Age problem

[Capthan]

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
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Please could someone explain this question to me. I can not figure out that the ages represent consecutive integers as it says in its explaination.

[minerr]

I think the answer is: 54.

If we see the age of all 4 w.r.t Kylie's age, then it will look like below:
L J M Kylie
K-3 K-2 K-1 K.

Adding all = 4K-6 = 2(2K-3). Therefore the sum of tthe ages should be an even number. There are 2 options - 52 and 54.
4k-6 = 52 => K=29/2, but Kylie is celeberating her birthday today, so K should be a integer. So this option discarded.

4k-6=54 ==> k=15. So the answer.

[RonPurewal]

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
------------------------------------------------------------------------------------------------------------------------------------------------
Please could someone explain this question to me. I can not figure out that the ages represent consecutive integers as it says in its explaination.

you could also just guess numbers, especially because it's pretty easy to estimate how big the ages should be: the ages are pretty close together, and the total of all four is fifty-something. therefore, (fifty-something)/4 is around thirteen or so, so let's just randomly guess that joan (the first one mentioned - no special reason) is 13.
then kylie is 15, lillian is 12, and miriam is 14.
sum = 54.
lucky guess!

if we were to have guessed joan = 12, then we'd get 12, 14, 11, 13, for a sum of 50; that'd be too small, so we'd just crank up our estimate by 1 year for each girl, and, voilà, 54.

--

still, you should be able to generate algebraic expressions such as the ones in the previous post at a moment's notice; the ones in this problem should be absolutely routine. if you're having trouble generating such expressions, consider borrowing an algebra book from the local library and working the problems that introduce algebraic word translations (usually in the chapters that are introducing algebraic expressions like these for the first time). good times!

[Guest]

In its explanation the ages are consecutive integers, they can all be expressed in term of Lillian or L. I am having hard time to express them in term of L.

My translation of the problem looks like

Joan is 2 yrs younger then Kylie: J + 2=K

Kylie is 3 yrs older then Lillian: k-3=L

Miriam is on yr older then Joan: m-1=j

Could u explain how can I go from here to form an expression in term of Lillian?

[esledge]

Here's how I would set up the problem: Draw a number line the scrapboard, and use dots or letters to represent the ages.

Here's an attempt to reproduce it:

"Joan is 2 years younger than Kylie" becomes <---|----|----(J)----|----(K)----|----|---> (note that | represents integers)

"Kylie is 3 years older than Lillian lets me put Lillian on the line: <---|----(L)----(J)----|----(K)----|----|--->

"Miriam is 1 year older than Joan" puts M one notch to the right of J: <---|----(L)----(J)----(M)----(K)----|----|--->

This method might serve you better than the more abstract algebraic proof.

[BradK592]

I am able to come up with 4L+6, but I am having a difficult time understanding why we need to add 2 to the multiple of 4? Why aren't we adding 6 to the multiple of 4 (4L +6)? I thought the answer should be 58 (52+6), but that is not an answer choice. Can someone please explain how to get from 4L+6 to 4L+2 in a different way than the explanation below, which i took from the CAT exam solutions:
4L + 6 = (4L + 4) + 2
[4L + 4 describes a multiple of 4, since it can be factored into 4(L + 1) or 4 * an integer.]

[RonPurewal]

If you can get 4L + 6, you can solve the problem. You just have to pick the answer choice that can actually be 4L + 6 (with "L" = whole number).
You can just do this by trial and error. You'll figure out soon enough that 54 works.

[RonPurewal]

Regarding your question about the answer key"”
It's difficult to answer that question unless you reproduce that portion of the answer key here. (While moderating the forum, we don't necessarily have access to answer keys for random problems.)

Without seeing the key, my best guess is that they're trying to use the patterns inherent in multiples of 4.
I.e., 4L is a multiple of 4. So is 4L + 4, and 4L + 8, and so on.
By the same token, since 4L + 2 is two more than a multiple of 4, the same must be true for 4L + 6, 4L + 10, and so on.

So, the answer key might just be overzealous about demonstrating this sort of thing. You can just look for something that can be 4L + 6 and be done with it.
(On the other hand, if you were looking for something that could be, say, 4L + 771, then this sort of "reduction" could be extremely useful.)

[JbhB682]

Why should we assume the ages are whole integers ?

52 should be a legitimate answer if the ages are 13.5 or 12.5 ( dont think it says anywhere the ages have to be absolute integers)

Please assist

[Sage Pearce-Higgins]

Sure, but do you celebrate your birthday when you are 13.5?!