Source: Manhattan Prep
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
The OA is C
Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires
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Let T = TOTAL COSTBTGmoderatorLU wrote: ↑Wed Jun 16, 2021 6:42 pmSource: Manhattan Prep
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
The OA is C
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