Problem Solving

Hi All,

We're told that a certain disability plan pays monthly benefits of 60 percent of the FIRST $2000 of monthly salary plus 40 percent of any portion in EXCESS of $2000, with the total monthly benefit not to exceed $2,500. We're asked for the SMALLEST monthly salary that will yield the MAXIMUM monthly benefit under this plan. This question can be solved in a number of different ways. Here's how you can solve it with some basic Algebra:

The first $2000 in salary would pay a benefit of (.6)($2000) = $1200

Since we want a total of $2500 in benefits, we need an additional $2500 - $1200 = $1300... and that money would have to come from the 40% of salary ABOVE the original $2000. We can set up the following equation:

(.4)(X) = $1300
(2/5)(X) = $1300
X = ($1300)(5/2) = $6500/2 = $3250

The total salary would be the original $2000 + the additional $3250 = $5250.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:A certain disability plan pays monthly benefits of 60 percent of the first $2000 of monthly salary plus 40 percent of any portion in excess of $2000 - the total monthly benefit not to exceed $2,500. What is the smallest monthly salary that will yield the maximum monthly benefit under this plan?

A. $5,750
B. $5,250
C. $4,500
D. $3,250
E. $2,200

We can create the equation:

2500 = 0.6 x 2000 + 0.4(T - 2000)

2500 = 1200 + 0.4T - 800

2100 = 0.4T

T = 2100/0.4 = 21,000/4 = 5,250

Answer: B

BTGmoderatorLU wrote: ↑

Mon May 21, 2018 1:57 pm

A certain disability plan pays monthly benefits of 60 percent of the first $2000 of monthly salary plus 40 percent of any portion in excess of $2000 - the total monthly benefit not to exceed $2,500. What is the smallest monthly salary that will yield the maximum monthly benefit under this plan?

A. $5,750
B. $5,250
C. $4,500
D. $3,250
E. $2,200

The OA is B.

Please, can anyone assist me with this PS question? I don't have it clear. Thanks!

Let x = monthly salary
So, x - $2000 = the amount that's in excess of $2000

So, we can write: monthly benefit = (60% of $2000) + (40% of x - 2000)
The maximum total monthly benefit is $2,500

We get: $2500 = (60% of $2000) + (40% of x - $2000)
Simplify: 2500 = (1200) + 0.4(x - 2000)
Simplify: 2500 = 1200 + 0.4x - 800
Simplify: 2500 = 400 + 0.4x
Subtract 400 from both sides: 2100 = 0.4x
Divide both sides by 0.4 to get: 2100/0.4 = x
Simplify: x = 5250

Answer: B

Cheers,
Brent