For a set X, call the sum of its mean, mode, median, and range S.

Question

For a set  X , call the sum of its mean, mode, median, and range  S . If set  X  contains the number  m , and we remove  m  from the set, does the value of  S  decrease?

(1)  m  is the largest number in the set.

(2)  m  is not the smallest number in the set.

AvidDreamer09 · Answer

s = {Mean+Median+Range}

Median = when the set is arranged in an order, the middle value is the median
Mode = is the value that appears most often in the set
Range=Maximum Value–Minimum Value

Using A and B
We do know much about set X,
1) The number of terms in set X,
2) whether there are more than one term that repeats

Answer E

SanjaySrini · Answer

Experts kindly help.

IanStewart · Answer

There are many problems with this question:

- a "set" in math does not have a "mode", because by definition, sets do not have repeated elements. 
- even if we assume the question is discussing a list or data set, the value S here is not well-defined, because it's not clear what the value of S would be for lists with two modes 1, 1, 99, 99, or for lists with no mode, say 1, 2, 3, 4

To avoid these issues with the mode, if we instead let S be the sum of the mean, median and range of a list of (at least two) values, then removing the largest value from the list will never increase the mean, median or range. So in that case, the sum S of those three statistics will always either decrease, or, in the one case where the list contains just one value repeated many times, stay the same. Because we can't be sure S decreases for that reason, Statement 1 is not sufficient, but since Statement 2 ensures the list contains more than one different value, the two Statements are sufficient together.

So the answer should be C if the question is rephrased to avoid the issues I mention above (as written it's not answerable since S can be undefined, and there's no logically correct way to answer a DS question that asks about a value that might exist or might be undefined).

For a set X, call the sum of its mean, mode, median, and range S.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

For a set X, call the sum of its mean, mode, median, and range S.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards