Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March?

A. 5% B. 10% C. 20% D. 25% E. 50%

(D) Let us denote the amount of the stocks by x and y in February and in March respectively. In January the stocks were 0.9x on the one hand and 1.2y on the other. Therefore we can write the equality: 0.9x = 1.2y y/x = 0.9/1.2 = 3/4 = 0.75 Therefore the percentage decrease was 100% – 75% = 25%.

The correct answer is D. -------------

It is not clear that both relative differences are referring to the same reference point.

Such assumption follows from the characteristic itself, since this characteristic is compared in months. There is no sense in comparing stocks on January, 31st and February 1st. Otherwise, it would be specified. This monthly parameter could be measured on the same day, or it could be some kind of average, etc. In any case, the way it is stated in the problem implies that we should refer to it as to a monthly parameter.

I was confused with this question, I'm not sure if the wording threw me off. I took it as stocks were X in February, .9X in Jan, and (.8)(.9)X in March, so the difference from Feb to March was 100 – 72. Can you please explain further? Thanks!

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".

Hello and thanks for the help. I'm having a hard time understanding the wording of this question, as well as your explanation. Can you explain this question, giving dollar values for January, Feb and March?

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