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# Health insurance Plan A requires the insured to pay $1000 or  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Manager Joined: 07 Feb 2010 Posts: 160 Followers: 2 Kudos [?]: 205 [0], given: 101 Health insurance Plan A requires the insured to pay$1000 or [#permalink]  17 Dec 2010, 07:33
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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? A.$600
B. $1000 C.$3800
D. $5300 E.$6200
[Reveal] Spoiler: OA
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Re: Health insurance Plan [#permalink]  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. _________________ Intern Status: Happy Joined: 17 Jan 2011 Posts: 4 Location: USA Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Health insurance Plan [#permalink] 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... _________________ Any sufficiently advanced technology is indistinguishable from magic. Director Joined: 28 Jul 2011 Posts: 566 Location: United States Concentration: International Business, General Management GPA: 3.86 WE: Accounting (Commercial Banking) Followers: 2 Kudos [?]: 91 [0], given: 16 Re: Health insurance Plan A requires the insured to pay$1000 or [#permalink]  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] 22 May 2012, 19:37 4 This post received KUDOS 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. Director Joined: 28 Jul 2011 Posts: 566 Location: United States Concentration: International Business, General Management GPA: 3.86 WE: Accounting (Commercial Banking) Followers: 2 Kudos [?]: 91 [0], given: 16 Re: Health insurance Plan A requires the insured to pay$1000 or [#permalink]  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.

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] 01 Dec 2012, 21:37 1 This post received KUDOS 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 _________________ Impossible is nothing to God. GMAT Club Legend Joined: 09 Sep 2013 Posts: 5330 Followers: 310 Kudos [?]: 60 [0], given: 0 Re: Health insurance Plan A requires the insured to pay$1000 or [#permalink]  03 Dec 2013, 06:50
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] 10 Aug 2014, 18:08 Algebra is truly a loser in this question. Backsolving is the fastest and most effective method here. Manager Joined: 20 Jul 2013 Posts: 63 Followers: 1 Kudos [?]: 45 [0], given: 55 Re: Health insurance Plan A requires the insured to pay$1000 or [#permalink]  22 Mar 2015, 04:33
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
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