Question

When a subscription to a new magazine was purchased for \( m \) months, the publisher offered a discount of 75 percent off the regular monthly price of the magazine. If the total value of the discount was equivalent to buying the magazine at its regular monthly price for 27 months, what was the value of \( m \)? [Official GMAT-2018]

Hint:

When dealing with discounts and price reductions, use the percentage to find the total amount saved or paid, and set up an equation to find the unknown variable.

Answer 1

Step 1: Define the regular monthly price.
Let the regular monthly price of the magazine be \( p \).
Step 2: Calculate the total discount.
The discount is 75 percent off the regular price, so the discounted price is 25 percent of the regular price, i.e.,: \[ \text{Discounted price per month} = 0.25p \] For \( m \) months, the total cost paid is: \[ \text{Total paid} = m \times 0.25p \] The total discount is the difference between the regular price for \( m \) months and the total paid: \[ \text{Total discount} = m \times p - m \times 0.25p = m \times 0.75p \] Step 3: Use the given equivalence for the discount.
We are told that the total value of the discount is equivalent to buying the magazine at the regular monthly price for 27 months: \[ m \times 0.75p = 27 \times p \] Step 4: Solve for \( m \).
Cancel \( p \) from both sides: \[ m \times 0.75 = 27 \] Solve for \( m \): \[ m = \frac{27}{0.75} = 36 \] Step 5: Conclusion.
Thus, \( m = 36 \) months.