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

The question asks about the percentage change between the old mean and the mean of the new set. How is the change 100%?

Hi HuongShashi,

I think that you're confusing the 'MEDIAN' with the 'MEAN'...

While you're correct that the MEDIAN (0) will stay the same in both groups, the question does NOT ask about the change in median, it asks about the percentage change in the MEAN.

The groups (-10, 0, 6) and (-8, 0, 6) have DIFFERENT averages/means, so the percentage change from the original mean will be DIFFERENT. By extension, this gives us two different answers to the question and Fact 1 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

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

Question asked- percentage change in its mean?

Inference:- We need to know those two numbers in order to find % drop in mean

(1) The median of the set will remain the same
Median will remain '0'. That means one number from -10, -8 is dropped and one number from 6,7 is dropped.

This doesn't give us exact numbers. Hence, Insufficient

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

Current range = 7- (-10)= 17
New range= 14
Out of given numbers only 6 and -8 will yield the desired range. Hence, the dropped out numbers are -10 and 7. We can find % drop now

B is the answer

Answer:B
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
1- The median will remain the same ⇒ one number before 0 (-10, or -8) and one number after 0 (6 or 8) should be removed.
As long as we have 4 different variations of numbers that can be removed, we cannot have a single answer -- INSUFFICIENT
2- The range of X is 17. the new range will be 17-3=14 ⇒ -10 and 7 should be removed. we have just one answer for the new mean -- SUFFICIENT

The average (mean) of set X is \(\frac{-10-8+6+7}{5}=\frac{-5}{5}=-1\)

(1) The median of set X will remain the same. This means that two elements that are dropped from X, one will be in {-10, -8} and one will be in {6, 7} so that the median of X will be 0.

If we drop -10 and 7, new set X'={-8, 0, 6} and the average is \(\frac{-8+6}{3}=\frac{-2}{3}\). The average changes.

If we drop -8 and 6, new set X''={-10, 0, 7} and the average is \(\frac{-10+7}{3}=\frac{-3}{3}=-1\). The average remains the same.

Insufficient.

(2) The range of X is \(7-(-10)=17\). The range of new set (or X') decrease by 3, or \(17-3=14\).

In set X = {-10, -8, 0, 6, 7}, there are only 2 elements that one is 14 greater than another: -8 and 6. Hence, we must drop -10 and 7 so X' = {-8, 0, 6} will have the range 14.

Now, if we know what new set is, we'll know the percentage change in its mean, does't matter how many. Sufficient.


The answer is B

Hi anairamitch1804,

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:

GMAT assassins aren't born, they're made,
Rich

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