PrepLattice
Sign in
QuantProblem Solving

Free GMAT Problem Solving Practice Question

PrepLattice is an independent test-preparation service and is not affiliated with or endorsed by GMAC, the organization that administers the GMAT. GMAT and GMAT Focus are trademarks of GMAC, used here only to name the exam this question is designed to prepare you for.

A subscription software business reports the following for a typical customer: average monthly revenue of $50, average monthly gross margin of $40 (the rest is the cost of serving the customer), and a monthly cancellation rate of 5 percent, meaning that in any month a customer has a 5 percent chance of leaving and that the average customer's lifetime in months equals 1 divided by the monthly cancellation rate. The business spends $200 in sales and advertising to acquire each new customer. Using lifetime gross margin as the customer's lifetime value, what is the ratio of a customer's lifetime value to the cost of acquiring that customer?

Five fresh questions every day, your progress tracked, every miss explained. Free with an account.

Start Today's Free Set

Answer & Explanation

Correct answer

C

Lifetime value must compose two separate ideas, and neither alone gets the answer. First, lifetime: with a 5 percent monthly cancellation rate, the average lifetime is 1 ÷ 0.05 equals 20 months. Second, value is built from gross margin, not revenue, because the question defines lifetime value as lifetime gross margin. So lifetime value equals $40 of margin per month times 20 months equals $800. The acquisition cost is $200, so the ratio is 800 to 200, which is 4 to 1.

The strongest trap is choice D (5 to 1): a solver who correctly finds the 20-month lifetime but reaches for monthly revenue ($50) computes 50 × 20 equals 1000, then 1000 to 200 equals 5 to 1. That uses the right lifetime but the wrong per-month figure, leaving out the cost of serving the customer. Choice B (2.4 to 1) is the second trap: a solver who uses margin correctly but ignores cancellation, assuming a 12-month lifetime, gets 40 × 12 equals 480, then 480 to 200 equals 2.4 to 1.

The two coupled disciplines: lifetime equals 1 over the churn rate (not an assumed contract length), and value uses margin (not revenue).