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Health insurance

by j_shreyans » Sat Aug 30, 2014 8:48 pm
Guys ,

Health insurance Plan A requires the insured to pay $1,000 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

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by [email protected] » Sat Aug 30, 2014 10:45 pm
Hi j_shreyans,

This question can be solved with algebra or by TESTing THE ANSWERS. Here's how using the answers can help you to find the solution...

Both insurance plans require the insured to pay part of the total cost, then the insurance company pays "the rest", so it's important to keep track of what the insured pays. We're asked for the cost level in which both plans pay out the same amount.

Lets' start with B: $1,000

Plan A: insured pays $1,000 or 50%, whichever is smaller....
The insured pays 50%($1,000) = $500
The Plan pays $500

Plan B: insured pays the first $300, then 20% of what's left...
The insured pays $300 + 20%($700) = $440
The Plan pays $560

The two values ($500 and $560) are different, so B is NOT the answer.

Now try D: $5300

Plan A:
The insured pays $1,000
The Plan pays $4300

Plan B:
The insured pays $300 + 20%($5000) = $1300
The Plan pays $4000

The two values ($4300 and $4000) are different, so D is NOT the answer.

Notice when we tested Answer B that Plan B PAID MORE, but when we tested Answer D that Plan B PAID LESS. At some point between those two values, a "switch" occurred. The only answer that could be the same for both plans will be between B and D. Here's the proof:

Answer C: $3800

Plan A:
The insured pays $1000
The Plan pays $2800

Plan B:
The insured pays $300 + 20%($3500) = $1000
The Plan pays $2800

Both Plans pay the same amount!

Final Answer: C

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Rich
Contact Rich at [email protected]
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by j_shreyans » Sun Aug 31, 2014 3:26 am
Hey Rich ,

Can you please also advise the another method.
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by Brent@GMATPrepNow » Sun Aug 31, 2014 6:50 am
j_shreyans wrote:Guys ,

Health insurance Plan A requires the insured to pay $1,000 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
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
Brent Hanneson - Creator of GMATPrepNow.com
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