I took it as stocks were X in february, .9X in Jan, and (.8)(.9)X in March
You should always keep in mind what the base of a comparison is.
If the stocks were X
in February, then in January they were 0.9X
. That is correct, since the base for this comparison are the stocks in February.
But the base for comparison of the stocks in January and in March are the stocks in March. So the stocks in January make (100% + 20%) = 120% of the stocks in March. Therefore the formula for the stocks in March is (0.9X
)/1.2 = 0.75x
. In other words the stocks in March make 75% of the stocks in February. The decrease was 100% – 75% = 25%.
P.S. The formula "(.8)(.9)X
" would be TRUE, IF the question statement was "The stocks in March were 20% less than the stocks in January.
" In this case the base for the comparison (100%) would be the stocks in January.
Try to feel the difference between that statement and the original one "... stocks in January were ... 20% greater than they were in the March