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x and y on different sides of zero point

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by abhi332 » Wed Feb 24, 2010 5:02 am
In the number line, are x and y on different sides of zero point?

1). The distance from x to zero is equal to the distance from y to 1
2). The sum of the distance from x to zero and the distance from y to 1 is less than 1
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Source: — Data Sufficiency |
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by kstv » Wed Feb 24, 2010 6:25 am
IMO E
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by firdaus117 » Wed Feb 24, 2010 11:03 am
It's Option E
Note that it is not necessary that x and y are integers only.They can be any real numbers on the number line.
x=-0.25 and y=0.75 AND x=0.25 and y=0.75.These two sets of values satisfy both conditions yet they are respectively on opp. sides and same sides of zero point. :)
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by girish3131 » Thu Feb 25, 2010 5:26 am
@Abhi

Good Ques...

IMO Ans is C

Plz put OA ...

Thanks!
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by abhi332 » Thu Feb 25, 2010 5:34 am
[spoiler]OA: E[/spoiler]
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by sairamGmat » Thu Feb 25, 2010 8:15 am
I think

Let dx be the distance from x to 0 and dy be the distance from y to 1

Then, from (1) dx = dy [scenarios like x is 0.1 and y is 0.9 where the distance from x to 0 is 0.1 and y to 1 is 0.1 and also
it can be x is -0.2 and y is 0.8.]
so, this is InSufficient
from (2) dx+dy < 1
i.e. |(0-x) | + | 1-y| < 1 . With the same example above we cant really determine if x and y lie on the different sides
X and y can be 0.1 and 0.9 where dx+dy = 0.1 + 0.1 = 0.2 < 1
X and y can be -0.2 and 0.8 in which case dx+dy = 0.2 + 0.2 = 0.4 < 1 INSUFFICIENT

Combining both, dx = dy
dx+dy <1
2dx < 1
dx < 1/2
That means, distance from x to 0 is less than 1/2. so, x can be on either side of the zero before 0.5. Similarly, y
can be also the same dy < 1/2, which means y can also be on either side of the zero. INSUFFICIENT

IMO, E is the answer.

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