## Health insurance Plan A requires the insured to pay $1000... ##### This topic has expert replies Moderator Posts: 1980 Joined: 15 Oct 2017 Followed by:6 members ### Health insurance Plan A requires the insured to pay$1000...

by BTGmoderatorLU » Tue Mar 13, 2018 3:03 pm
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 â‰¤ 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 â‰¤ 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 â‰¤ 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.

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. Mitch Hunt Private Tutor for the GMAT and GRE [email protected] If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at [email protected]. Student Review #1 Student Review #2 Student Review #3 Legendary Member Posts: 2663 Joined: 14 Jan 2015 Location: Boston, MA Thanked: 1153 times Followed by:127 members GMAT Score:770 by [email protected] » 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.
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Save $100 off any live Veritas Prep GMAT Course ### GMAT/MBA Expert GMAT Instructor Posts: 15760 Joined: 08 Dec 2008 Location: Vancouver, BC Thanked: 5254 times Followed by:1266 members GMAT Score:770 by [email protected] » 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.

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by [email protected] » 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.