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Health insurance Plan A requires the insured to pay $1000 or [#permalink] ### Show Tags 17 Dec 2010, 07:33 3 This post received KUDOS 26 This post was BOOKMARKED 00:00 Difficulty: 85% (hard) Question Stats: 55% (02:29) correct 45% (01:46) wrong based on 480 sessions ### HideShow timer Statistics 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 Math Expert Joined: 02 Sep 2009 Posts: 35912 Followers: 6852 Kudos [?]: 90043 [10] , given: 10402 Re: Health insurance Plan [#permalink] ### Show Tags 17 Dec 2010, 08:04 10 This post received KUDOS Expert's post 10 This post was BOOKMARKED 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.

Hope it's clear.
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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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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.

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01 Dec 2012, 21:37
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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.

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

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10 Aug 2014, 18:08
Algebra is truly a loser in this question. Backsolving is the fastest and most effective method here.
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28 Oct 2015, 08:21
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Expert's post
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

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

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Health insurance Plan A requires the insured to pay $1000 or [#permalink] ### Show Tags 20 Nov 2015, 10:56 "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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06 Sep 2016, 14:01
Definitely C ! .. According to my calculations, C should be the answer. Please let me know if it's right.
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