CAT2, Question 16, " Joan, Kylie, Lillian, and Mariam"

[Alexander]

Hi -

I don't understand the setup of this question and the highlighted portion of the explanation. How are we to assume the ages are consecutive integers? How should we know to start with L? I know in these types of problems you look to simplify to a common variable. I just don't understand how it is L. Perhaps I'm missing an assumption.

Thanks,
Alexander

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 people today?

Answer choices: 51, 52, 53, 54, 55.

Explanation:

It may be easiest to represent the ages of Joan, Kylie, Lillian and Miriam (J, K, L and M) on a number line. If we do so, we will see that the ages represent consecutive integers as shown in the diagram:

Since the ages are consecutive integers, they can all be expressed in terms of L: L, L + 1, L + 2, L + 3. The sum of the four ages then would be 4 L + 6. Since L must be an integer (it’s Lillian’s age), the expression 4 L + 6 describes a number that is two more than a multiple of 4:

[tommywallach]

Hey Alexander,

We aren't assuming that. Did you try placing the 4 people on a number line? If you do, you'll see that the constraints of the question MAKE them consecutive. The rest follows pretty logically, but let me know if that doesn't clear things up.

-t

[Alexander]

Thanks Tommy.

It makes sense now, the wording confused me - especially J & M's ages.

I knew we had to simplify everything to one variable, L, but just didnt see the connection under the timed pressure.

[tommywallach]

Hey Alexander,

Totally. It's a funky age question. You can always do these in one of two ways:

1) Picking numbers and seeing what becomes what (Assuming there are NO defined ages in the question or answers)

2) Setting one as a variable and defining the others relative to that first variable.

-t