anilnandyala 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?
A. $600
B. $1000
C. $3800
D. $5300
E. $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 PLAN A pays the remainder.
If $1000 is MORE than 50% of the cost level, then THE INSURED pays 50% of the cost level, and PLAN A pays the remainder.
Plan B:
THE INSURED pays the first $300.
PLAN B pays 80% of the remainder.
We can PLUG IN THAN ANSWERS.
When the correct answer is plugged in, the amount paid by Plan A will be equal to that paid by Plan B.
B: 1000
Plan A:
Since 0.5(1000) = 500 -- which is LESS than $1000 -- the insured pays $500.
The remainder is paid by Plan A:
1000-500 = 500.
Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by Plan B:
0.8(700) = 560.
In this case, the amount paid by Plan A is LESS than that paid by Plan B.
Eliminate B.
D: 5300
Plan A:
Since 0.5(5300) = 2650 -- which is greater than $1000 -- the insured pays $1000.
The remainder is paid by Plan A:
5300-1000 = 4300.
Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by Plan B:
0.8(5000) = 4000.
In this case, the amount paid by Plan A is GREATER than that paid by Plan B.
Eliminate D.
When the cost level = 1000, the amount paid by Plan A is LESS than that paid by Plan B.
When the cost level = 5300, the amount paid by Plan A is GREATER than that paid by Plan B.
Implication:
For the two amounts to be EQUAL, the cost level must be BETWEEN 1000 AND 5300.
C: 3800
Plan A:
Since 0.5(3800) = 1900 -- which is greater than $1000 -- the insured pays $1000.
The remainder is paid by Plan A:
3800-1000 = 2800.
Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by Plan B:
0.8(3500) = 2800.
Success!
Here, the amount paid by each plan is the same: $2800.
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