GMAT Percentages: In which month were sales closest…
Question
Last year, sales at Company X were 10 % greater in February than in January, 15% less in March than in February, 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 the sales in January?
- February
- March
- April
- May
- June
Topics: percentages, word problems, relative changes, revenue/cost, translations, approximations
Solution
Step 1
We define variables for the sales in each month using clear names to avoid ambiguity.
Jan = sales in January Feb = sales in February Mar = sales in March Apr = sales in April May = sales in May Jun = sales in June
Step 2
We translate "sales at Company X were 10% greater in February than in January" into a multiplication factor.
Feb = 1.10 × Jan
Step 3
We translate "15% less in March than in February" into a multiplication factor.
Mar = 0.85 × Feb
Step 4
We translate "20% greater in April than in March" into a multiplication factor.
Apr = 1.20 × Mar
Step 5
We translate "10% less in May than in April" into a multiplication factor.
May = 0.90 × Apr
Step 6
We translate "5% greater in June than in May" into a multiplication factor.
Jun = 1.05 × May
Step 7
We express each month's sales as a multiple of January sales by chaining the factors and apply rounding for simplicity.
Feb = 1.10 × Jan Mar = 0.85 × (1.10 × Jan) = 0.935 × Jan Apr = 1.20 × (0.935 × Jan) = 1.122 × Jan 1.12 × Jan May = 0.90 × (1.122 × Jan) = 1.0098 × Jan 1.01 × Jan Jun = 1.05 × (1.0098 × Jan) = 1.06029 × Jan 1.06 × Jan
Step 8
We calculate the absolute deviation of each month's factor from 1 (January) to find which is smallest.
|1.10 - 1.00| = 0.10 |0.935 - 1.00| = 0.065 |1.122 - 1.00| = 0.122 |1.01 - 1.00| = 0.01 |1.06 - 1.00| = 0.06
Step 9
We see that May's deviation (0.01) is the smallest, so May's sales are closest to January's.
May is closest because 0.01 is the smallest deviation.
Answer
May (D)
