Problem Solving

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










oa is c. but not satisfied with explanation .can anyone help .
thanks

The wording is a little tricky because it's easy to confuse which party is paying what. Also, the question starts out by explaining what the insured customer pays, and then asks for the level in which the insurance COMPANY pays the same.

Insurance company payments
1) A: $300 (insured pays 50% of 600), B: $240 (insured pays first $300, company pays 80% of remaining $300)
2) A: $500 (insured pays 50% of 1000), B: $560 (insured pays first $300, company pays 80% of remaining $700)
3) A: $2800 (insured pays $1000, company pays remaining $2800), B: $2800 (insured pays first $300, company pays 80% of remaining $3500)

You can solve all the answers until you get to the right one. This worked out nicely because the first question where the insured is capped at $1000 proved to be the right one. However, this may not always be the case, so if you realize that the insured is capped at $1000 in the remaining questions, you can solve for x (where x is the cost level) with the equation:
x-1000=0.8(x-300)
x/5=760
x=3800

Nice explanation

good explanation!!!

Hi GMAT Experts,

Apart from testing the answer choices, how to go about actual solution please? I can see one solution, but I don't understand.

Thanks

newgmattest wrote: Apart from testing the answer choices, how to go about actual solution please? I can see one solution, but I don't understand.

Thanks

Hi,
As you have said you understood the plug-in , I will try to explain the other method that you are looking for.
Let x be the total cost.
As the payment of 'A' depends on the lower of 0.5x and 1000, we have two cases: 0.5x<1000 and 0.5x>1000 i.e x<2000 and x>2000
case-1: x<2000
A will play 0.5x. So, the remaining 0.5x will be paid by the insurance company
B will pay 300$. So, the insurance company will pay (0.8)*(x-300)
For them to be equal: 0.5x = 0.8*(x-300) => x=800

case-2: x>2000
A will play 1000$. So, the remaining (x-1000) will be paid by the insurance company
B will pay 300$. So, the insurance company will pay (0.8)*(x-300)
For them to be equal: x-1000 = (0.8)*(x-300) => 0.2x = 760 =>x=3800.

So it means that we can have two values of x. But solution first proposed have only one final value of x. Can you elaborate please....

x be the total amount to be paid..

Incase of A
A pays either 1000 or x/2
Insurance pays either x -1000 or x/2..

Incase of B
x = 300 + (x -300) * 80/100 + (x -300) *20/100
B pays 300 + (x - 300) *20/100

objective A and B shud pay same amount..

case 1:
x/2 = 300 + (x -300)/5
solve for x
5x/2 = 1500 + x - 300
5x/2 -x = 1200
5x -2x = 1200 *2
3x = 2400
x = 800

case 2:
1000 = 300 + (x - 300)/5
slove for x
700 = (x - 300)/5
3500 = x -300
x = 3800

let me if i have done anything wrong..i believe in this case amount payed by A and B can be same in 2 cases. Just that 3800 is in the option.

key is in understanding the wordings of the question:
plan B requires the insurer to pay..., but then pays 80%...
subject - verb.
it was the plan that pays 80%; there I lost my steam under the heat of the test.