Problem Solving

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

Here's a solution 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

Hi j_shreyans,

The first part of this question requires translating sentences into formulas:

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

Even if you translated these formulas differently, you still have a relationship among the 4 variables that needs to be discovered. You can TEST VALUES to figure out the relationship:

If K = 10, then
J = 8
L = 7
M = 9

Now we know that the 4 values are consecutive.

To solve, you can either use "brute-force" (since the answers are small) or algebra:

Brute-Force:
11 + 12 + 13 + 14 = 50 NOT ENOUGH BASED ON THE ANSWERS
12 + 13 + 14 + 15 = 54 WINNER

Algebra:
Call the youngest person X
X + (X+1) + (X+2) + (X+3) = 4X + 6
If X = 11, total = 50 NOT ENOUGH BASED ON THE ANSWERS
If X = 12, total = 54 WINNER

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