List Q contains 3 elements. What is the median of list Q ?

[BTGmoderatorDC]

List Q contains 3 elements. What is the median of list Q ?

(1) The mean of list Q is 7.
(2) The mode of list Q is 5.

OA B

Source: Princeton Review

[Jay@ManhattanReview]

List Q contains 3 elements. What is the median of list Q ?

(1) The mean of list Q is 7.
(2) The mode of list Q is 5.

OA B

Source: Princeton Review

Let's take each statement one by one.

(1) The mean of list Q is 7.

=> Sum of the three numbers = 7*3 = 21

Case 1: Say the three numbers are 2, 5, 14. Median = 5.
Case 2: Say the three numbers are 7, 7, 7. Median = 7.

No unique answer. Insufficient.

(2) The mode of list Q is 5.

In a list, a mode is the value of the number that occurs most of the times. Since there are only 3 numbers in the list, and the mode is 5, there are at least two 5s in the list.

Case 1: Say the three numbers are 5, 5, 5. Median = 5.
Case 2: Say the three numbers are 5, 5, 10. Median = 5.
Case 3: Say the three numbers are 2, 5, 5. Median = 5.

Unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Classes Zurich | GMAT Prep Courses Jakarta | LSAT Prep Courses Dallas | SAT Prep Classes Las Vegas | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

[deloitte247]

What is the median of list Q?
Let Q = [w, x, y]; find x.
Statement 1=> The mean of list Q is 7.
$$Mean=\frac{sum\ of\ fx}{sum\ of\ f}=\frac{w+x+y}{3}=7$$
$$w+x+y=21$$
w and y are unknown, hence, median cannot be evaluated. Therefore, state,emt 1 is INSUFFICIENT.

Statement 2=> The mode of list Q is 5.
A mode is an element with the highest frequency. This means that 5 must occur in the list at least twice.
If list Q = [5, 5, 5], then 5 is the median
If list Q = [5, 5, y], then 5 is the median
If list Q = [w, 5, 5], then 5 is the median
Hence, statement 2 alone is SUFFICIENT.

Our answer, therefore, is option B.