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# Is x > y^2? 1. x > y + 5 2. x^2 - y^2 = 0

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Is x > y^2? 1. x > y + 5 2. x^2 - y^2 = 0 [#permalink]

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28 Sep 2009, 17:32
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Is x > y^2?

1. x > y + 5
2. x^2 - y^2 = 0

[Reveal] Spoiler:
OA C IMO E
Manager
Joined: 08 Nov 2005
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28 Sep 2009, 17:43
1
KUDOS
IMO B.

1.
x=-5, y=-11 is x> y^2->No
x=6, y=0 Ans is Yes
Insufficient

2.
(x-y)(x+y)=0 i.e x=y or x=-y
x=y i.e is x>y^2 NO
x=-y that means only sign is different
y^2 is always positive is x>y^2 NO
plugin numbers: x=1, y=-1 NO
x=-2 y=2 No
x=0 y=0 No
Always No. Sufficient
Manager
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28 Sep 2009, 17:48
silly mistake. Did not consider fraction for
2. x=y if x=y=1/2 then 1/2 > 1/4 so answer is Yes
so 2 is insufficient too

lets consider together
x=y and x>y+5 this is impossible because we are saying is x>x+5 so we cant consider this.
now x=-y and x>y+5 i.e -2y > 5
for example x=4 y=-4 i.e 8>5
is x>y^2 4 >16 NO
now for any number this will be true.

whats OA? I hope I am not wrong. I am making tons of silly mistakes lately.
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29 Sep 2009, 08:36
1
KUDOS
orsang8 wrote:
silly mistake. Did not consider fraction for
2. x=y if x=y=1/2 then 1/2 > 1/4 so answer is Yes
so 2 is insufficient too

lets consider together
x=y and x>y+5 this is impossible because we are saying is x>x+5 so we cant consider this.
now x=-y and x>y+5 i.e -2y > 5
for example x=4 y=-4 i.e 8>5
is x>y^2 4 >16 NO
now for any number this will be true.

whats OA? I hope I am not wrong. I am making tons of silly mistakes lately.

Nice explanation orsang8. Here is an alternative to part of your explanation.

Your explanation of x = y ruling out is good.

For x = -y and x>y = 5 ==> x > -x+5
==> 2x>5 ==> x> 2.5.

When ever X > 1, X^2 > X ==> Y^2 > X(since X = -Y)

This way with the both the clues, we can say whether X > Y^2. Hence Ans is C.
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29 Sep 2009, 18:41
yeah Ans C

Good explanation guys
Intern
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03 Oct 2009, 00:00
Now ,my way.guys please let me know if it is wrong.

The only situation that makes 2 false is when x=y=1 or x=1 y=-1.
So C.
Intern
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05 Oct 2009, 14:06
good explanation both mrsmarthi and orsang8. Thanks.
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23 Oct 2009, 15:40
abhivarma03 wrote:
Now ,my way.guys please let me know if it is wrong.

The only situation that makes 2 false is when x=y=1 or x=1 y=-1.
So C.

I am afraid it is wrong, as already explained, anything between 0 and 1 also makes 2 not work. Or did you mean something else?
Re: DS = Inequality   [#permalink] 23 Oct 2009, 15:40
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