P = {15, 25, 30, 40, 60, 70, x}.
In set P above, if y is the median and z is the mode, what is the ratio y:z?
(1) If 40 is discarded from the set then the average of the remaining terms is 40.
(2) The median of set P is 40.
OE:
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In set P above, if y is the median and z is the mode, what is the ratio y:z?
(1) If 40 is discarded from the set then the average of the remaining terms is 40.
(2) The median of set P is 40.
OE:
[Reveal] Spoiler:
(1): Sum of the 6 remaining terms after exclusion of 40 is 640 = 240
Sum of the 5 known terms (other than x) is 200
-> x=40, thus median=mode=40, and the wanted ratio = 1:1.
Sufficient
(2): Since median is 40, x has to be at least 40, so that 3 terms are smaller than 40 and 3 are equal to or larger than 40.
Even so, you cannot find the mode
For example, if x is equal to 60 (and then the mode is 60) or it can be equal to 70 (and then the mode is 70).
Since more than one value of the mode, cannot calculate the ratio between the median and the mode
Insufficient
Sum of the 5 known terms (other than x) is 200
-> x=40, thus median=mode=40, and the wanted ratio = 1:1.
Sufficient
(2): Since median is 40, x has to be at least 40, so that 3 terms are smaller than 40 and 3 are equal to or larger than 40.
Even so, you cannot find the mode
For example, if x is equal to 60 (and then the mode is 60) or it can be equal to 70 (and then the mode is 70).
Since more than one value of the mode, cannot calculate the ratio between the median and the mode
Insufficient