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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Thu Apr 28, 2011 10:28 am

Is x + y > 2 sqrt(xy)?

1) (x+y)Â² > (2sqrt(xy))Â²
2) x is not equal to y

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Source: Beat The GMAT — Data Sufficiency | Thu Apr 28, 2011 10:28 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Apr 28, 2011 8:31 pm

MAAJ wrote:Is x + y > 2 sqrt(xy)?

1) (x+y)Â² > (2sqrt(xy))Â²
2) x is not equal to y

(1) (x+y)Â² > [2âˆš(xy)]Â²
If x = -4, y = 0, then x + y = -4 and 2âˆš(xy) = 0; here x + y < 2 sqrt(xy)
If x = 9, y = 4, then x + y = 13 and 2âˆš(xy) = 12; here x + y > 2 sqrt(xy)
It can be seen that we don't get a definite answer.
So, (1) is NOT SUFFICIENT.

(2) Again, the examples taken in statement (1) implies that (2) is NOT SUFFICIENT.

Combining (1) and (2), also we take the same examples. Hence, combining also is NOT SUFFICIENT.

The correct answer is E.

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Fri Apr 29, 2011 9:53 am

hi Anurag
one more question, if possible, concerning above problem
i see here that we compare simple average-(x+y)/2 with geometric average (xy)^1/2
if x and y>0, then always (x+y)/2>=(x*y)^1/2. it can be equal if x=y
we are given that x is not euqal to y, but we are not given sign of either x or y
so even without plugging numbers the answer is E
can you share your ideas on above?
thanks

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