Interesting Set problem - Gmat800

netigen

This is an interesting Range problem. I am trying to figure out the best approach to solve it

kbm1975 · Posted: Thu May 08, 2008 5:34 pm Post subject: answer -> a?

in case
set X={1,4,5,6}
set Y={-1,4,5,6}

(1) no -> sufficient from set X
(2) no(from set X), yes(from set Y) -> insufficinet

therefore A

Is it right?

arorag · Posted: Thu May 08, 2008 6:20 pm Post subject:

Ans should be A. B is not giving anything abt the sign of nos

Stuart Kovinsky · Posted: Thu May 08, 2008 7:06 pm Post subject:

Just a quick note:

(1) is not sufficient alone.

The range of {1, 4, 14} is 13. Adding 13 to the set doesn't increase the range.

The range of {50, 51, 63} is 13. Adding 13 to the set does increase the range.

We can get both a yes and a no, insufficient.

netigen · Posted: Thu May 08, 2008 7:40 pm Post subject:

OA is C

netigen · Posted: Mon May 12, 2008 2:35 pm Post subject:

This is the solution I found for this Q

1. A is insufficient for the reason noted by Stuart above
2. Lets look at option 2

Avg of set A(n) = Total of Set A(n) / n (assuming n=numbers in set A)

Avg of set A(n+1) = Total of Set A(n) + R/ (n+1) < R

Total of Set A(n) + R < R (n+1)

Total of Set A(n) + R < Rn + R

or Total of Set A(n) / n < R

which means that Avg of set A(n) < R

This means that there are number less than and greater than R in the A hence the range will not increase by addition of R hence the ans C

ricaototti · Posted: Tue Sep 02, 2008 9:54 pm Post subject:

I am sorry but I really dont get it why it should be C.
I think it should be E.
I understand why 1 and 2 are wrong... but not why C is correct. Please, can someone explain it better.

Thanks

Nycgrl · Posted: Tue Sep 02, 2008 10:02 pm Post subject:

It should be E...what's OA?

4meonly · Posted: Wed Sep 03, 2008 10:38 am Post subject:

E agree
Waiting for OA

parallel_chase

Ian Stewart · Posted: Wed Sep 03, 2008 3:54 pm Post subject:

The range of a set A is R. A number having a value of R is added to set A. Will the range of set A increase?
1) All numbers in set A are positive.
2) The mean of the new set is smaller than R.

I think the above posts confirm that the answer is either C or E, so I won't bother looking at the statements individually. Let's look at both statements together.

When we add R to set A, the range will only increase if R is either the largest element in the new set, or the smallest element in the new set. We want to know if R could be the largest or the smallest element in the new set.

Let's assume A contains at least two elements, and call the largest g, and the smallest s. So set A is {s, other stuff, g}. Then R = g - s. From this, because g and s are positive, R must be less than g. So R can't be the largest element in the new set.

The only question is whether R might be the smallest; that is, we want to know if it's possible that R < s. This would make R smaller than everything else in the set, since s was the smallest element of the old set. But if R is the smallest element of the new set, there's no way statement 2 could be true; the mean of a set cannot be smaller than its smallest element. So R can neither be the smallest nor the largest element in the set, and the range of the new set must be equal to the range of the old set. Sufficient. C.

Ian Stewart