• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn

tagged by: AAPL

## Health insurance Plan A requires the insured to pay $1000 or ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Manhattan Prep 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 OA C. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10111 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that 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 IT then pays 80% of the cost over$300. We're asked which of the following is a cost level for which both insurance plans pay out the SAME amount. 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 Answers C, D and E... 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.

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

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12743 messages
Followed by:
1247 members
5254
GMAT Score:
770
AAPL wrote:
Manhattan Prep

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

OA C.
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 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15203 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: Manhattan Prep 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 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.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

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.
Student Review #1
Student Review #2
Student Review #3

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

GMAT Instructor
Joined
25 Apr 2015
Posted:
2244 messages
Followed by:
17 members
43
AAPL wrote:
Manhattan Prep

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.

_________________
Scott Woodbury-Stewart Founder and CEO

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

### Top First Responders*

1 GMATGuruNY 56 first replies
2 Brent@GMATPrepNow 43 first replies
3 Jay@ManhattanReview 43 first replies
4 Ian Stewart 31 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

217 posts
2 fskilnik@GMATH

GMATH Teacher

124 posts
3 Max@Math Revolution

Math Revolution

89 posts
4 GMATGuruNY

The Princeton Review Teacher

82 posts
5 Brent@GMATPrepNow

GMAT Prep Now Teacher

66 posts
See More Top Beat The GMAT Experts