acfuture wrote:

Joan, Kylie, Lillian, and Miriam all celebrate their birthdays today. Joan is 2 years younger than Kylie, Kylie is 3 years older than Lillian, and Miriam is one year older than Joan. Which of the following could be the combined age of all four women today?

1. 51

2. 52

3. 53

4. 54

5. 55

Let the ages be denoted by their starting name J K L M

J = K-2

K = L +3

M = J + 1

We need J+K+L+M

represent K L M in terms of J

k=J+2

L = K -3 --> L = J + 2 -3 --> L = J-1

M= J + 1

Hence J+K+L+M =J + J +2 + J -1 + J +1

= 4J + 2

J has to be an integer and multiple of 4 since Bday is today

If J =11, sum of ages = 4*11+2 = 46

If J =12, sum of ages = 4*12+2 = 50

If J =13, sum of ages = 4*13+2 = 54

Hence D --> 54

Heman