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two DS problems

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by kishokbabu » Thu Dec 29, 2011 1:01 pm
problem 1.:

If S is a set of 4 nos w,x,y, & z , is the range of the nos in S greater than 2?

1) w-z >2
2) z is the least number in S.

Problem 2.:


If Y is greater than 110 percent of X, is Y greater than 75 ?

a) X >75
b) Y-X = 10
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Source: — Data Sufficiency |
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by neelgandham » Thu Dec 29, 2011 1:09 pm
If S is a set of 4 nos w,x,y, & z , is the range of the nos in S greater than 2?
1)w-z >2
Implies that the difference between one pair of numbers in the set is more than 2. For e.g. if set S = {1,2,5,6} and w = 5 and z = 2(w-z>2), the range is 6-1 = 5>2. It is Sufficient to tell that the range of the numbers in set S is greater than 2.
2)z is the least number in S.
Insufficient and Irrelevant

IMO A
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by neelgandham » Thu Dec 29, 2011 1:18 pm
If Y is greater than 110 percent of X, is Y greater than 75 ?
a)X >75
If X > 75, Y > 1.1X >82.5. So Y is greater than 82.5(and greater than 75). Hence Sufficient!
b)Y-X = 10
Y = X + 10
If X+10(=Y) > 1.1X
i.e If X<100 then is Y greater than 75
Let X = 10, then Y = 20, and Y is not greater than 75
Let X = 70, then Y = 80, and Y is greater than 75. Two different answers. Hence Insufficient!

IMO A
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by Anurag@Gurome » Fri Dec 30, 2011 4:54 am
If y is greater than 110 percent of x, is y greater than 75?
(1) x < 75
(2) y - x = 10
y > 110% of x => y > (1.1)x

Statement 1: x < 75
If x = 10 => y > 11 => y may be less than or greater than 75.

Not sufficient

Statement 2: (y - x) = 10
Implies, x = (y - 10)
Hence, y > (1.1)*(y - 10)
=> y > (1.1y - 11)
=> 11 > 0.1y
=> y < (11/0.1) = 110

Not sufficient

1 & 2 Together: x < 75 and y = (x + 10)
If x = 40, y = 50 < 75
If x = 70, y = 80 > 75

Not sufficient

The correct answer is E.
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by ArunangsuSahu » Fri Dec 30, 2011 9:05 am
@Anurag..

x>75 or x<75?
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