Members Of A Wrestling Team Were Weighed Twice. Was The Standard GMAT Data Sufficiency

Question: Members of a wrestling team were weighed twice. Was the standard deviation of their weights at the second weighing greater than the standard deviation of their weights at the first weighing?

(1) The second weighing showed that, since the first weighing, half of the team had lost 1 pound, while the other half had gained 1 pound.
(2) The standard deviation of all the weights at the first weighing was 0 pounds.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. ​BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Solutions and Explanation
Approach Solution : 1

Statement - 1 : The second weighing showed that, since the first weighing, half of the team had lost 1 pound, while the other half had gained 1 pound.
The information given in the first statement of this question sets up a very cunning trap. According to this, one pound was gained by one team member while one pound was lost by another during the second weighing. It has been good so far. However, it doesn't say which half of the population lost weight and which one gained. It doesn't indicate whether the weights of different people are equal or not. This basically means that we can all assume our own values and arrive at different conclusions.
For illustration, let's imagine that the team consists of four students who are each 10, 20, 30, and 40 pounds. Mean = 25. The individual numbers' deviations from the mean are -15, -5, 5, and 15 respectively.
These deviations' squares are 225, 25, 25, and 225.
Now, in the second weighing, if the first two are reduced by one each and the last two are increased by one each, the mean will be 25 and the deviations will be -16, -6, 6, and 16 respectively. The standard deviation will rise in direct proportion to these deviations.
In another case, if the first two are increased by 1 each and the last two are decreased by 1 each, then the mean value is 25 and the deviations are -14, 4, 4, and 14. The standard deviation will drop as a result of these deviations.
The answer to the posed question is either YES or NO.
Therefore this statement is not sufficient.

Statement - 2 : The standard deviation of all the weights at the first weighing was 0 pounds
We can assume that everyone on the team weighs the same amount (or Zero, which is illogical considering that we are talking about the weights of members of a Wrestling team). The standard deviation will not be zero until all values are equal.
However, this statement says nothing about the second weighing.
Therefore this statement is not sufficient.
We can conclude that all of the values in the data set are equal by combining the two statements. Additionally, the first weighing standard deviation is zero. The deviations from the mean will rise if one half of the values is now increased by 1, while the other half is decreased by 1. The standard deviation in the second weighing will rise as a result. Since all values are equal, it doesn't matter if half of the values are higher or lower than the other half.
The statements when combined are sufficient.

Correct Answer: (C)

“Members of a wrestling team were weighed twice. Was the standard” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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