Problem Solving

At company X senior sales representatives visit the home office once every 30 days, and junior sales representatives visit the home office once every 20 days. The number of visit that junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?

A) 10%

B) 25%

C) 33%

D) 50%

E) 67%

OA D

Please explain

Notice the common multiple of both periods is 60.

In 60 days, the senior rep makes 60/30 = 2 visits.

In 60 days, the junior rep makes 60/20 =3 visits.

The difference is 1 visit. The percentage this represents of the senior reps visits is 1/2 or 50%.

So, over a two year period the numerator and denominator are both multiplied by approximately 12, and since they
ARE both multiplied by the same number, they cancel and the answer remains the same.

Another approach:

Two years is 730.50 days, which is pretty close to 720, a nice choice of number, since it divides by 20 and by 30.

Our senior rep visits ≈ (720/30) => 24 times.

Our junior rep visits ≈ (720/20) => 36 times.

So our junior rep visits about 50% more often.