A wolf in sheep skin??

[yregister]

Source: 198 level 700+ Questions

26) If the average of five numbers, x, 7, 2, 16, and 11 = the median, what is x?
a. 7 < x > 11
b. x is median of the five numbers

OA:D
IMO:E

[mp2437]

Statement 2 gives the same inequality as statement 1. If it is given that x is the median, and you are given the other numbers there, then you know x has to be between 7 and 11.

Also, the stem of the question tells you that the average of the 5 numbers is equal to the median. Therefore, (36 + x)/5 = x (average = median), so you can solve for x. x = 9. Either statement is sufficient to give you this, so answer is D.

[yregister]

Crap, i made the silly mistake of dividing the second avg by 4 instead of 5. Thanks a lot

[nakul_anand]

Looks to me like the answer is B.

Are you sure about the 1st statement?
Is it 7<x>11?or is it 7<x<11?

If we go with 7<x>11 -

Statement(II)

(x+2+7+11+16)/5 = x
so x = 9
II is SUFF

Statement (I)

x=9 and x=19 will both satisfy the criteria.

we know that x=9 works.

Now if x=19 , the series becomes 2,7,11,16, and 19. The average of this series is equal to 11 and so is the median.
If this is the case, then Statement I is INSUFF
Hence, the answer is (B)

We cannot assume x as the median in this statement.

But if statement (I) is 7<x<11, then we know for sure that x=9. And if that's the case, (D) is the right answer.

But again, not sure if the inequality given in statement (I) is - 7<x>11 or 7<x<11. Could you please shed some light on this?

Thanks