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06 Oct 2018, 15:38
Kudos
Bookmarks
anilnandyala
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
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.
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.
25 Oct 2020, 23:12
Kudos
Bookmarks
Plan A: insured has to pay $1,000 or 50$(Cost) ---- whichever is lower
Insurer PAYS OUT the Rest
Plan B: insured has to pay $300 and then 20% of Any Cost ABOVE $300
Insurer PAYS OUT = 80% * (Cost = $300)
-C- if the Cost Level = $3,800
Plan A: will make the insured pay $1,000 because it is less than 50%*($3,800)
Plan A will PAY OUT = 3,800 - 1,000 = $2,800
Plan B: will PAY OUT --- 80% * (3,800 - 300) = .8 * (3,500) = $2,800
-C- when the Cost Level = $3,800, Both Insurance Plans will PAY OUT to the insured the same amount = $2,800
Insurer PAYS OUT the Rest
Plan B: insured has to pay $300 and then 20% of Any Cost ABOVE $300
Insurer PAYS OUT = 80% * (Cost = $300)
-C- if the Cost Level = $3,800
Plan A: will make the insured pay $1,000 because it is less than 50%*($3,800)
Plan A will PAY OUT = 3,800 - 1,000 = $2,800
Plan B: will PAY OUT --- 80% * (3,800 - 300) = .8 * (3,500) = $2,800
-C- when the Cost Level = $3,800, Both Insurance Plans will PAY OUT to the insured the same amount = $2,800
14 Mar 2021, 04:53
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BrentGMATPrepNow
anilnandyala
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
Here's an algebraic approach:A. $600
B. $1000
C. $3800
D. $5300
E. $6200
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
BrentGMATPrepNow when you say "20% of anything over $300." doesnt it mean if for example item costs 400 this--> 20% of 400
0r this 20% of item costing 300+
