Problem Solving

Roland2rule 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
OA is c
what is wrong with option C in this question? Can you figure the error out too?

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

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: C

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

BTGmoderatorRO 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

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