Under a certain company’s medical insurance plan, the amount an employ

Question

Under a certain company’s medical insurance plan, the amount an employee must pay for medical expenses consists of payment for the first $450 of expenses plus 20 percent of additional expenses, up to a maximum total payment of $1,350 per year. All remaining expenses are paid by the plan. Last year, if an employee paid the maximum amount for medical expenses, what is the least amount that the plan could have paid?

A. $720
B. $1,080
C. $3,600
D. $4,500
E. $4,950

PS21180

A. $720
B. $1,080
C. $3,600
D. $4,500
E. $4,950

PS21180

IanStewart · Accepted Answer

If the employee pays 20% of expenses, the insurer pays 80%, so their expenses are in a 1 to 4 ratio. Here, ignoring the first $450 of expense, the employee is paying $900, and the insurer is paying 4 times as much, or $3600, assuming the insurer is paying the minimum possible amount.

northofthegmat · Answer

Here is the algebraic approach:

Let E= Total Expense

If employee pays up to max ($1,350):

$450+20%(E-450)=$1350
20%(E-450)=900
E-450=$4500
E=$4950

Therefore, the total expense would be $4950 before the insurance company pays for 100% of the rest of the expenses. Therefore, up to $4950, the insurance company must pay...  
80%(E-450)
=80%(4950-450)
=80%(4500)
= $3,600

The answer is C.

GMATinsight · Answer

Amount paid = 1350 ≤ 450 + (20% of additional expense)

i.e. (20% of additional expense) ≥ 900

i.e. (1/5) of additional expense ≥ 900

i.e. additional expense ≥ 4500

Total Expense ≥ 450+4500 = 4950
Payment done by employee = 1350

Lest Payment made by Insurance company = 4950-1350 = 3600

Answer: Option C

yashikaaggarwal · Answer

Sir how's the least amount is the additional expense which is to be paid by company. And if the company is liable to pay at the max of 1350 per year why will they pay 4500?

Posted from my mobile device

Maniac19 · Answer

Can someone explain this in better way

IanStewart · Answer

This solution is incorrect because you're calculating the minimum amount of the additional expense, after the first $450. The insurer is not paying the entirety of that additional expense, only 80% of it.

yashikaaggarwal · Answer

Answer is 3600 because insurer is paying 4x of employee?

Posted from my mobile device

NitishJain · Answer

C ?

Qtn states the employee needs to pay first $450 and then 20% of additional expenses, rest will be paid by the insurance company.

maximum total payment by employee = $1,350 per year.

For the min amount to be paid by Insurance Company, employee has paid maximum yearly amount and no extra bill came for the insurance company to pay
i.e. 1350 = 450 + 20% of x

900 = (20/100)*x
x = 4500

For $4500, $900 has been paid by the employee, hence insurance company will pay $3600.

Any bill beyond that, will be fully borne by insurance company and hence this is the minimum amount paid by the insurance company when employee has paid full $1350 for the yearly medical expense.

Hence C.

Archit3110 · Answer

for $1350 company has paid $450 ; i.e $900 is being paid by employee direct
also being paid is 20% of additional expenses say x which is 
20/100* x=900
x= $4500 ( max amount which is used by employee)
so company can pay at least ; 4500-900; $3600
OPTION C

ScottTargetTestPrep · Answer

Solution:

The maximum amount an employee paid is $1,350, and we need to determine the least amount that the medical plan could have paid, given that the employee paid $1,350.

Since 1,350 - 450 = $900 and if $900 is exactly 20% of the additional medical expenses, then the additional medical expenses are 900/0.2 = $4,500. In other words, the total medical expenses are 450 + 4,500 = $4,950. Since the employee paid $1,350 of this total, then the (least) amount the insurance plan could have paid is 4,950 - 1,350 = $3,600.

Answer: C

Basshead · Answer

The maximum amount an employee will spend is $1,350 per year

$1,350 - $ 450 (deductible that's not covered by insurance) = $900

If the employee spent the maximum amount, then the employee spent $1,350

$900 = 20%
$3,600 = 80%

At a minimum, the plan paid $3,600. Answer is C.

rahul5657 · Answer

pls explain, why are you ignoring first $450 of expense in the further calculation?

Fish181 · Answer

Quick logic way to solve it. It's asking for the total the PLAN paid. Surely there will be a trap answer that has the amount the employee plus the plan paid. I just looked for answer choices that had a difference of 1350 (amount you subtract out from total employee payment) and voila if you take E) trap answer and subtract 1350 you get C.

Kinshook · Answer

Given: Under a certain company’s medical insurance plan, the amount an employee must pay for medical expenses consists of payment for the first $450 of expenses plus 20 percent of additional expenses, up to a maximum total payment of $1,350 per year. All remaining expenses are paid by the plan.

Asked:  Last year, if an employee paid the maximum amount for medical expenses, what is the least amount that the plan could have paid?

Last year, the employee paid a maxium amount of medical expenses of $1350.
First $450 are paid solely by the employee. Remaining ($1350 - $450 = $900) are 20% of additional expenses.
Remaining (80%=$900/20%*80% = $3600) is paid by the plan

IMO C

DanTheGMATMan · Answer

Best to set it up algebraically. The short cuts are themselves hard to see under pressure and you have to do half the math anyway:

https://www.youtube.com/watch?v=lBz1tAvKhkg

ashdank94 · Answer

The explanation from  ScottTargetTestPrep  is awesome!

450 + 0.2(E - 450) = 1350 
E = 4950

4950 = Employee + Plan 
To minimize the plan payment, maximize what employee pays which is 1350. So minimum plan payment = 4950 - 1350 = 3600

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Under a certain company’s medical insurance plan, the amount an employ

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Under a certain company’s medical insurance plan, the amount an employ

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