Bunuel wrote:

If a jar of candies is divided among 3 children, how many candies did the child that received the fewest pieces receive?

(1) The two children that received the greatest number of pieces received a total of 13 pieces.

(2) The two children that received the fewest number of pieces received a total of 11 pieces.

Let the three children be \(A\), \(B\) & \(C\) where candy distribution is \(A>B>C\). we need to find \(C\) the lowest

Statement 1: implies that \(A+B = 13\). or \(A=13-B\).

Hence \((A,B)\) can be: (12,1), (11,2), (10,3), (9,4), (8,5), (7,6). No information given about the lowest distribution Hence

Insufficient,

Statement 2: implies that \(B+C=11\). or \(C=11-B\)

Hence \((B,C)\) can be: (10,1), (9,2), (8,3), (7,4), (6,5). There are multiple values of C possible. Hence

InsufficientCombining 1 & 2, we know that \(A>B>C\) and \(A+B=13\) and \(B+C=11\), from the given pair of possible values for \((A,B)\) and \((B,C)\), only one value satisfies the given conditions simultaneously

\(A=7\), \(B=6\) and \(C=5\). Hence

SufficientOption

C