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15 Sep 2021, 04:05
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C
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What is the median of the set {a, b, c, d}?
1) The average (arithmetic mean) of a and b is 110.
2) The average (arithmetic mean) of c and d is 110.
1) The average (arithmetic mean) of a and b is 110.
2) The average (arithmetic mean) of c and d is 110.
17 Sep 2021, 00:14
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What is the median of the set {a, b, c, d}?
We require middle two values, as median is the average of middle two number when there are even number of integers.
1) The average (arithmetic mean) of a and b is 110.
Nothing about other two numbers.
a+b=110*2=220
a and b are equidistant from 110, that is if a = 100-x, b=100+x
2) The average (arithmetic mean) of c and d is 110.
Nothing about other two numbers.
c+d=110*2=220
c and d are equidistant from 110, that is if c = 110-y, d=110+y
Combined.
So two cases:-
1) If x>y, that is a and b are farther away from 110 than c and d, then the order is 110-x, 110-y, 110+y, 110+x.
Median = \(\frac{110-y+110+y}{2}=110\)
2) If x<y, that is a and b are closer to 110 than c and d, then the order is 110-y, 110-x, 110+x, 110+y.
Median = \(\frac{110-x+110+x}{2}=110\)
In each cases, irrespective of the value of a, b, c and d, the answer is 110.
C
We require middle two values, as median is the average of middle two number when there are even number of integers.
1) The average (arithmetic mean) of a and b is 110.
Nothing about other two numbers.
a+b=110*2=220
a and b are equidistant from 110, that is if a = 100-x, b=100+x
2) The average (arithmetic mean) of c and d is 110.
Nothing about other two numbers.
c+d=110*2=220
c and d are equidistant from 110, that is if c = 110-y, d=110+y
Combined.
So two cases:-
1) If x>y, that is a and b are farther away from 110 than c and d, then the order is 110-x, 110-y, 110+y, 110+x.
Median = \(\frac{110-y+110+y}{2}=110\)
2) If x<y, that is a and b are closer to 110 than c and d, then the order is 110-y, 110-x, 110+x, 110+y.
Median = \(\frac{110-x+110+x}{2}=110\)
In each cases, irrespective of the value of a, b, c and d, the answer is 110.
C
General Discussion
18 Sep 2021, 07:37
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sjuniv32
Statement 1:
We don't know c and d. Insufficient.
Statement 2:
We don't know a and b. Insufficient.
Combined:
a and b are equidistant from 110. c and d are also equidistant from 110. We either have {a, b} or {c, d} as the middle two terms, since one pair must be closer to 110 (or we have a = c, b = d for example). In any case, the median is the average of a and b, or the average of c and d which is 110.
Ans: C
