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.

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

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

Sunil strikes again! Thanks Sunil. :-)

_________________
Jamie Nelson
ManhattanGMAT Instructor