What is the SD of a Given Set of Numbers Whose Average is 5? GMAT Data Sufficiency

Question: What is the SD of a given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average
(2) The Standard deviation is 0 when value of each of the given number is increased by 7

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

In order to answer this, we must be aware of a few crucial properties:
Each term in a set will change in value by the same constant if we add or subtract a constant from it.
SD won't modify it.

The mean will change by the same percentage whether we increase or decrease each term in a set by the same percentage (multiply all terms by the constant).
SD will change either way by the same percentage.
A list will contain only identical elements if the range or standard deviation of the elements is 0. Conversely, if a list has just identical members, its range and standard deviation are both 0. If there is only one element in the list, the range and SD are both 0.

This is so that SD = 0 since there is no deviation from the mean when a list comprises only identical members.

(1) None of the values exceed this Average — if no number exceeds the mean, then no number below the mean must also be present, indicating that all of the entries in this list are identical (or that there is only one element that is identical), therefore SD is equal to zero.
(2) The Standard deviation is 0 when the value of each of the given numbers is increased by 7 — hence, the SD remains constant whether we add or subtract a constant from each term in a set. Sufficient.

D is the correct choice

Approach Solution 2:

from:1
All items in the set are identical because the mean is 5 and none of the elements are bigger than the mean, hence the SD is 0 and all items in the set are 5.

from: 2
The SD won't change even if all the objects have a constant added to them. Consequently, the original set's SD is equal to 5

By the way, since both assertions provide SD, the correct response is D.

Approach Solution 3:
(1) None of the numbers are greater than this Average --> if no number is more than the mean then no number is less than mean, which implies that this list contains all identical elements (or which is the same just one element), so SD=0. Sufficient.
(2) The Standard deviation is 0 when the value of each of the given numbers is increased by 7 --> if we add or subtract a constant to each term in a set SD will not change, so SD=0. Sufficient.

“What is the SD of a given set of numbers whose average is 5?”- 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 Quant Questions:

• 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