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# Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal  [#permalink]

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15 Jul 2018, 20:41
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:51) correct 17% (01:38) wrong based on 42 sessions

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Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal to y, what is the median of the set S?

(1) The average (arithmetic mean) of X and Y is 308.
(2) The mode of Set S is 0.

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Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal  [#permalink]

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Updated on: 15 Jul 2018, 22:33
Statement 1:
mean of x and y is 308
x= 1 and y = 307
-9,0,1,11,100,307 Median = 6
x = -2 y = 310
-9,-2,0,11,100,310 Median = 5.5
NS

Statement 2:
Mode is 0
x = 0 y =101
-9,0,0,11,100,101 Median = 5.5
x = 0 y = 3
-9,0,0,3,11,100 Median = 1.5
NS

Statement 1&2:
x = 0/308 y = 308/0
-9,0,0,11,100,308 Median = 5.5
Sufficient.

Therefore C
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Originally posted by vaibhav1221 on 15 Jul 2018, 20:56.
Last edited by vaibhav1221 on 15 Jul 2018, 22:33, edited 1 time in total.
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Re: Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal  [#permalink]

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15 Jul 2018, 21:29
Bunuel wrote:
Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal to y, what is the median of the set S?

(1) The average (arithmetic mean) of X and Y is 308.
(2) The mode of Set S is 0.

St1:- Given, A.M(x,y)=308 or x+y=616 ;with $$x\neq{y}$$,
There are many possibilities of (x,y) which yield x+y=616
So, We have more than one value of median.
Insufficient.

St2:- Mode of set is 0; implies 0 is appears more than one time in the set S.
Since all other members are fixed; hence, either x or y can be 0 not both.
So, when x=0, y may be any number except 0. So, we can't determine a unique median value.
Similarly, when y=0, x may be any number except 0. So, we can't determine a unique median value.
Insufficient.

(1)+(2), we need to fix x+y=626 and x=0 or y=0.

Two cases:
When x=0; then y=626, set S={-9,0,0,11,100,616} So, Median(S)=$$\frac{(0+11)}{2}$$=5.5

When y=0; then x=626, set S={-9,0,0,11,100,616} So, Median(S)=$$\frac{(0+11)}{2}$$=5.5

We have obtained an unique value of median in both the cases.

Sufficient.

Ans. (C)
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PKN

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Re: Set S consist of the values 11, -9, 100, 0, x, and y. if x not equal &nbs [#permalink] 15 Jul 2018, 21:29
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