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Question

During the first six months of last year, profits at Company Y were 8% greater in February than in January, 12% less in March than in February, 25% greater in April than in March, 15% less in May than in April, and 10% greater in June than in May. In which month were profits closest to the profits in January?

Answer Choices

A. $February$
B. $March$
C. $April$
D. $May$
E. $June$

Steps

Explanation	Calculations	Help
$We name the variables for monthly profits to avoid ambiguity.$	$J an = profits in January F e b = profits in February M a r = profits in March A p r = profits in April M a y = profits in May J u n = profits in June$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "profits at Company Y were 8% greater in February than in January" into a multiplication factor.$	$F e b = 1.08 \times J an$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "12% less in March than in February" into a multiplication factor.$	$M a r = 0.88 \times F e b$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "25% greater in April than in March" into a multiplication factor.$	$A p r = 1.25 \times M a r$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "15% less in May than in April" into a multiplication factor.$	$M a y = 0.85 \times A p r$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "10% greater in June than in May" into a multiplication factor.$	$J u n = 1.10 \times M a y$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We express each month's profits as a multiple of January's profits by chaining the factors and then round for simplicity.$	$F e b = 1.08 \times J an M a r = 0.88 \times 1.08 \times J an = 0.95 \times J an A p r = 1.25 \times 0.95 \times J an = 1.19 \times J an M a y = 0.85 \times 1.19 \times J an = 1.01 \times J an J u n = 1.10 \times 1.01 \times J an = 1.11 \times J an$	Theory & Tactics Method Card CALC1-B Click to view full details
$We calculate each month's absolute deviation from 1.00 to see which is smallest.$	$∣1.08 - 1.00∣ = 0.08 ∣0.95 - 1.00∣ = 0.05 ∣1.19 - 1.00∣ = 0.19 ∣1.01 - 1.00∣ = 0.01 ∣1.11 - 1.00∣ = 0.11},{$
$We see that May's deviation 0.01 is the smallest, so May's profits are closest to January's.$	$May is closest because 0.01 is the smallest deviation.$

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Final Answer

D

Question

During the first six months of last year, profits at Company Y were 8% greater in February than in January, 12% less in March than in February, 25% greater in April than in March, 15% less in May than in April, and 10% greater in June than in May. In which month were profits closest to the profits in January?

Answer Choices

A. $February$
B. $March$
C. $April$
D. $May$
E. $June$

Steps

Explanation	Calculations	Help
$We name the variables for monthly profits to avoid ambiguity.$	$J an = profits in January F e b = profits in February M a r = profits in March A p r = profits in April M a y = profits in May J u n = profits in June$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "profits at Company Y were 8% greater in February than in January" into a multiplication factor.$	$F e b = 1.08 \times J an$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "12% less in March than in February" into a multiplication factor.$	$M a r = 0.88 \times F e b$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "25% greater in April than in March" into a multiplication factor.$	$A p r = 1.25 \times M a r$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "15% less in May than in April" into a multiplication factor.$	$M a y = 0.85 \times A p r$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "10% greater in June than in May" into a multiplication factor.$	$J u n = 1.10 \times M a y$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We express each month's profits as a multiple of January's profits by chaining the factors and then round for simplicity.$	$F e b = 1.08 \times J an M a r = 0.88 \times 1.08 \times J an = 0.95 \times J an A p r = 1.25 \times 0.95 \times J an = 1.19 \times J an M a y = 0.85 \times 1.19 \times J an = 1.01 \times J an J u n = 1.10 \times 1.01 \times J an = 1.11 \times J an$	Theory & Tactics Method Card CALC1-B Click to view full details
$We calculate each month's absolute deviation from 1.00 to see which is smallest.$	$∣1.08 - 1.00∣ = 0.08 ∣0.95 - 1.00∣ = 0.05 ∣1.19 - 1.00∣ = 0.19 ∣1.01 - 1.00∣ = 0.01 ∣1.11 - 1.00∣ = 0.11},{$
$We see that May's deviation 0.01 is the smallest, so May's profits are closest to January's.$	$May is closest because 0.01 is the smallest deviation.$

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Final Answer

D