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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...

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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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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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Quote:
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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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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GMAT/MBA Expert

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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,
Brent

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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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scott@targettestprep.com



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