math ps, source manhattan cat tests

[karan13]

hey i think the question is wrong once i have read the solution for it ... In the first sentence of the question it is said that we have to pay 1000 or 50% whicever one is lower but the answer is saying that we have to x-1000 or 50% where is the total amount due... please explain....

Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
$600
$1000
$3800
$5300
$6200


explanation:
We can approach this problem in two ways. The first, and probably easier, method is to work backward from the answer choices and calculate how much Plans A and B pay out in each case. When the two calculated amounts are the same, we will have found our answer. For example, when the total cost is $600, Plan A requires the insured to pay $300, and the insurance plan pays the remaining $300. In contrast, Plan B requires the insured to pay the initial $300, and 20% of the excess of $600 - $300 = $300, which amounts to a total of $300 + (20%) × $300 = $360 out of the pocket of the insured. The plan pays for the remaining $240. We can see that the two amounts are not the same, so A is not our answer. We would then proceed to check the remaining answer choices in a similar manner.

An algebraic approach is the other possibility. First we need to determine how much Insurance Plan A pays. The question states that the insured pays either $1000 or 50% of the total cost, whichever is lower. Let x be the total cost. If the insured pays $1000, then the insurance plan pays x - 1000. If the insured pays 50% of the total cost, then the insurance plan also pays 50% of the cost, or .5x.

For Insurance Plan B, the insured pays the first $300, and the insurance plan pays 80% of everything over $300. So Insurance Plan B pays .8(x - 300).

Because there are two possible payment structures for Plan A, so we need to set up 2 equations. We are looking for the cost level for which both plans pay out the same amount, so we can set the two plans equal to each other. The two equations are:

.8(x - 300) = x - 1000 OR .8(x - 300) = .5x

Solving the first equation gives us x = 3800, and solving the second equation gives us x = 800.

$800 isn't one of our options, but $3800 is.

The correct answer is C.

[messi10]

Hi Karan,

Not quite sure I am understanding your question. But I will have a go.

My understanding is that you are OK with the first method, which is picking answers and testing them. You seem to have an issue with the algebraic method. If I have assumed wrong, please post back.

Plan A: The insured person pays $1000 or 50% of the cost, whichever is lower.

The explanation says: Let x be the total cost. Lets pick a number at this point. Let x be $5000.
Cost paid by the insured person: $1000
Cost paid by the insurance company: x - $1000 = $5000 - $1000 = $4000

So when the explanation says x - $1000, it is referring to the amount paid by the insurance company, not the insured person.

Hope this helps

Regards

Sunil

[karan13]

hey sunil thanks a lot.... got it ....

[jnelson0612]

Sunil strikes again! Thanks Sunil. :-)

[prachi.dalvi]

I find this question ambiguous.

Which of the following is a cost level for which both insurance plans pay out the same amount?

Does it mean the Insured or the Insurance company?

[jnelson0612]

I find this question ambiguous.

Which of the following is a cost level for which both insurance plans pay out the same amount?

Does it mean the Insured or the Insurance company?

Sure. "Insured" means the individual person covered by the insurance.

"Insurance plan" is the insurance company paying out money.

Please let me know if you have further questions.

[KatyH311]

Hello,

I got this question wrong and am still confused after reading the previous posts here. I approached this from a non-algebraic approach, and working backwards from the correct answer choice (C), here is what I came up with:

If the total cost is $3800

Under Plan A:
the insurance will pay out $1000 (it pays out the lower of 1/2 cost or $1,000. In this case 1/2 cost would be $1900. $1,000 is lower than $1900, so my understanding is that the insurance would pay $1000 in this case).

Under Plan B:
The insurance will pay out 80% of 300 less than the total cost. So, $3800-300 = $3500. The insurance pays out 80% of $3500 = $2800.

So, I am confused because the amount paid out by insurance under Plan A and Plan B according to my above calculations is not equal. Can someone help me understand why the above is wrong?

[Sage Pearce-Higgins]

There's another thread discussing the same problem here: https://www.manhattanprep.com/gmat/foru ... 10086.html

Well done for working backwards; the words 'which of the following...' are a clue that working backwards from the answer choices is a good strategy here.

The error you've made is that, for plan A, the insured is required to pay $1000 or 50% of the cost, implying that the insurance plan pays the rest of the cost. (It would be a pretty cruel health insurance policy that had a maximum payout of $1000.) That means that, for a cost level of $3800, the insured will pay $1000, and the insurance plan will pay $2800.