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03 May 2020, 23:37
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The average of 10, 15, and 20 is 15. The SD of these three numbers is 5,0, and 5.
Statement (1) is insufficient. No information about Y
Statement (2) is insufficient. No information about X
Statements (1) and (2) together are sufficient. Why?
X=Z-10
Y=Z-5
Z=Z
These numbers are in ascending order (X<Y<Z). Let set everything in terms of Z and let's find the average and the SD of these numbers
The average of this set of numbers is Z-5. Now find the SD of this set by subtracting the average from each and every number in the set.
SD for X is Z-10 - (Z-5) = Z - 10 - Z + 5 = 5
SD for y is Z - 5 - (Z-5) = Z - 5 - Z + 5 = 0
SD for z is Z - 5 - Z = 5
So the SD of x, y, and z is the same as the SD of 10, 15, and 20.
The correct answer is (C).
Statement (1) is insufficient. No information about Y
Statement (2) is insufficient. No information about X
Statements (1) and (2) together are sufficient. Why?
X=Z-10
Y=Z-5
Z=Z
These numbers are in ascending order (X<Y<Z). Let set everything in terms of Z and let's find the average and the SD of these numbers
The average of this set of numbers is Z-5. Now find the SD of this set by subtracting the average from each and every number in the set.
SD for X is Z-10 - (Z-5) = Z - 10 - Z + 5 = 5
SD for y is Z - 5 - (Z-5) = Z - 5 - Z + 5 = 0
SD for z is Z - 5 - Z = 5
So the SD of x, y, and z is the same as the SD of 10, 15, and 20.
The correct answer is (C).
24 Nov 2020, 12:37
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fozzzy
(1) We have no information regarding Y; INSUFFICIENT.
(2) We have no information regarding X; INSUFFICIENT.
(1&2) We have the following two equations:
\(Z - X = 10\)
\(Z - Y = 5\)
One scenario: \(X = -10, Y = -5, Z = 0 \)
The SD of X, Y, and Z is equal to the SD of 10, 15, 20 because they are spaced out the same way. Notice we could have utilized the numbers 10, 15, and 20 in our set.
SUFFICIENT.
Answer is C.
25 Jun 2025, 04:58
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
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