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

GMATGuruNY wrote:

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

THE INSURED is the person covered by the insurance.

Plan A:
If $1000 is LESS than 50% of the cost level, then THE INSURED pays $1000, and THE PLAN pays the remainder.
If $1000 is MORE than 50% of the cost level, then THE INSURED pays 50% of the cost level, and THE PLAN pays the remainder.

Plan B:
THE INSURED pays the first $300.
THE PLAN pays 80% of the remainder.

I've added the answer choices, which we can plug in for the cost level.
When the correct answer is plugged in, the amount paid by Plan A will be equal to the amount paid by Plan B.

Answer choice C: 3800
Plan A:
Since .5(3800) = 1900 -- which is greater than $1000 -- the insured pays $1000.
The remainder is paid by the plan:
3800-1000 = 2800.

Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by the plan:
.8(3500) = 2800.

Success!

The correct answer is C.