Problem Solving

Health insurance Plan A requires the insured to pay $1,000 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?

A.$600
B.$1,000
C.$3,800
D.$5,300
E.$6,200

mysseo wrote:Health insurance Plan A requires the insured to pay $1,000 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?

A.$600
B.$1,000
C.$3,800
D.$5,300
E.$6,200

The question is asking for the cost level at which both the insurance plans would pay the same amount to the insured.

Work from the answer choices:

A)600: Plan A pays: 300 (50% of 600)
Plan B pays: 240 (80% of 300)
the two amounts are not same. Hence incorrect

B)1000: Plan A pays: 500 (50% of 1000)
Plan B pays: 560 (80% of 700)
the two amounts are not same. Hence incorrect

C)3800: Plan A pays: 2800 (3800-1000)
Plan B pays: 2800 (80% of 3500)
the two amounts are same. Hence correct

You can work the remaining options too, for checking.

So the correct answer is C

Pay out for $2800..Plan A: min(1000, 50% of 3800) = 1000

Plan B: 300 +80% (3800- 300) = 3100 ..How come both are same?

ramlal wrote:Pay out for $2800..Plan A: min(1000, 50% of 3800) = 1000

Plan B: 300 +80% (3800- 300) = 3100 ..How come both are same?

IMO: C
The question asks for: A cost level for which both insurance plans pay out the same amount
Plan A: the insured to pay $1000 or 50% of the amount (whichever is lower)
So for an amount of $3800: Insurer will pay $1000 and Insurance plan pays $2800
Plan B: he insured to pay the initial $300, but then pays 80% of the cost over $30
So for an amount of $3800: Insurer will pay $300 and Insurance plan pays 80% (3800-300) = $2800

Thanks Mdewan for clarification. Now I got it. The cost is allocated to insured and insurance plan. It is asking about insurance plan cost. It was on Mahattan CAT, but I was confused about what it is asking for. OA is C.