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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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.

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...

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

Ya you are i misread the question....thanks for that and +1 kudos for you

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

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

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 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

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.

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.

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.

I'll start with the smallest option from that sub-group...

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
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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!!
The correct answer is C

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
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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.

Answer: C
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"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.!!

Hi Micky1005,

YES, that is exactly what the prompt means. With Plan A, ANY total that is GREATER than $2000 will require that the insured pay $1,000 (since that would be LESSER of the two values).

GMAT assassins aren't born, they're made,
Rich
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Hi Rich,
Thanks for the reply.

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

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

GMAT assassins aren't born, they're made,
Rich
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