The profits of a new company were x percent higher in the second year

Question

The profits of a new company were x percent higher in the second year than the first year and y percent lower in the third year than the second year. Were the profits higher in the third year than the first year?

(1) 1 - x < 1 - y
(2) xy/100 < x - y

(1) 1 - x < 1 - y
(2) xy/100 < x - y

Bunuel · Answer

Similar question from OG to practice: https://gmatclub.com/forum/the-annual-r ... 89184.html

aayushigupta123 · Answer

Profits increases by x% in the 2nd year and reduces by y% in the 3rd year.
Total percentage change in profits at the end of 3rd year will be (x-y-xy/100).
(1) 1 - x < 1 - y: According to this, x>y, but we do not know the magnitude i.e. by how much.
Hence, this is not sufficient.

(2) xy/100 < x - y: According to this, (x-y-xy/100) > 0, and hence profit will increase by 3rd year.
Hence, this is sufficient to answer the question.

Ans should be option B

garcmillan · Answer

For DS problems, we shouls always get the relationships of the variables in the equation in order to know what conditions are needed to be able to answer the question

A=profits first year
B=profits second year
C=profits third year

1ºequation: B=(1+x)A
2ºequation: C=(1-y)B
Question to answer C>A? in other words (1-y)(1+x)A>A. Crossing off A in both sides of the equation: (1-y)(1+x)>1

Therefore we need to know if (1-y)*(1+x)>1,

but what is the relationship between x and y in this equation? It does not seem we know the relationship very well to be able to answer. Let's multiply the brackets (1-y)*(1+x)=1-y+x-x*y

Ok, so now we know that we need to know both the x+(-)y reationship and the x*y one

Option (1): 1-x<1 -y, which is -x<-y, which is x>y. This option tells me the x+(-)y relationship, but what about the multiplication? NOT SUFFICIENT

Option (2): xy/100<x-y. We inmediately see we have the x+(-)y reationship and the x*y one. No need to calculate. If we know the relationship between both, we can already conclude if C>A or not. Therefore: SUFFICIENT

Option B

Bunuel · Answer

Video Explanation

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Kinshook · Answer

The profits of a new company were x percent higher in the second year than the first year and y percent lower in the third year than the second year. Were the profits higher in the third year than the first year? Q. (100+x)(100-y)/10000 -1 = (x-y)/100-xy/10000 = (x-y) -xy/100> 0 ? (1) 1 - x < 1 - y x - y > 0; x > y; In (x-y)-xy/100, x-y>0 but -xy/100<0 NOT SUFFICIENT (2) xy/100 < x - y x-y - xy/100>0 SUFFICIENT IMO B

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The profits of a new company were x percent higher in the second year

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The profits of a new company were x percent higher in the second year

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