Problem Solving

Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers and Set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

A. C, A, B
B. A, B, C
C. C, B, A
D. B, C, A
E. B, A, C

The OA is E.

I tried to solve this PS question but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. Can anyone help me with it, please? Thanks.

swerve wrote:Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers and Set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

A. C, A, B
B. A, B, C
C. C, B, A
D. B, C, A
E. B, A, C

The OA is E.

I tried to solve this PS question but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. Can anyone help me with it, please? Thanks.

Hello swerve.

This is how I'd solve it.

We know that: $$A=\left\{11,\ 13,\ 17,\ 19,\ 23\right\}$$ Hence, A, B and C have 5 terms each one.

Now, $$B=\left\{5\ \text{consecutive}\ \text{even}\ \text{integer}s\right\},\ example\ \Rightarrow\ \ \left\{8,\ 10,\ 12,\ 14,\ 16\right\}.$$ $$C=\left\{5\ \text{consecutive}\ \text{multiples}\ \text{of}\ 7\right\},\ example\ \Rightarrow\ \ \left\{7,\ 14,\ 21,\ 28,\ 35\right\}.$$ Now, since the standard deviation shows how much variation there is from the mean, that is to say "how widespread a given set is" we can see that:

- Set C is the most widespread.
- Set B is the least widespread.

Therefore, if we order the sets in an ascending order of the standard deviation we will get: B, A, C.

The correct answer is the option E.