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Health insurance Plan A requires the insured to pay $1000 or

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Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 17 Dec 2010, 07:33
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Question Stats:

56% (02:33) correct 44% (01:58) wrong based on 211 sessions
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
[Reveal] Spoiler: OA
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Re: Health insurance Plan [#permalink] New post 17 Dec 2010, 08:04
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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?

$600
$1000
$3800
$5300
$6200


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.

Hope it's clear.
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Re: Health insurance Plan [#permalink] New post 18 Jan 2011, 22:12
Well i think the Ans would be C because i use the same method as the other member showed you above and i don't think there is another way of finding that pay out plan... :)
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 22 May 2012, 18:54
Hi Bunnel.

According to me the 2 equations are:
0.8(C – 300) + 300= 1000 OR 0.8(C – 300) + 300= 0.5C

But i am confused with the question you formed the two equations

C-1,000=0.8(C-300)--->1^st and 0.5C=0.8(C-300)

Since the questions says if the cost is above 1000 he will pay which ever is lower, but according to your 1st equation he is paying more that 1000 i.e is 2800, please clarify if i am wrong, awaiting for your reply
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 22 May 2012, 19:37
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kotela wrote:
Hi Bunnel.

According to me the 2 equations are:
0.8(C – 300) + 300= 1000 OR 0.8(C – 300) + 300= 0.5C

But i am confused with the question you formed the two equations

C-1,000=0.8(C-300)--->1^st and 0.5C=0.8(C-300)

Since the questions says if the cost is above 1000 he will pay which ever is lower, but according to your 1st equation he is paying more that 1000 i.e is 2800, please clarify if i am wrong, awaiting for your reply


You are reading the question wrong. It is asking when the insurance company will pay the same amount of money not the insured.

0.8(C–300) = C–1000
OR
0.8(C–300) = 0.5C

Solving the first equation gives us C=3800
Solving the second equation gives us C=800

Since 800 isn't one of the answers we can eliminate it and 3800 is the only possible answer.

The correct answer is C.
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 22 May 2012, 21:19
Cares wrote:
kotela wrote:
Hi Bunnel.

According to me the 2 equations are:
0.8(C – 300) + 300= 1000 OR 0.8(C – 300) + 300= 0.5C

But i am confused with the question you formed the two equations

C-1,000=0.8(C-300)--->1^st and 0.5C=0.8(C-300)

Since the questions says if the cost is above 1000 he will pay which ever is lower, but according to your 1st equation he is paying more that 1000 i.e is 2800, please clarify if i am wrong, awaiting for your reply


You are reading the question wrong. It is asking when the insurance company will pay the same amount of money not the insured.

0.8(C–300) = C–1000
OR
0.8(C–300) = 0.5C

Solving the first equation gives us C=3800
Solving the second equation gives us C=800

Since 800 isn't one of the answers we can eliminate it and 3800 is the only possible answer.

The correct answer is C.


Ya you are i misread the question....thanks for that and +1 kudos for you
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 01 Dec 2012, 21:37
Insured pays out:
Plan A==>1000 or C/2
Plan B==>300

Insurance pays out:
Plan A==>C-1000 or C/2
Plan B==>.8(C-300)

We are concerned with the payout made by Insurance.

C-1000=.8(C-300)
C=1000+.8C-240
.2C=760
C=3800

Answer:3800
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 03 Dec 2013, 06:50
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] New post 10 Aug 2014, 18:08
Algebra is truly a loser in this question. Backsolving is the fastest and most effective method here.
Re: Health insurance Plan A requires the insured to pay $1000 or   [#permalink] 10 Aug 2014, 18:08
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