Need detailed help !!!! Insurance Problem

Question

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 ?

Unfortunately No Options given from the unknown source!!!!

hemant_rajput · Answer

Plan A say either pay $1000 or pay $(x/2), i.e. min(1000,x/2)

Plan B say pay 300 + .8(x-300).

now we want a value of "x" for which both plan require same investment.

so here is first equation
300 + .8(x-300) = 1000 ==> x=1175
but here again x/2 of is min , i.e. 587.5
Second equation
300 + .8(x-300) = x/2 ==> x = -(200)

here x can't be a negative value

so IMO there is no value exist for which both plan can have equal premium

GMATGuruNY · Answer

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.

I've added the answer choices, which we can plug in for the cost level.
When the correct answer is plugged in, the amount paid by Plan A will be equal to the amount paid by Plan B.

Answer choice C: 3800
Plan A:
Since .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:
.8(3500) = 2800.

Success!

The correct answer is C.

hemant_rajput · Answer

GMATGuruNY 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? $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 THE PLAN pays the remainder. If $1000 is MORE than 50% of the cost level, then THE INSURED pays 50% of the cost level, and THE PLAN pays the remainder. Plan B: THE INSURED pays the first $300. THE PLAN pays 80% of the remainder. I've added the answer choices, which we can plug in for the cost level. When the correct answer is plugged in, the amount paid by Plan A will be equal to the amount paid by Plan B. Answer choice C: 3800 Plan A: Since .5(3800) = 1900 -- which is greater than $1000 -- the insured pays $1000. The remainder is paid by the plan: 3800-1000 = 2800. Plan B: Amount paid by the insured = 300. 80% of the remainder is paid by the plan: .8(3500) = 2800. Success! The correct answer is C. Hi Guru, please correct me if I'm wrong this line "Plan B requires the insured to pay the in, but then pays 80% of the cost over $300" means 300 + .8(x-300), won't it?

hemanthkumarmn · Answer

Hi Hemant,

With reference to Gmatguru's post I understood that the question is about how much the insurance company pays..

Your equation is 300 + .8(x-300)which is absolutely correct.. only thing is that the first part i.e, $300 is to be paid by the insured person and the rest {0.8(x-300)} to be paid by the insurance company pertaining to the plan.. and we are concerned about the later only..

Gmatguru : am i with you on this????

hemant_rajput · Answer

After much thought I think GMATGuru explanation addresses correct problem. I've misunderstood the question. Thanks by the way.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Need detailed help !!!! Insurance Problem

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER