If the set S consists of five consecutive positive integers, what is..

(1) The integer 11 is in \(S\), but 10 is not in \(S\).
Since numbers in the series S are consecutive, there cannot be any skipping among the number.
If 10 is not there but 11 is there, then the series should start with 11
S={11,12,13,14,15};
out of these 12 and 14 are even
SUM OF THE SERIES CAN BE EASILY FOUND (11+12+13+14+15)
SUFFICIENT

(2) The sum of the even integers in \(S\) is 26
Since there are total of 5 consecutive integers in the series so there are two possibilities

O+E+O+E+O=SUM TOTAL of the series (In this case there are two even numbers in the series)
E+O+E+O+E= SUM TOTAL of the series (In this case there are three even numbers in the series)

O+E+O+E+ O means two consecutive even number and the sum of these even number = 26
==>E+(E+2)=26
==>2E=24
==>E=12
==> therefore First even = 12 ; second even (12+2) =14

EOEOE means there are three consecutive even numbers
E+(E+2)+(E+4)=26
==>3E+6=26
==>3E=26-6
==> 3E= 20
==> E=20/3
==> E= 6.666666666

This value of E is NOT ACCEPTABLE because its not an integer value. Therefore it means that the Series E+O+E+O+ E cannot exist.

Therefore we that only two even number exist in series S such that their sum = 26 which we know are 12 & 14 (since only 12 +14 can yield 26)

SO in any case both cases gives unique values

ANSWER IS D