Ques)If two elements are dropped from set X {-10, -8, 0, 6,

[alanforde800Maximus]

Ques)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 assist with above problem.

[crackverbal]

Hi alanforde800Maximus,

DS questions on the GMAT are very intricate and actually quicker to solve as you can reason out what information will be sufficient to answer the question without actually doing the ugly math.

Here we have a list {-10, -8, 0 , 6, 7} and we need to check if the statements give us sufficient information to find the percentage change in the mean of the list if 2 elements are removed. Keep in mind that this is a value DS question, so we need the statement/s to give us one UNIQUE answer for sufficiency.

Statement 1 : Median of the set remains the same

The median of the list {-10, -8, 0 , 6, 7} is 0. Now if the median has to remain 0 and we have to drop two elements of the list, then this can be done in two ways

1. Drop the elements -10 and 7 from the list which will result in some value of percentage change
2. Drop the elements -8 and -6 from the list which will result in a different value of percentage change than the one obtained in the first case.

Now statement 1 gives us two possible answers for percentage change and since we need one unique answer, statement 1 is insufficient.

Statement 2: The range of the set will decrease by 3

The definition of range is the largest element of the list - the smallest element of the list.

The range for the list {-10, -8, 0 , 6, 7} is 7 - (-10) = 17.

Now since we need to reduce the range of the list by 3 to 14 by dropping two elements of the list, the only possible elements we can drop are -10 and 7 which will leave us with a list {-8, 0, 6} which has a range of 14.

OA : B

Hope this helps!

CrackVerbal Academics Team

[Jay@ManhattanReview]

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 assist with above problem.

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. Well, 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 other 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 (since -10 < -8) and 7 (since 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

_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | London | Dubai | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

[[email protected]]

Hi All,

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

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