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Health insurance Plan A requires the insured to pay $1000...

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Health insurance Plan A requires the insured to pay $1000 of 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

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

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by ErikaPrepScholar » Wed Mar 14, 2018 9:42 am
First, we'll figure out what each plan will pay at different levels of total cost.

Plan A
Up to $2000 in total cost, 50% of total cost will be less than $1000, so the insured will pay 50%. This means that the plan will pay out the other 50%. So
If c ≤ 2000, p = 0.5c
(where c = total cost and p = amount the plan pays out)
Above $2000, $1000 will be less than 50%, so the insured will pay $1000. This means that the plan will pay out anything above $1000. So
If c > 2000, p = c - 1000

Plan B
Up to $300 in total cost, the insured will pay the total cost. This means that the plan will pay out nothing. So
If c ≤ 300, p = 0.
Above $300 in total cost, the insured will pay the initial $300, but the plan will pay out 80% of anything above $300. So
If c > 300, p = 0.8(c - 300)

We want to find a value for c where p for Plan A equals p for plan B. None of our answer options are below $300, so we can discount that equation. This leaves us with two possibilities:
If 300 < c ≤ 2000, 0.5c = 0.8(c - 300)
If c > 2000, c - 1000 = 0.8(c - 300)

Solving for for both gives:
0.5c = 0.8(c - 300) --> 0.5c = 0.8c - 240 --> 0.3c = 240 --> c = 800
c - 1000 = 0.8(c - 300) --> c - 1000 = 0.8c - 240 --> 0.2c = 760 --> c = 3800

So the plans will pay out the same amount when the total cost is either $800 or $3800. Only $3800 is an answer choice, so we pick C.
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by GMATGuruNY » Wed Mar 14, 2018 10:50 am
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
THE INSURED is the person covered by the insurance.

Plan A:
If $1000 is LESS than 50% of the cost level, then THE INSURED pays $1000, and PLAN A pays the remainder.
If $1000 is MORE than 50% of the cost level, then THE INSURED pays 50% of the cost level, and PLAN A pays the remainder.

Plan B:
THE INSURED pays the first $300.
PLAN B pays 80% of the remainder.

We can PLUG IN THAN ANSWERS.
When the correct answer is plugged in, the amount paid by Plan A will be equal to that paid by Plan B.

B: 1000
Plan A:
Since 0.5(1000) = 500 -- which is LESS than $1000 -- the insured pays $500.
The remainder is paid by Plan A:
1000-500 = 500.

Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by Plan B:
0.8(700) = 560.

In this case, the amount paid by Plan A is LESS than that paid by Plan B.
Eliminate B.

D: 5300
Plan A:
Since 0.5(5300) = 2650 -- which is greater than $1000 -- the insured pays $1000.
The remainder is paid by Plan A:
5300-1000 = 4300.

Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by Plan B:
0.8(5000) = 4000.

In this case, the amount paid by Plan A is GREATER than that paid by Plan B.
Eliminate D.

When the cost level = 1000, the amount paid by Plan A is LESS than that paid by Plan B.
When the cost level = 5300, the amount paid by Plan A is GREATER than that paid by Plan B.
Implication:
For the two amounts to be EQUAL, the cost level must be BETWEEN 1000 AND 5300.

The correct answer is C.

C: 3800
Plan A:
Since 0.5(3800) = 1900 -- which is greater than $1000 -- the insured pays $1000.
The remainder is paid by Plan A:
3800-1000 = 2800.

Plan B:
Amount paid by the insured = 300.
80% of the remainder is paid by Plan B:
0.8(3500) = 2800.
Success!
Here, the amount paid by each plan is the same: $2800.
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by DavidG@VeritasPrep » Wed Mar 14, 2018 10:50 am
LUANDATO 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

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
You could also try back-solving. Say you tested B, 1000

Plan A would require the insured to pay $500, leaving the insurance to pay $500.
Plan B would require the insured to pay 300. If the insurance is covering 80% of the remaining cost, then the insured is covering 20% of that cost. 20% of the remaining 700 is 140. If the insured pays 300 + 140 = 440, the insurance must cover 560.
In this scenario the insurance pays more in Plan B. Answer choice B is out

Try D, 5300.

Plan A would require the insured to pay $1000, leaving the insurance to cover the remaining 4300
Plan B would required the insured to pay 300 and then 20% of the remaining 5000, or1000. Now the insured pays 1300 and the insurance pays 4000.
Now the insurance pays more in Plan A.

If Plan A paid out more when the cost is $1000 and Plan B paid out more when cost is 5300, there's good reason to believe that the answer will fall in between.
You could always test if you were paranoid.

C:3800
Plan A would require the insured to pay $1000, leaving the insurance to cover the remaining 2800
Plan B would required the insured to pay 300 and then 20% of the remaining 3500, or700. Now the insured pays 1000 and the insurance pays 2800.
Success! the answer is C
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by Brent@GMATPrepNow » Wed Mar 14, 2018 11:02 am
LUANDATO wrote:Health insurance Plan A requires the insured to pay $1000 of 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

The OA is C.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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,
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by Scott@TargetTestPrep » Thu Mar 15, 2018 9:22 am
LUANDATO wrote:Health insurance Plan A requires the insured to pay $1000 of 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.

Answer: C

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