problem solving

[ddm]

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?
A.51
B.52
C.53
D.54
E.55

[singhr10]

we have the following equations.
J = K-2
K= 3+L
M = 1+J

J+K+L+M = SUM OF AGE

K-2 +K+L+1+J
K-2 +K-2+3+L+J= SUM
K-2+K-2+K+K-2 = SUM (SUB FOR J AND K)
4K-6 =SUM

FROM THE BELOW OPTIONS
4K = 6+54 (SINCE THIS OPTION WILL ONLY BE DIVISIBLE BY 4

K= 60/4 = 15
Hence ans is 54....

[JohnRapp]

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?
A.51
B.52
C.53
D.54
E.55

First set up the relationships into equations:
J=K+2
K=L+3
M=J+1

Given these relationships, I ordered them from youngest to oldest with the difference in between.
L +3 K +2 J +1 M +0

The sum of the differences in relationships = 6.

The only age divisible by 6 is [spoiler]D (54)[/spoiler]

[Anurag@Gurome]

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?
A.51
B.52
C.53
D.54
E.55

Say, age of Kylie is n years.
=> Age of Joan is (n - 2) years
=> Age of Lilian is (n - 3) years
=> Age of Miriam is (n - 1) years

Hence, total age = (4n - 6) years

Hence, the total age must be 6 less than an integer multiple of 4, i.e. 2 less than an integer multiple of 4. Only such option is 54.

Hence, the correct answer is D.

[chaitanyabhansali]

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?
A.51
B.52
C.53
D.54
E.55

Answer:

Let lillian's age be x today.
then, joan's age = x+1, kylie's age = x+3 and Miriam's age = x+2.

combined age = x+x+1+x+2+x+3 = 4x+6

Put the expression equal to given options one by one.

Only option 'D' i.e 54 satisfies the equation i.e when x comes out to be an integer.

4x+6 = 54
=> 4x = 48
=> x = 12

IMO: D

[GMATGuruNY]

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?
A.51
B.52
C.53
D.54
E.55

We can guess and check VERY quickly.
Given the answer choices, the average age must be around 52/4 = 13.

Let J = 13.
Then:
K = J+2 = 15.
L = K-3 = 12.
M = J+1 = 14.
Sum = 13+15+12+14 = 54.

The correct answer is D.

[tuanquang269]

+ 1 for D