Combined age

[prernamalhotra]

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

Thank you,
Prerna

[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?

· 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.

[kvcpk]

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

Thank you,
Prerna

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

Combined ages = J+K+L+M = K-2+K+K-3+K-1 = 4K-6

Hence Answer+6 should be a multiple of 4. Hence 54.

Hope this helps!!

[Brent@GMATPrepNow]

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 also solve the question using ONE VARIABLE.

Let's let Joan's age = J (aside: we could assign the initial variable to someone else's age, but at first glance Joan appears to be one of the younger people, and it's often easier to assign the first variable to the smallest/smaller value)

Joan is 2 years younger than Kylie: So, Kylie's age = J+2
Kylie is 3 years older than Lillian: In other words, Lillian's age is 3 years less than Kylie's age. So, Lillian's age = (J+2)-3 = J-1
Miriam is one year older than Joan: So, Miriam's age = J+1

The sum of all 4 ages = J + (J+2) + (J-1) + (J+1) = 4J+2

IMPORTANT: The sum of the ages is 2 more than some multiple of 4.
Scan the answer choices.
52 is a multiple of 4.
So, 54 is 2 more than some multiple of 4
Answer = D

Cheers,
Brent

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Hi Prerna,

Along with all of the "math" solutions offered, this question can also be solved "visually" (and with a bit of TESTing Values). Here's how:

I'm going to put the women "in order" from least to greatest in age.

"Joan is 2 years younger than Kylie"

Joan, <1 year>, Kylie

"Kylie is 3 years older than Lillian"

Lillian, Joan, <1 year>, Kylie

"Miriam is 1 year older than Joan"

Lillian, Joan, Miriam, Kylie

We now know that the ages are CONSECUTIVE. Since the answers are all in the 50s, we know that the youngest needs to be older than 10.

If the ages were:
11, 12, 13, 14....then the total would be 50, which is not a match to any of the answers.

12, 13, 14, 15...then the total would be 54, which IS a match.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich