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?

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May, because the sales in May (1.01) have the smallest deviation (0.01) from January sales. 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 We translate "sales at Company X were 10% greater in February than in January" into a multiplication factor. Feb = 1.10 Jan We translate "15% less in March than in February" into a multiplication factor. Mar = 0.85 Feb We translate "20% greater in April than in March" into a multiplication factor. Apr = 1.20 Mar We translate "10% less in May than in April" into a multiplication factor. May = 0.90 Apr We translate "5% greater in June than in May" into a multiplication factor. Jun = 1.05 May 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 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 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.

Explanation	Calculations	Help
$We define variables for the sales in each month using clear names to avoid ambiguity.$	$Jan = sales in January Feb = sales in February Mar = sales in March Apr = sales in April May = sales in May Jun = sales in June$
$We translate "sales at Company X were 10% greater in February than in January" into a multiplication factor.$	$Feb = 1.10 \times Jan$
$We translate "15% less in March than in February" into a multiplication factor.$	$Mar = 0.85 \times Feb$
$We translate "20% greater in April than in March" into a multiplication factor.$	$Apr = 1.20 \times Mar$
$We translate "10% less in May than in April" into a multiplication factor.$	$May = 0.90 \times Apr$
$We translate "5% greater in June than in May" into a multiplication factor.$	$Jun = 1.05 \times May$
$We express each month's sales as a multiple of January sales by chaining the factors and apply rounding for simplicity.$	$Feb = 1.10 \times Jan Mar = 0.85 \times (1.10 \times Jan) = 0.935 \times Jan Apr = 1.20 \times (0.935 \times Jan) = 1.122 \times Jan \approx 1.12 \times Jan May = 0.90 \times (1.122 \times Jan) = 1.0098 \times Jan \approx 1.01 \times Jan Jun = 1.05 \times (1.0098 \times Jan) = 1.06029 \times Jan \approx 1.06 \times Jan$
$We calculate the absolute deviation of each month's factor from 1 (January) to find which is smallest.$	$∣1.10 - 1.00∣ = 0.10 ∣0.935 - 1.00∣ = 0.065 ∣1.122 - 1.00∣ = 0.122 ∣1.01 - 1.00∣ = 0.01 ∣1.06 - 1.00∣ = 0.06$
$We see that May's deviation (0.01) is the smallest, so May's sales are closest to January's.$	$May is closest because 0.01 is the smallest deviation.$

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