Group X has 6 students, 3 boys who are each j years old, and 3 girls who are each k years old. Group Y has...

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Group X has 6 students, 3 boys who are each j years old, and 3 girls who are each k years old. Group Y has 4 students, 1 boy who is j years old and 3 girls who are each k years old. What is the variance of the ages in group Y?

1) The standard deviation of X is 0
2) j=k

OA D
Source: — Data Sufficiency |

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AAPL wrote:
Mon Jun 08, 2020 4:53 am
Economist GMAT

Group X has 6 students, 3 boys who are each j years old, and 3 girls who are each k years old. Group Y has 4 students, 1 boy who is j years old and 3 girls who are each k years old. What is the variance of the ages in group Y?

1) The standard deviation of X is 0
2) j=k

OA D
Given that information, the data in the groups are

Group X: j, j, j, k, k, k;
Group Y: j, k, k, k

Note that the computation of Standard Deviation / Variance is not within the scope of the GMAT; however, its interpretation is.

Variance is the square of Standard Deviation (SD).

Standard Deviation (SD) is a measure of the spread of data. Closer the data are to their mean, less is their SD and vice-versa.

Let's take each statement one by one.

1) The standard deviation of X is 0.

Since SD = 0, each data of group X is equal to its mean. This means that j = k.

Since j = k, SD of group Y would also be 0.

So, the variance of the ages in group Y = SD^2 = 0^2 = 0. Sufficient.

2) j = k

This statement is same as statement 1. Sufficient.

Correct answer: D

Hope this helps!

-Jay
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Given that:
- group X has 6 students
- group X has 3 boys
- group X has 3 girls
- all boys in X are j years old
- all girls in X are k years old

Group Y has 4 students
- group Y has 1 boy
- group Y has 3 girls
- all boys in group Y are j years old
- all girls in group Y are k years old

Target question => What is the variance of the ages in group Y?

Statement 1 => The standard deviation of X is 0
Standard deviation can only be 0 only if all the data/values are identical
Therefore j = k
For group Y with 4 students and j = k
Assuming j = 2
$$mean=\frac{2+2+2+2}{4}=\frac{8}{4}=2$$
$$variance\ =\frac{\left(data\ value-mean\right)^2}{data\ set}$$
$$=\frac{\left(2-2\right)^2}{4}=\frac{0^2}{4}=\frac{0}{4}=0$$
So variance = 0 when standard deviation = 0 and data values are identical. Statement 1 is SUFFICIENT

Statement 2 => j = k
data value are identical variance will be = 0. This is the same as statement 1 hence, statement 2 IS SUFFICIENT

Since each statement alone IS SUFFICIENT,
Answer = D