GMAT Practice Question: Last year, sales at Company X were 10 \% greater in February than in January, 15\%...
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.
\text{Jan} = \text{sales in January} \text{Feb} = \text{sales in February} \text{Mar} = \text{sales in March} \text{Apr} = \text{sales in April} \text{May} = \text{sales in May} \text{Jun} = \text{sales in June}
Step 2
We translate \textbf{\text{"sales at Company X were 10\% greater in February than in January"}} into a multiplication factor.
\text{Feb} = 1.10 \times \text{Jan}
Step 3
We translate \textbf{\text{"15\% less in March than in February"}} into a multiplication factor.
\text{Mar} = 0.85 \times \text{Feb}
Step 4
We translate \textbf{\text{"20\% greater in April than in March"}} into a multiplication factor.
\text{Apr} = 1.20 \times \text{Mar}
Step 5
We translate \textbf{\text{"10\% less in May than in April"}} into a multiplication factor.
\text{May} = 0.90 \times \text{Apr}
Step 6
We translate \textbf{\text{"5\% greater in June than in May"}} into a multiplication factor.
\text{Jun} = 1.05 \times \text{May}
Step 7
We express each month's sales as a multiple of January sales by chaining the factors and apply rounding for simplicity.
\text{Feb} = 1.10 \times \text{Jan} \text{Mar} = 0.85 \times (1.10 \times \text{Jan}) = 0.935 \times \text{Jan} \text{Apr} = 1.20 \times (0.935 \times \text{Jan}) = 1.122 \times \text{Jan} \approx 1.12 \times \text{Jan} \text{May} = 0.90 \times (1.122 \times \text{Jan}) = 1.0098 \times \text{Jan} \approx 1.01 \times \text{Jan} \text{Jun} = 1.05 \times (1.0098 \times \text{Jan}) = 1.06029 \times \text{Jan} \approx 1.06 \times \text{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.
\text{May is closest because }0.01\text{ is the smallest deviation.}
Answer
May, because the sales in May (1.01\timesJanuary) have the smallest deviation (0.01) from January sales.
