Question

Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?

a. Feb
b. Mar
c. Apr
d. May
e. June

Answer 1

d. May

Explanation:

Working through the chain, we have ...

Feb = 1.10×Jan

Mar = 0.85×Feb = 0.935×Jan

Apr = 1.20×Mar = 1.122×Jan

May = 0.90×Apr = 1.0098×Jan

Jun = 1.05×May = 1.06029×Jan

The multiplier that is closest to 1 is 1.0098, so May has sales closest to January.

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The percentage increase or decrease can be converted to a multiplier by adding it to 1. If p% is the percentage change, then adding it to an original value looks like ...

original + p% × original = original × (1 +p%) . . . . . . . distributive property

And p% translates to a decimal number by replacing % with /100 or ×0.01.

10% increase: original × (1 + 10/100) = original × 1.10

15% decrease: original × (1 - 15/100) = original × 0.85