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DS question

by MAAJ » Thu Apr 28, 2011 10:28 am
Is x + y > 2 sqrt(xy)?

1) (x+y)² > (2sqrt(xy))²
2) x is not equal to y
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by Anurag@Gurome » Thu Apr 28, 2011 8:31 pm
MAAJ wrote:Is x + y > 2 sqrt(xy)?

1) (x+y)² > (2sqrt(xy))²
2) x is not equal to y
(1) (x+y)² > [2√(xy)]²
If x = -4, y = 0, then x + y = -4 and 2√(xy) = 0; here x + y < 2 sqrt(xy)
If x = 9, y = 4, then x + y = 13 and 2√(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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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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