Try Picking Numbers with the GMAT practice problem of the day!

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

A. k/m
B. (k – m)
C. [100 (k – m)]/ (100 + k)
D. [100 (k – m)]/(100 + m)
E. [100 (k – m)]/ (100 + k + m)

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If the original price per share of Stock X = 100
Let’s say k = 20
New price per share = 120

Original earnings per share of Stock X = 100
Let’s say m = 5 (since k > m)
New earnings per share = 105

Old ratio of price/earnings = 100/100 = 1
New ratio of price/earnings = 120/105 = approx 1.14

The percent increase is approx 14%.

Plug in our numbers into the answer choices, and look for the choice that also yields 14%:

A. k/m = 20/5 = 4 too small

B. (k – m) = 20 – 5 = 15 too big

C. 100 (15) / 100 + 20 = 1500 / 120 = 12.5 too small

D. 100 (15) / 100 + 5 = 1500/105 = approx 14. CORRECT!

E. 100 (15) / 100 + 20 + 5 = 1500/125 = 12

The answer is (D).