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Re: Health insurance Plan A requires the insured to pay $1000 or 50% of to [#permalink]
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GeminiHeat 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


Let the total cost for plan A and plan B be \(C\)
Payable amount (plan A) = \(C -1000\) or \(0.5C\)
payable amount (plan B) = \(0.80(C - 300)\)


Case I:
\(C - 1000 = 0.80(C - 300)\)
\(0.2C = 760\)
\(C = 3800\)

Case II:
\(0.5C = 0.80(C - 300)\)
\(0.3C = 240\)
\(C = 800\)

We do not have 800 as the option choice - Hence, option C
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Health insurance Plan A requires the insured to pay $1000 or 50% of to [#permalink]
Hi. I was interested in your question, but I ran into some difficulties. KarunMendiratta is right in his theory. I am in solidarity with him. He suggested a really good solution. I wish I could be just as witty. I probably would have been better at it, but I use financial advisor functions for medical professionals. They allow me to manage my finances wisely. It might be helpful for you to read about it, as a financial advisor has many useful features. I do not worry about my expenses and enjoy my life. I hope my advice will be helpful. Best of luck to you.

Originally posted by eliseuwrites on 21 Oct 2022, 04:15.
Last edited by eliseuwrites on 24 Oct 2022, 05:47, edited 1 time in total.
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Re: Health insurance Plan A requires the insured to pay $1000 or 50% of to [#permalink]
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Pay out for plan A: Cost-$1,000 or Cost-0.5*Cost=0.5*Cost, when 0.5*Cost<$1,000;
Pay out for plan B: 0.8(Cost-$300);

The question is: for which of the following costs the pay outs are the same.

C-1,000=0.8(C-300) --> for C=3,800 and 0.5C=0.8(C-300) --> for C=800. As we have only $3,800 listed then it must be a correct answer.

Or you can use backsolving for this question:
A. C=$600: pay out for plan A will be 0.5*600=300 (as 0.5*600<1,000) and pay out for plan B will be 0.8*(600-300)=240;

B. C=$1000: pay out for plan A will be 0.5*1,00=500 (as 0.5*1,000<1,000) and pay out for plan B will be 0.8*(1,000-300)=560;

C. C=$3800: pay out for plan A will be 3,800-1,000=2,800 (as 0.5*3,800>1,000) and pay out for plan B will be 0.8*(3,800-300)=2,800 --> 2,800=2,800;

D. C=$5300: pay out for plan A will be 5,300-1,000=4,300 (as 0.5*5,300>1,000) and pay out for plan B will be 0.8*(5,300-300)=4,000;

E. C=$6200:pay out for plan A will be 6,200-1,000=5,200 (as 0.5*6,200>1,000) and pay out for plan B will be 0.8*(6,200-300)=4,720.

Answer: C.
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