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16 Sep 2014, 01:06
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If set \(T\) is obtained by multiplying every elements of set \(S\) by 2, is the median of set \(T\) greater than that of set \(S\) ?
(1) All elements of set \(S\) are positive.
(2) The median of set \(S\) is positive.
(1) All elements of set \(S\) are positive.
(2) The median of set \(S\) is positive.
16 Sep 2014, 01:06
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Official Solution:
If set \(T\) is obtained by multiplying every element of set \(S\) by 2, is the median of set \(T\) greater than that of set \(S\) ?
The median of a set is either the middle term or the average of two middle terms of the set, when the terms are arranged in ascending or descending order. This implies that when all elements of a set are multiplied by 2, its median is also multiplied by 2.
Consider three cases:
• If the median of \(S\) is negative, the media of \(T\) will be less than that of \(S\). For example, if the median of \(S\) is -10, the median of \(T\) will be -20, and hence less than that of \(S\).
• If the median of \(S\) is 0, the media of \(T\) will also be 0, and the medians will be equal.
• If the median of \(S\) is positive, the media of \(T\) will be greater than that of \(S\). For example, if the median of \(S\) is 10, the median of \(T\) will be 20, and hence greater than that of \(S\).
(1) All elements of set \(S\) are positive. This implies that the median of set \(S\) is positive. Therefore, the median of \(T\) is greater than that of \(S\). Sufficient.
(2) The median of set \(S\) is positive. As discussed earlier, this means that the median of \(T\) is greater than that of \(S\). Sufficient.
Answer: D
If set \(T\) is obtained by multiplying every element of set \(S\) by 2, is the median of set \(T\) greater than that of set \(S\) ?
The median of a set is either the middle term or the average of two middle terms of the set, when the terms are arranged in ascending or descending order. This implies that when all elements of a set are multiplied by 2, its median is also multiplied by 2.
Consider three cases:
• If the median of \(S\) is negative, the media of \(T\) will be less than that of \(S\). For example, if the median of \(S\) is -10, the median of \(T\) will be -20, and hence less than that of \(S\).
• If the median of \(S\) is 0, the media of \(T\) will also be 0, and the medians will be equal.
• If the median of \(S\) is positive, the media of \(T\) will be greater than that of \(S\). For example, if the median of \(S\) is 10, the median of \(T\) will be 20, and hence greater than that of \(S\).
(1) All elements of set \(S\) are positive. This implies that the median of set \(S\) is positive. Therefore, the median of \(T\) is greater than that of \(S\). Sufficient.
(2) The median of set \(S\) is positive. As discussed earlier, this means that the median of \(T\) is greater than that of \(S\). Sufficient.
Answer: D
02 Nov 2016, 10:31
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What if the elements are Fractions? the statement does not say that the numbers are integers, for example if Set S is (1/4, 1/3 and 1/2) then if you multiply all elements by 2 then the new set would be (1/8, 1/6 and 1/4) thus the median would not be greater in any of the 2 statements. hat am I not seeing?
