A certain disability plan pays monthly benefits of 60

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2550; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon May 21, 2018 1:57 pm

Timer

00:00

Answers

Stats

Difficulty—

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!

Like this post

Source: Beat The GMAT — Problem Solving | Mon May 21, 2018 1:57 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon May 21, 2018 6:32 pm

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

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue May 29, 2018 6:43 am

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: A certain disability plan pays monthly benefits of 60

by Brent@GMATPrepNow » Tue Feb 04, 2020 7:56 am

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

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review