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SVP  V
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x, 0, 13, −7, y, 7 In the list of numbers above, if x < y and the  [#permalink]

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x, 0, 13, −7, y, 7

In the list of numbers above, if x < y and the median of the numbers in the list is 8, what is the value of x ?

a. 7

b. 8

c. 9

d. 17

e.17.5

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Re: x, 0, 13, −7, y, 7 In the list of numbers above, if x < y and the  [#permalink]

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MyTurnNow wrote:
x, 0, 13, −7, y, 7

In the list of numbers above, if x < y and the median of the numbers in the list is 8, what is the value of x ?

a. 7

b. 8

c. 9

d. 17

e.17.5

The median of the six numbers is 8 which means that the sum of the third and fourth no is 16
"x" cannot be less than 7 because in that case "7" will be the fourth number {x,-7,0},7, {13,y}. so the third number will be less than or equal to 7. hence in this case maximum sum of third and fourth number will be 14

"x" cannot be greater than or equal to 13 because in that case third and forth term will be be 7 & 13 - {-7,0},7,13,{x,y}. hence the sum of 3rd and 4th term will be 20

So "x" has to be the 4th term of the set. then the sequence will be -7,0,7,x,{13,y}
therefore x+7 =16 or x = 9

Option C
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2759
x, 0, 13, −7, y, 7 In the list of numbers above, if x < y and the  [#permalink]

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MyTurnNow wrote:
x, 0, 13, −7, y, 7

In the list of numbers above, if x < y and the median of the numbers in the list is 8, what is the value of x ?

a. 7

b. 8

c. 9

d. 17

e.17.5

An even number of terms means that median is the average of the two middle terms.

So there will be three terms to the left of the median, and three terms to the right of it.

List integer values in ascending order: -7, 0, 7, 13

Median is 8. There are six numbers. 8 is greater than 7, and it's the average of two middle terms. You can't get an average of 8 from two terms, where one term is 7, unless the second term is greater than 7 and 8. (7+7 divided by 2 = 7, and 7+8 divided by 2 is 7.5.) Answers A and B are out.

So -7, 0, and 7 have to be the first three of the six numbers. There must be three numbers to the right of median 8. They are 13, x, and y.

If 13 were the fourth number, the median would be (13 + 7)/2 = 10. Hence one of the variables has to be the fourth number, and because x<y, it's x.

(x + 7)/2 = 8 (median)
x + 7 = 16
x = 9

Answer C
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Get two SC questions to practice, whose links you can find by date, here. x, 0, 13, −7, y, 7 In the list of numbers above, if x < y and the   [#permalink] 10 Jul 2017, 04:50
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