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by divya23 » Thu Jun 02, 2011 9:19 pm
if x and y are postive which of the followinf must b greater than
1/within root(x+y)
within root(x+y)/2x
root x + root y /x +y
root x- root y /x +y
none
1 only
2 only
1 and 3
2 AND 3
answer is 2 only

here my doubt is wat are the magic numbers to be tested upon and also dey have to b distinct or same or
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by Anurag@Gurome » Thu Jun 02, 2011 9:26 pm
Refer to this post : https://www.beatthegmat.com/those-radica ... tml#320556
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by Anurag@Gurome » Thu Jun 02, 2011 9:26 pm
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by cans » Thu Jun 02, 2011 9:31 pm
Que - if x and y are positive which of the following must b greater than 1/root(x+y)
a)root((x+y)/2x)
b)(root x + root y)/(x+y)
c)(root x- root y)/(x +y )
a)1/root(x+y) > root ((x+y)/2x)
squaring, 1/(x+y) >(x+y)/2x or (x+y)^2<2x. if x=1,y=3; 16<2 false
b) (root x + root y) / (x+y ) >1/root(x+y)
root x + root y > root (x+y)
squaring both sides,
x + y + 2root(xy) > x+y
root(xy)>0 true always

c)(root x - root y) / (x+y ) >1/root(x+y)
root x - root y > root (x+y)
squaring both sides,
x + y - 2root(xy) > x+y
root(xy)<0 false

Thus only b) is correct.
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by driftmaster » Fri Sep 02, 2011 10:41 am
Why can't we just pick numbers for x and y in the question stem expression and see which Roman Numeral choices are greater w/ the same x and y values?

I understand that the answer will depend on which values you pick for x and y, but I'm under the impression that since it says it MUST be true, then any x and y value work and the expression will ALWAYS be greater or ALWAYS be less than.

Can someone please clarify? Thx
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by GmatKiss » Sat Sep 03, 2011 10:29 am
Anurag@Gurome wrote:Refer to this post : https://www.beatthegmat.com/those-radica ... tml#320556
Hi,

Could you please help us with an easier solution!

TIA,
GK
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by knight247 » Sat Sep 03, 2011 11:49 am
At gmatkiss,
Very simple solution to this. You don't have to get into inequalities at all. I'm sure u know the method of comparing two fraction is cross multiplication eg 11/7 and 8/6, by cross multiplying u get
66 56. The product on the left corresponds to the fraction on the left side and similarly with the right side fraction. 66>56 so 11/7>8/6. This rule only applies to +ve fractions. If both fractions are negative i.e. -11/7 and -8/6 After cross multiplying u get -66 and -56. Right side greater than left side so -8/6> -11/7. If one is negative and one is +ve then no need to cross multiply as the -ve fraction is obviously smaller.

Coming to the problem
if x and y are positive which of the following must b greater than 1/√(x+y)
a)√(x+y)/2x
b)(√x + √y)/(x+y)
c)(√x- √y)/(x +y )

Compare each one with 1/√(x+y)
A)√(x+y)/2x and 1/√(x+y)
Cross multiplying u get,
x+y and 2x. U can plug in numbers for this by urself and u'd conflicting answers. So this statement is not always true

B)(√x + √y)/(x+y) and 1/√(x+y)
(√x + √y)√(x+y) and (x+y)

Dividing both sides by √(x+y) we get
(√x + √y) and (x+y)/√(x+y) So we have

(√x + √y) and √(x+y)
Squaring both sides we get
x+2√xy+y and x+y
Left hand fraction greater than right side fraction so B is greater than 1/√(x+y)

C)(√x- √y)/(x +y ) and 1/√(x+y)
Cross multiplying we get
(√x- √y)√(x+y) and x+y
Dividing both sides by √x+y
(√x- √y) and x+y
Squaring both sides we have
x-2√xy+y and x+y. Since x and y are both +ve the left side is obviously smaller than the right side so C is smaller than 1/√(x+y). Answer is B Only
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