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02 Oct 2025, 09:51
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Set S consists of five consecutive integers, and set T consists of seven consecutive integers.
Is the median of the numbers in set S equal to the median of the numbers in set T?
Let S = {a-2,a-1,a,a+1,a+2}
and let T = {b-3,b-2,b-1,b,b+1,b+2,b+3}
Is a = b ?
(1) The median of the numbers in Set S is 0
a = 0
Since b is unknown
NOT SUFFICIENT
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T
a-2 + a-1 + a + a+1 + a+2 = 5a = b-3 + b-2 + b-1 + b + b+1 + b+2 + b+3 = 7b
a = 7b/5
If b = 0; a = b = 0
otherwise a is not equal to b.
NOT SUFFICIENT
(1) + (2)
(1) The median of the numbers in Set S is 0
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T
a-2 + a-1 + a + a+1 + a+2 = 5a = b-3 + b-2 + b-1 + b + b+1 + b+2 + b+3 = 7b
a = 7b/5 = 0
a = b = 0
SUFFICIENT
IMO C
Is the median of the numbers in set S equal to the median of the numbers in set T?
Let S = {a-2,a-1,a,a+1,a+2}
and let T = {b-3,b-2,b-1,b,b+1,b+2,b+3}
Is a = b ?
(1) The median of the numbers in Set S is 0
a = 0
Since b is unknown
NOT SUFFICIENT
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T
a-2 + a-1 + a + a+1 + a+2 = 5a = b-3 + b-2 + b-1 + b + b+1 + b+2 + b+3 = 7b
a = 7b/5
If b = 0; a = b = 0
otherwise a is not equal to b.
NOT SUFFICIENT
(1) + (2)
(1) The median of the numbers in Set S is 0
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T
a-2 + a-1 + a + a+1 + a+2 = 5a = b-3 + b-2 + b-1 + b + b+1 + b+2 + b+3 = 7b
a = 7b/5 = 0
a = b = 0
SUFFICIENT
IMO C
07 Oct 2025, 01:38
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I was a little bit confused. I thought there are no alternatives of the median being 0. For that case, statement 2 would have been sufficient. But the thing is:
statement (2) is not sufficient because it allows both possibilities:
statement (2) is not sufficient because it allows both possibilities:
- Example where medians are equal: S = {-2,-1,0,1,2}, T = {-3,-2,-1,0,1,2,3}. Sum = 0, medians = 0.
- Example where medians are not equal: S = {5,6,7,8,9}, T = {2,3,4,5,6,7,8}. Sum = 35 for both, but medians are 7 and 5.
mydreambschool
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