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.

Suggested GMAT Data Sufficiency Samples

• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• 2x+3y GMAT Data Sufficiency
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Data Sufficiency
• What is the Value of m? (1) |m| = −36/m (2) 2m + 2|m| = 0 GMAT Data Sufficiency
• Do The Diagonals Of A Quadrilateral ABCD Bisect Each Other GMAT Data Sufficiency
• If X = 0.rstu, Where r, s, t, And u Each Represent A Nonzero Digit GMAT Data Sufficiency
• Is The Product Of a And b Equal To 1? GMAT Data Sufficiency
• Material A Costs $3 Per Kilogram, And Material B Costs $5 Per Kilogram GMAT Data Sufficiency
• Is the Product of a Positive and a Negative Integer Less Than -10? GMAT Data Sufficiency
• If k is not Equal to 0, 1, or -1 is 1/k>0? GMAT Data Sufficiency
• If x Is A Positive Integer, What Is The Value Of (x+24)^(½) − x^(½) GMAT Data Sufficiency
• Points x And y Lie On A Line Segment. How Many Units Long Is The Line GMAT Data Sufficiency
• Which Sport Utility Vehicle has a Higher List Price, the Touristo or GMAT Data Sufficiency
• What is The Average (arithmetic mean) Annual Salary of the 6 Employees GMAT Data Sufficiency
• If S is a Set of Ten Consecutive Integers, is the Integer 5 GMAT Data Sufficiency
• What is the Perimeter of a Square Chessboard, If a Chessboard is made GMAT Data Sufficiency
• Is the sum of four different positive prime integers an odd integer? GMAT Data Sufficiency
• Is Positive Integer x Divisible By 24? GMAT Data Sufficiency
• 10 Students took a Chemistry Exam that was Graded on a Dcale of 0 to 100 GMAT Data Sufficiency
• If m and n are positive integers, is the remainder of GMAT Data Sufficiency
• In quadrilateral ABCD, is AC longer than BD GMAT Data Sufficiency
• N is a positive integer. Is n the square of an integer? GMAT Data Sufficiency
• If z Is An Integer Smaller Than Integer n But Greater Than Zero GMAT Data Sufficiency
• If y Is An Odd Number And x^3 ∗ y^4 = 648, y=? 1) y Is Positive 2) x Is GMAT Data Sufficiency
• A Pyramid-Shaped Box To Protect A Plant Is Constructed With 4 Lateral Faces GMAT Data Sufficiency
• Is abc/d an Integer if a, b, c, and d are Positive integers? GMAT Data Sufficiency
• If n is a positive integer, is (1/10)^n < 0.01? GMAT Data Sufficiency
• If m and n are nonzero integers, is m^n an integer? GMAT Data Sufficiency
• In A Certain Office, 50 Percent Of The Employees Are College GMAT Data Sufficiency
• As Shown Above, A Rectangle Is Divided Into Smaller Rectangles Of The GMAT Data Sufficiency
• The Revenue of a Company is Directly Proportional to the Number of Customers GMAT Data Sufficiency
• Starting from the same point, a sparrow and a hawk flew in opposite directions GMAT Data Sufficiency
• Even/Odd: Are Negative Numbers and Decimals Even or Odd? GMAT Data Sufficiency
• If x,y and z are positive numbers, is z between x and y? GMAT Data Sufficiency
• What Is The Value Of 2^X + 2^(-X)? GMAT Data Sufficiency