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?

Answer Choices

Correct answer marked below

$600

$1000

$3800

Correct

$5300

$6200

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

Pay out for plan A: Cost - $1,000 or Cost - 0.5*Cost = 0.5*Cost, when 0.5*Cost < $1,000.

Pay out for plan B: 0.8(Cost - $300).

The question asks for which cost the pay outs are the same.

Case 1: C - 1,000 = 0.8(C - 300) → C = 3,800.

Case 2: 0.5C = 0.8(C - 300) → C = 800.

Only $3,800 is listed among the options.

Alternatively, use backsolving:

A. C = $600: pay out for plan A = 0.5*600 = 300 (since 0.5*600 < 1,000); pay out for plan B = 0.8*(600 - 300) = 240.

B. C = $1000: pay out for plan A = 0.5*1,000 = 500 (since 0.5*1,000 < 1,000); pay out for plan B = 0.8*(1,000 - 300) = 560.…

Read the full explanation

Create free account Sign in

Comments

No comments yet

Be the first to share your thoughts and help others understand it better.

What this question tests

What it tests

Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.

Common trap

Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.