## BdMO National Primary 2011/10 (Junior 2011/3)

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### BdMO National Primary 2011/10 (Junior 2011/3)

Problem 10:
\$A, B, C, D, E, F\$ are six children of different ages in the range of 11 to 16. It is known that C and F always speak truth whereas among the rest two are truthful and the other two lie. When they are asked about their ages, they replied as follows-

A: The sum of the ages of the other five is an even number.
B: A is the eldest.
C: The sum of the ages of the other five is divisible by 5.
D: E is elder than A by two years.
E: The sum of the ages of A, B, D, E is an odd number.
F: The sum of the ages of the other five is divisible by 5.
Find out: (i) What is the sum of the ages of C and F? (ii) Which two among these six children lie? (iii) What are the ages of A and E?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

1)the sum of the ages of C and F is 27. 2) B and E is telling lie.  3) A is 13 and E is 15 years old.   