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inequality

by Gurpinder » Tue Aug 31, 2010 2:36 pm
Hey guys,

if we manipulate statement:

(1)
x-y=1/2 or x=y+1/2

(2)
x>y

But how does this answer whether x and y are both positive?
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Source: — Data Sufficiency |

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by Rahul@gurome » Tue Aug 31, 2010 7:05 pm
Solution:
Consider first statement (1) alone.
2x - 2y = 1.
Let x = 1 and y = 1/2.
So 2x - 2y = 1 and x and y are both positive.
Next let x = 1/4 and y = -1/4.
Again 2x - 2y = 1 and x is positive and y is negative.
So we cannot say definitely from statement (1) alone whether x and y are both positive or not.

Next consider statement (2) alone.
It says x/y > 1 or (x-y)/y > 0.
So either case (1) x > y and y > 0
Or case (2) x < y and y < 0.
For example let x = 4 and y = 2, then x/y = 4/2 = 2 > 1.
Here both x and y are positive.
Next let x = -4 and y = -2, then x/y = (-4)/(-2) = 2 >1.
Here both x and y are negative.
So again from statement (2) alone, we cannot say definitely whether x and y are both positive or not.

Next combine both the statements together and check.
On combining we have that x = y + 1/2 .
Since (x-y)/y > 0, we have that (y+1/2 - y)/y > 0.
Or 1/2y > 0.
Or 2y > 0.
Or y > 0.
Also if y > 0, as seen from case (1), x > y and so x > 0.
Or both x and y are positive.

The correct answer is hence (C).
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by pradeepkaushal9518 » Tue Aug 31, 2010 11:57 pm
are x and y both positive means x>0 and y>0 ?

1.2x-2y=1

x-y=1/2

x=-1/2 y=-1 x-y=1/2
x=1 y=1/2 x-y=1/2 so cant say not suff

2.x/y>1

x=-2 y=-1 x/y=2>1
x=2 y=1 x/y>1 so cant say not suff

left wid c and E

combine both x-y=1/2 and x/y>1

x=1 y=1/2 x-y=1/2 and x/y= 2> 1 hence both positive
x=-1/2 y=-1 x-y=1/2 and x/y= 1/2 < 1

hence both the conditions are satisfaied if both x and y are positive hence together they are sufficient

so C
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