j_shreyans 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?
51
52
53
54
55
GmatKiss 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?
· 51
· 52
· 53
· 54
· 55
The ages are all close together.
The answer choices imply that the sum of the 4 ages is between 51 and 55, inclusive.
Since 52/4 = 13, the average age must be around 13.
Let J=13.
Since Joan is 2 years younger than Kyle, K=15.
Since Kyle is 3 years older than Lillian, L=12.
Since Miriam is 1 year older than Joan, M=14.
Sum = 13+15+12+14 = 54.
The correct answer is
D.
Algebra:
Let K = Kylie's age.
Since Joan is 2 years younger than Kylie, J = K-2.
Since Kylie is 3 years older than Lilian, L = K-3.
Since Miriam is 1 year older than Joan, M = (K-2) + 1 = K-1.
Sum of all four ages:
K + (K-2) + (K-3) + (K-1) = 4K - 6.
Implication:
The sum of the ages must be 6 less than a multiple of 4.
The smallest multiple of 4 greater than all of the answer choices is 60.
6 less than 60 = 60-6 =
54.
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