In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

Question

In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

A. 1
B. 2
C. 3
D. 4
E. 5

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gmatophobia · Answer

The set has odd number of integers, which means the median has to be a part of the set.

Case 1 :

{a, 0, 1,   6  , 9, 10, 11}

We know the sum / difference in the numbers should cancel out with respect to mean.

{a, -6, -5,   0  , +3, +4, +5}

We see that the right side of the mean sums to +12, while the left side of the mean sums to -11. To balance and create a set where the mean is 6, a = 6-1 = 5

{0, 1, 5,   6  , 9, 10, 11}

Due to its value, the position of 'a' should be between 1 and 6.

Case 2:

Lets assume a is the mean.

We know that the set consists of only distinct integer, hence the possible values of a include either 7 or 8

{0, 1, 6,   a  , 9, 10, 11}

Lets take a = 7

{0, 1, 6,   7  , 9, 10, 11}

To balance the set around mean -

{-7, -6, -1,   0  , +2, +3, +4}

We see that that the set is not balanced. Hence a  cannot  be 7.

Lets take a = 8

{0, 1, 6,   8  , 9, 10, 11}

To balance the set around mean -

{-8, -7, -2,   0  , +1, +2, +3}

We see that that the set is not balanced. Hence a  cannot  be 8.

Case 3:

Let's assume a to be at the right of 9

{0, 1, 6,   9  , 10, 11, a}

To balance the set around mean -

{-9, -8, -3,   0  , +1, +2, a}

Thus the value of 'a' should be 19 + 17 = 26. Also note that a can only be placed to the right of 11 due to its value.

Therefore, we can have only 2 sets possible.

IMO - B

Suriya28 · Answer

We can directly answer the question, as the required value a is the mean and median of the seven-numbered set. It can take up values between 7 and 9, considering distinct numbers, the number of values is 2(ie 8 and 9).

vijayakrishnan · Answer

Try substituting 7 and 8 for a. It won’t work. The first answer is the correct approach

shisingh · Answer

As per above explanation, A can only take one value 26 such that median = mean. Where are we getting the second value from?

sum of 0+1+6+9+10+11 = 37
37+A / 7 = 9 = Median

A= 26

Yosemite98 · Answer

When we consider the mean to be 6, we get -> 6*7 = 42 = 37+a -> a=5.

then the set would be  6 ,9,10,11] and 6 is indeed the median and mean, so we have two possibilities, for the mean to be 6 & 9

hope it helps!

In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

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