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If two elements are dropped from set X {-10, -8, 0, 6, 7}, w

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Source: — Data Sufficiency |

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by [email protected] » Sun Dec 11, 2016 7:09 pm
Hi Anaira Mitch,

From the prompt, we can calculate the MEAN of the original 5 values... -5/5 = -1. We're asked for the percentage change in the MEAN after we remove two of the numbers from the original set:

{-10,-8, 0, 6, 7}

1) The median of the set will remain the same.

The current median is 0. If the median remains the same after removing the two values, then we could end up with a four different groups:

{-10, 0, 6] Avg = -4/3
{-10, 0, 7} Avg = -3/3 = -1
{-8, 0, 6} Avg = -2/3
{-8, 0, 7} Avg = -1/3

Each of these groups has a different average, so the percentage change would be different for each.
Fact 1 is INSUFFICIENT

2) The range of the set will decrease by 3.

The current range is 7 - (-10) = 17. If we decrease that value by 3, we'll end up with a range of 14. With the set of numbers that we're working with, there's only one sub-group that can occur:

{-8, 0 , 6}
Fact 2 is SUFFICIENT

Final Answer: B

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by Jay@ManhattanReview » Thu Dec 15, 2016 12:41 am
Anaira Mitch wrote:If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean?
(1) The median of the set will remain the same.
(2) The range of the set will decrease by 3.

Please help with above problem.
Hi Anaira,

Let's not be tempted to calculate the mean as of now. Maybe you need not do so at all.

S1: Let's first arrange set X in an ascending order. It is already arranged so.

Currently the median = 0 (the middle-most number).

Since the median remains 0 after the drop of two elements, one of them would be one between -10 and -8 and one between 6 and 7. We can conclude that mean would vary depending on which two elements are removed. We will NOT get a unique answer for the percentage change in mean value. Insufficient!

S2: Currently, the range = 7 - (-10) = 17; New range = 17 - 3 = 14. We see that for Set X: {-10, -8, 0, 6, 7}, only two elements -8 and 6 make 14 [new range = 6 - (-8) = 14]. This means that -8 and 6 are must in the set. This implies that only one among -10, 0, and 7 is there is the set.

Since -8 should be the smallest and 6 should be the largest value in the set, there is no place for -10 (-10 < -8) and 7 (7 > 6) in the set.

=> 0 is there in the set.

=> The new set is: {-8, 0, 6}. We can surely calculate the mean, thus the percentage change. There is no need to calculate mean and the percentage change. This is a DS question and one must be sure that one gets a unique answer. Sufficient!

Hope this helps!

-Jay

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