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OG Quant Review DS#41

Expert replies
by erjamit » Sun Feb 03, 2008 7:46 am
If S is a set of four numbers w,x,y and z, is the range of the numbers in S greater than 2?

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

My approach was, since range is the difference between maximum and minimum numbers we need to check whether the range of S can be computed.

Statement 1. w-z > 2, however we don't know that w is the max and and z is the minimum. So NOT Sufficient

Statement 2. NOT Sufficient

Combining both since z is the least number so we can assume either w is the maximum number or w is only greater than z and smaller than x and y. Thus, IMO both together are sufficient and hence, answer should be C.

However, the OA is A.

Can someone explain where I am making a mistake.

Thanks
Amit
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Source: — Data Sufficiency |

by Suyog » Sun Feb 03, 2008 8:52 am
before solving, just think about it....

there are 4 numbers and the range is greater than 2..i.e. the difference between any two numbers is more than 2...i.e. if there are 2 numbers out of 4 have difference greater than 2...then it doesn't matter what are the remaining 2 numbers...which is what exactly A says...

Your approach.... i agree that we dont know whos max or min...but what matters here is the difference is > 2....

hope this helps...
Last edited by Suyog on Sun Feb 03, 2008 11:42 am, edited 1 time in total.
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by erjamit » Sun Feb 03, 2008 8:58 am
I am confused since range means difference between the largest and the smallest numbers in a set, and from statement 1 we only know the difference between 2 numbers.
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by Suyog » Sun Feb 03, 2008 9:25 am
Okay....
take any two numbers with cond A, that is the difference is greater than 2... Now for the rest 2.... take any 2 numbers in the world.... Try to solve... Let me know....
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by erjamit » Sun Feb 03, 2008 9:33 am
the answer is ok...so does it mean that the range of a set of numbers will be > than the difference of any two numbers....

i mean we can generalize it for a set containing n numbers
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by Stuart@KaplanGMAT » Sun Feb 03, 2008 11:26 am
erjamit wrote:the answer is ok...so does it mean that the range of a set of numbers will be > than the difference of any two numbers....

i mean we can generalize it for a set containing n numbers
Range is the GREATEST possible difference between 2 numbers in the set.

Therefore, the range will ALWAYS be >= the difference between any pair of numbers in the set.
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