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Bunuel
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Set S = {4, x, 1, 4, 1} Is x the median of Set S? 02 Feb 2017, 11:08
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52% (01:10) correct 48% (01:00) wrong based on 156 sessions

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Set S = {4, x, 1, 4, 1}

Is x the median of Set S?

(1) x^2 = 16
(2) x is the mode of Set S.
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Set S = {4, x, 1, 4, 1} Is x the median of Set S? 02 Feb 2017, 22:06
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(1) x^2 = 16; So, x = 4, or x = -4;
Case 1: x = 4:
Set S = {4, 4, 1, 4, 1} = {1, 1, 4, 4, 4}; Median is 4 (x);

Case 2: x = -4:
Set S = {4, -4, 1, 4, 1} = {-4, 1, 1, 4, 4}; Median is 1 (not x);

Hence (1) is insufficient.

(2) x is the mode of Set S.
x can be either 1 or 4;
Case 1: x = 1:
Set S = {4, 1, 1, 4, 1} = {1, 1, 1, 4, 4};
Therefore Median = mode = 1 = x;

Case 2: x = 4:
Set S = {4, 4, 1, 4, 1} = {1, 1, 1, 4, 4};
Therefore Median = mode = 4 = x;

Hence, when x is the mode, irrespective of the value of x, mode = median = x. Sufficient.
Ans B.

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Set S = {4, x, 1, 4, 1} Is x the median of Set S? 03 Mar 2017, 04:07
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saswata4s
(1) x^2 = 16; So, x = 4, or x = -4;
Case 1: x = 4:
Set S = {4, 4, 1, 4, 1} = {1, 1, 4, 4, 4}; Median is 4 (x);

Case 2: x = -4:
Set S = {4, -4, 1, 4, 1} = {-4, 1, 1, 4, 4}; Median is 1 (not x);

Hence (1) is insufficient.

(2) x is the mode of Set S.
x can be either 1 or 4;
Case 1: x = 1:
Set S = {4, 1, 1, 4, 1} = {1, 1, 1, 4, 4};
Therefore Median = mode = 1 = x;

Case 2: x = 4:
Set S = {4, 4, 1, 4, 1} = {1, 1, 1, 4, 4};
Therefore Median = mode = 4 = x;

Hence, when x is the mode, irrespective of the value of x, mode = median = x. Sufficient.
Ans B.

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hi

can you clarify that whether i am right to what i thought about this problem, i think the question is asking is x can be median or not so in statement 2 ,we have two values for median 1 and 4 but we do need to think about it ,right, we need to answer that is x cane be median or not ?
please explain
thanks
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Set S = {4, x, 1, 4, 1} Is x the median of Set S? 03 Mar 2017, 05:59
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So, to be the median of set x must be 1<=x<=4
(1)|x|=4, thus x may be or may be not the median. Insufficient.
(2) to be the mode of subject set x should be equal either to 1 or 4, thus it will median of subject set for sure. Sufficient.
I do believe that it should be classified as an easy one, not (700+) for sure at least...
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Set S = {4, x, 1, 4, 1} Is x the median of Set S? 03 Mar 2017, 06:41
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nks2611
saswata4s
(1) x^2 = 16; So, x = 4, or x = -4;
Case 1: x = 4:
Set S = {4, 4, 1, 4, 1} = {1, 1, 4, 4, 4}; Median is 4 (x);

Case 2: x = -4:
Set S = {4, -4, 1, 4, 1} = {-4, 1, 1, 4, 4}; Median is 1 (not x);

Hence (1) is insufficient.

(2) x is the mode of Set S.
x can be either 1 or 4;
Case 1: x = 1:
Set S = {4, 1, 1, 4, 1} = {1, 1, 1, 4, 4};
Therefore Median = mode = 1 = x;

Case 2: x = 4:
Set S = {4, 4, 1, 4, 1} = {1, 1, 1, 4, 4};
Therefore Median = mode = 4 = x;

Hence, when x is the mode, irrespective of the value of x, mode = median = x. Sufficient.
Ans B.

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hi

can you clarify that whether i am right to what i thought about this problem, i think the question is asking is x can be median or not so in statement 2 ,we have two values for median 1 and 4 but we do need to think about it ,right, we need to answer that is x cane be median or not ?
please explain
thanks
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the question asks if x IS the median..the difference is that according to the question regardless of the value of x, it must always be the median and not only sometimes in which case answer would be D.
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