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Is the product of x and y greater than the sum of x and y?

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Pokhran II
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Is the product of x and y greater than the sum of x and y? [#permalink] New post   11 Aug 2005, 11:12
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A
B
C
D
E

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Is the product of x and y greater than the sum of x and y?

(1) xy -y



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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   11 Aug 2005, 11:49
C should be correct.

Statement 1) tells us that either x or y is negative:

If we pick x=2 and y=-1/2, we have 2*(-1/2) < 2-1/2

If we pick x=-2 and x=1/2, we have -2*(1/2) > 1/2 - 2

1) is not sufficient. You can use the same numbers as above to prove that 2) is also not sufficient, because it only tells us that at least one of the numbers is positive.

When we combine the two statements we have

xy < 0
x+y > 0

The sum is positive and the product is negative => we have enough info to answer the question.
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   11 Aug 2005, 13:20
hmmm

E makes sense to me :)
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   11 Aug 2005, 13:34
fresinha12 wrote:
hmmm

E makes sense to me :)


Why does it make sense to you ?

vasild has just given a very good answer with detailed reasons.
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   11 Aug 2005, 18:37
richardj wrote:
fresinha12 wrote:
hmmm, E makes sense to me :)
Why does it make sense to you ? vasild has just given a very good answer with detailed reasons.


hmmmmm....
the question is tough, because if we solve the equation, yes. but if we try some values, then probably not. lets have this example: if, x= -0.5, y = 1

(i) xy = -0.5 <0
(ii) x+y = -0.5. so not sufficient.

solving the equation,

i, xy<0
ii, x+y>0. so sufficient.... :roll:
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   11 Aug 2005, 22:14
HIMALAYA wrote:

hmmmmm....
the question is tough, because if we solve the equation, yes. but if we try some values, then probably not. lets have this example: if, x= -0.5, y = 1

(i) xy = -0.5 <0
(ii) x+y = -0.5. so not sufficient.

solving the equation,

i, xy<0
ii, x+y>0. so sufficient.... :roll:


Your particular example is wrong. -0.5 + 1 = 0.5 > 0

We have two non-zero numbers of different sign and different magnitude and we know that the positive one is larger in magnitude.

So the sum must be positive, and the product must be negative.
So the sum must always be greater than the product.
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   12 Aug 2005, 03:35
from the stem is XY>X+Y
From A) XY<0 insufficient by itself
From B) X+Y>0 insufficient byitself
both combined will give XY>X+Y so C) seems correct
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   12 Aug 2005, 06:10
richardj wrote:
HIMALAYA wrote:
hmmmmm....
the question is tough, because if we solve the equation, yes. but if we try some values, then probably not. lets have this example: if, x= -0.5, y = 1

(i) xy = -0.5 <0
(ii) x+y = -0.5. so not sufficient.

solving the equation,

i, xy<0
ii, x+y>0. so sufficient.... :roll:


Your particular example is wrong. -0.5 + 1 = 0.5 > 0

We have two non-zero numbers of different sign and different magnitude and we know that the positive one is larger in magnitude.

So the sum must be positive, and the product must be negative.
So the sum must always be greater than the product.

:beat
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   12 Aug 2005, 06:45
Hahaha

E makes sense...but it may not be correct...

fresinha12 wrote:
hmmm

E makes sense to me :)
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Re: Is the product of x and y greater than the sum of x and y? [#permalink] New post   14 Aug 2005, 01:38
The OA is C.

Follow vasild's reasoning.



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Re: Is the product of x and y greater than the sum of x and y? [#permalink]
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