Bunuel wrote:

Set A consists of five positive numbers. Set B consists of the square roots of each of the five numbers from Set A. If the standard deviation of Set B > standard deviation of Set A, which of the following must be true?

I. The range of the numbers in Set A is greater than 1

II. At least one of the numbers in Set A is less than 1

III. The range of Set A > Set B

(A) I only

(B) III only

(C) I and III

(D) I and II

(E) II only

I tried in this way

Set A = [1,4,144,144,144]

Set B = [1,2,12,12,12]

I. The range of the numbers in Set A is greater than 1

If all numbers are positive integers then range must be greater than 1.

Even if all numbers in set A are equal then range will be 0 and so it will be of B and hence it will contradict the statement [standard deviation of Set B > standard deviation of Set A]

hence not must be true

II. At least one of the numbers in Set A is less than 1

Not possible as its given that Set A consists of All positive integers

III. The range of Set A > Set B

I find this statement only to be true as None of the Above option is not given

I will go for (B)

Still i dont get it that if its true then according to the set i took , it will contradict the statement [standard deviation of Set B > standard deviation of Set A]

any kind of help will be appreciated

But my vote for B