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

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by BTGmoderatorDC » Wed Sep 04, 2019 4:32 pm

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Answers

A

B

C

D

E

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Difficulty—

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
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Sep 05, 2019 10:54 pm
BTGmoderatorDC wrote: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
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by deloitte247 » Sat Sep 07, 2019 11:26 pm
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.
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