Que: What is the standard deviation of four numbers a, b, c, and d?

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Que: What is the standard deviation of four numbers a, b, c, and d?

(1) Sum of a, b, c, and d is 24.
(2) Sum of squares of a, b, c, and d is 240.

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Elite Legendary Member
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A

B

C

D

E

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Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find ‘S.D. of a, b, c, and d.

Let A = mean of square numbers

B = square of mean of numbers

S.D. = \(\sqrt{A-B}\)


Follow the second and the third step: From the original condition, we have 4 variables (a, b, c, and d). To match the number of variables with the number of equations, we need 4 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Recall 3- Principles and Choose E as the most likely answer. Let’s look at both conditions together.

Condition (1) tells us that the sum is 24.

Condition (2) tells us that the sum is 240.

From 1st: Mean = 6 and square of mean = [m]36[/m]

From 2nd: Mean of squares of numbers = \(\frac{240}{4}=60\)

A = mean of square numbers = 60

B = square of mean of numbers = 36

S.D. = \(\sqrt{60-36=24\approx25}=5\)


The answer is unique, so the conditions combined are sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions together are sufficient.

Therefore, C is the correct answer.

Answer: C