Inequality Algebric Solution required

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navdeepbajwa: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Sun Aug 02, 2009 9:10 pmFollowed by: 1 member; Thanked: 1 times

by navdeepbajwa » Fri Oct 09, 2009 11:13 pm

Can you solve this algebrically

If x and y are integers, does x^y * y^-x = 1?

(1) x^x > y

(2) x > y^y

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question

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Source: Beat The GMAT — Data Sufficiency | Fri Oct 09, 2009 11:13 pm

Katrusya: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Tue May 19, 2009 10:48 am; Location: Chicago; Thanked: 1 times; GMAT Score:680

by Katrusya » Sat Oct 10, 2009 7:51 am

I think the answer is D
x^y * y^-x = 1 -> (x^y)/(y^x)=1 -> x^y=y^x - this can be true only if x=y=1, or y=x=0
neither of options gives us this solutions, hence
if 1 is true, then (x^y)/(y^x)definetely doesn't =1 - sufficient
if 2 is true, then (x^y)/(y^x)definetely doesn't =1 - sufficient

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Sat Oct 10, 2009 4:22 pm

I think the answer should be B.

Statement 1 - x^x > y

x = 2, y = 2 therefore x^x > y and x^y * y^-x = 1

x = 3, y = 2, therefore x^x > y but x^y * y^-x != 1

Statement 2 - x > y^y

x = 10, y = 2, satisfies statement 2 and x^y * y^-x != 1
x = 28, y = 3, satisfies statement 2 and x^y * y^-x != 1

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nithi_mystics: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Mon Sep 07, 2009 9:11 pm; Location: California; Thanked: 4 times

by nithi_mystics » Sat Oct 10, 2009 4:37 pm

B is the answer

Thanks
Nithi

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