Problem Solving

L, M, N and O are four mothers each of whom has two daughters. Peter wants to find out the
ages of each of the daughters of all the four mothers. However when he asks the mothers the
ages of their children the following is the response she receives
(i) L says when you multiply my daughters ages the answer is 9 and the youngest one was born
in January
(ii) M says when you add the ages of both my daughters and square the answer is 169 .The age
of my older daughter is a perfect cube
(iii)N says that the when you multiply the ages of her daughters the answer is 77. N's own age is
32 years
(iv) O says that upon adding the ages of her daughters the result is a two digit number XY. Upon
multiplying the ages of her daughters the result is a two digit number YX. The ages of both
her daughters are under 10 years
For how many of the mothers can Pater be absolutely sure of the ages of both daughters?

A) I & II

B) I , III, IV

C) II, III

D) IV

E)I,II, III, IV

OAB