we can take it common...no sign change)

x^4(1 + x) < x^2(x + 1)....on cancelling (1+x)...again it is evident

III) x^4 - x^5 < x^2 - x^3 ( apply same logic as in II...this is also true)

Hence E

if right Kudos plz ...trying to access exam :wink:
Attachments

Picture1.gif
Picture1.gif [ 4.67 KiB | Viewed 840 times ]


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Bhushan S.
If you like my post....Consider it for Kudos :-D

Kudos [?]: 113 [0], given: 37

Re: (Please solve this problem, anyone!) PS Problem #4. Thx!!   [#permalink] 24 Jul 2009, 14:43
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(Please solve this problem, anyone!) PS Problem #4. Thx!!

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