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17 Dec 2010, 08:33
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95% (hard)

Question Stats:

56% (02:37) correct 44% (02:54) wrong based on 465 sessions

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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
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17 Dec 2010, 09:04
12
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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;

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22 May 2012, 20:37
5
1
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.

##### General Discussion
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18 Jan 2011, 23:12
1
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, 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.

Ya you are i misread the question....thanks for that and +1 kudos for you
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10 Aug 2014, 19:08
Algebra is truly a loser in this question. Backsolving is the fastest and most effective method here.
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28 Oct 2015, 09:21
2
1
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, 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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30 Jul 2017, 07:49
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

Out of line .... this question is more of an SC question where you need to look at part "Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over$300" where 'but then pays 80%' is mentioned for insurance company... otherwise this question would be some 600 level.
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] ### Show Tags 26 Jan 2018, 14:14 1 Hi All, You can answer this question with Algebra or by TESTing THE ANSWERS. Either way though, you have to pay careful attention to the wording of the prompt. Since Plan A requires a$1000 payment OR 50% of total cost from the insured - whichever is LOWER - there's a great tactical shortcut here: any total bill that is over $2,000 will require that the insured pay$1,000 through Plan A. Since most of the answers are over $2,000, we can look to see if any of them would require that a total of$1,000 be paid by the insured through Plan B.

Answer C: $3,800 Insurance pays (3800 - 300)(.8) = (3500)(.8) = 2800 Insured pays initial 300 + whatever the insurance does NOT pay (3500 - 2800 = 700). 300 + 700 = 1,000 This is a MATCH for what we're looking for, so this MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ GMAT Club Legend Joined: 12 Sep 2015 Posts: 4065 Location: Canada Re: Health insurance Plan A requires the insured to pay$1000 or  [#permalink]

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14 Mar 2018, 12:05
1
Top Contributor
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

Here's an algebraic approach:

Let T = TOTAL COST

Plan A: Person pays EITHER $1000 OR 0.5T, whichever is LESS Plan B: Person pays$300 plus 20% of anything over $300. In other words, the person pays$300 + 0.2(T - 300)

Since Plan A has two different scenarios, we need to test both. That is, create equations that see both plans costing the insured the same amount.

Case #1) 1000 = 300 + 0.2(T - 300).....now SOLVE
Expand: 1000 = 300 + 0.2T - 60
Rearrange: 760 = 0.2T
Solve: T = 3800

Perfect!!

Just for "fun" let's check out case #2
Case #2) 0.5T = 300 + 0.2(T - 300).....now SOLVE
Expand: 0.5T = 300 + 0.2T - 60
Rearrange: 0.3T = 240
Solve: T = 800

Hmmm, it seems that if the TOTAL cost were $800, both plans would require the insured to pay the same amount ($400). That said, $800 is not one of the answer choices. Also notice that the question says, "Which of the following is a cost level for which both insurance plans pay out the same amount?" So, there are two possible correct answers, and the question asks us to find one of them. Cheers, Brent _________________ Test confidently with gmatprepnow.com Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8412 Location: United States (CA) Re: Health insurance Plan A requires the insured to pay$1000 or  [#permalink]

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15 Mar 2018, 10:17
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

We can let x = a cost level for which both insurance plans pay out the same amount.

Since 50% of $2000 is$1000, if x > 2000, Plan A will pay out x - 1000 and Plan B will pay out 0.8(x - 300). Setting them equal, we have:

x - 1000 = 0.8(x - 300)

x - 1000 = 0.8x - 240

0.2x = 760

x = 3,800

Now, if x < 2000, then Plan A will pay out 0.5x and Plan B will still pay out 0.8(x - 300).

0.5x = 0.8(x - 300)

0.5x = 0.8x - 240

240 = 0.3x

800 = x

We see that x could be either 3,800 or 800. However, since the question asks for a cost level (instead of the cost level) and only 3,800 is given, then 3,800 is the correct answer.

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Health insurance Plan A requires the insured to pay $1000 or [#permalink] ### Show Tags 05 Oct 2018, 06:46 1 "Health insurance Plan A requires the insured to pay$1000 or 50% of total cost"
Doesn't that mean that for over 2000 amount the insured would always pay 1000 because that will always be less than a value greater than 2000?
Example : 1000 or 2001/2. or 1000 or 3000/2. Obviously 1000 and so on.!!
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06 Oct 2018, 06:37
Hi Rich,

I dont know what am I missing.!! How is option C correct? Plan A is giving tax of 1000 and Plan B is giving tax of around 2000
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Re: Health insurance Plan A requires the insured to pay $1000 or [#permalink] ### Show Tags 06 Oct 2018, 15:07 Hi Micky1005, The prompt tells us what both insurance Plans require the INSURED to pay - meaning that the Insurance Plan would pay out everything else. We're looking for a dollar value that would lead to the SAME payout from the Insurance Plan (you can also think of this as "which dollar value will lead to the insured paying the SAME amount?") With a total bill of$3800:

Plan A requires that the insured pay $1000, meaning that the Plan pays out the remaining$3800 - $1000 =$2800

Plan B requires that the insured pay the initial $300, then the plan pays 80% of the remainder (meaning that the insured pays 20% of the remainder)$3800 - $300 =$3500
The insured pays 20% of the remaining $3500 = (.2)($3500) = $700 When combined with the initial$300, that is a total of $300 +$700 = $1000 that the insured pays. Therefore, Plan B would pay$3800 - $1000 =$2800

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