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Health insurance Plan A requires the insured to pay $1000 or [#permalink]

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17 Dec 2010, 08:33

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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?

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.

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]

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22 May 2012, 19:54

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]

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22 May 2012, 20:37

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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.

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

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22 May 2012, 22:19

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]

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03 Dec 2013, 07:50

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

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22 Mar 2015, 05:33

TooLong150 wrote:

Algebra is truly a loser in this question. Backsolving is the fastest and most effective method here.

Having to rely on backsolving is truly hit or miss when it comes to timing.

If you've mastered algebra, not only can you virtually solve most of the problems on the test, but this problem can also be completed around 30 seconds. Seems like a pretty fast time to me

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

Case 1: What Insured pay is 1000 (as per plan A) = 300+(20/100)*(C-300) Solving this equation, C = 3800

Case 2: What Insured pay is (50/100)*C (as per plan A) = 300+(20/100)*(C-300) Solving this equation, C = 800

Answer: Option C
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Health insurance Plan A requires the insured to pay $1000 or [#permalink]

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20 Nov 2015, 11:56

"Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower." - this confused me much. if i quoted the fee in my job this way i would be fired =)

my clients would understand this without doubt: if the cost is 10 000 then the client has to pay only 1000 =))) yuuuupi
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink]

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19 Jan 2016, 12:25

Absolutely agree...pathetic and horridly ambiguous wording....sch kind of wording never appears on gmat...pooh to Manhattan! The stmnt makes it seem as if we HV to choose whether 1000 bucks or C/2 is the payout, C being insurance cost...will sue GMAT if such poorly worded question appears.

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