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For company A, the amount profit earned in 1991 increased by

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For company A, the amount profit earned in 1991 increased by [#permalink] New post 22 May 2005, 08:40
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A
B
C
D
E

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For company A, the amount profit earned in 1991 increased by 20 percent than the year before and in 1992 increased 20 percent than the year before. For company B, the profit of 1991 increased by 40 percent than 1990 and in 1992, increased by 1 percent than 1991.If x expressed the percentage the total profit of A and B increased in 1991 and y expressed the percentage the total profit of A and B increased in the 1992. Which of the following is the relation between x and y?

1. x-y>2 2. 0<x-y<2 3. 0<y-x<2 4. y-x>0 5. y-x = -1
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Re: PS - Profit (700+ question) [#permalink] New post 22 May 2005, 09:06
pb_india wrote:
For company A, the amount profit earned in 1991 increased by 20 percent than the year before and in 1992 increased 20 percent than the year before. For company B, the profit of 1991 increased by 40 percent than 1990 and in 1992, increased by 1 percent than 1991.If x expressed the percentage the total profit of A and B increased in 1991 and y expressed the percentage the total profit of A and B increased in the 1992. Which of the following is the relation between x and y?

1. x-y>2 2. 0<x-y<2 3. 0<y-x<2 4. y-x>0 5. y-x = -1


I would go for 2 ( assuming the percentages x and y are expressed in fractions )

considering x as the percentage increase of the total profits in 91 over 90 , it would be 30% or .3

and y as the percentage increase of the total profits in 92 over 91 , it would be around 10% or .1

then x - y ~= .2

Have I interpreted the question correctly ?

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Re: PS - Profit (700+ question) [#permalink] New post 22 May 2005, 10:31
In my opinion, the quantity "total profit of A and B" is unmeasurable, because we don't know either the starting or ending relative values of profits of A and B. Thus, we just know that if A was A's profit in 1990, it was 1.2A in 1991 and 1.44A in 1992. Similarly, B's profit was B in 1990, 1.4B in 1991, and 1.414 in 1992. This still would not give us total profit, because we don't know the relative sizes of A and B.

Assuming equal (and I'd be very reluctant to make this assumption),
x is average of 0.2 + 0.4 = 0.3 = 30%, and
y is average of 0.2 and 0.01 = 0.105 = 10.5%
Obviously, x-y > 2.
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 [#permalink] New post 22 May 2005, 12:55
Here is my take on it.

It is probably wrong but, guys let me know what you think

20 < x < 40 (depending on initial shares of A and B profits)
1 < y < 20

if A is big then x and y are closer to 20, if B - x is closer to 40 and y is closer to 1

now, x - y > 0 so C and D are out

B is also out since x-y clearly can be greater than 2

E is fishy since it offers a constant relationship first, and x - y is clearly can be different from 1

A is left.
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 [#permalink] New post 22 May 2005, 18:53
0<x-y<2 for me

take some examples and let's say the companies A and B began with the same amount : 100

91 total profit (X): (100*1.2+100*1.4) / 100+100 = 260/200= 30%
92 total profit (Y): 120*1.2+140*1.01) / 120+140 = 277.4/260= 6%

means X = 0.3 and Y=0.06
only solution 2 is possible
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 [#permalink] New post 22 May 2005, 19:53
Hi Guys,

My answer is choice 1 i.e. x-y > 2

The way I will approach this problem is as follows.

Since this is a percentage question where we have no idea what A & B are we can safely assume A & B to be 100
1991 1992
A's increase 20 24 (20% of 120)

B's increase 40 1.4 (1% of 140)

Total x=60 y=25.4

Since x & y are percentages, we can divide the above by 100 to get the sum of percentage increase for each year.

Converting it x=0.60 y=0.254
to percentage

Therefore, x-y= 0.60 - 0.254=0.346 > 2. Hence x-y > 2. Hence choice 1 should be correct.
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Re: PS - Profit (700+ question) [#permalink] New post 22 May 2005, 21:26
pb_india wrote:
For company A, the amount profit earned in 1991 increased by 20 percent than the year before and in 1992 increased 20 percent than the year before. For company B, the profit of 1991 increased by 40 percent than 1990 and in 1992, increased by 1 percent than 1991.If x expressed the percentage the total profit of A and B increased in 1991 and y expressed the percentage the total profit of A and B increased in the 1992. Which of the following is the relation between x and y?

1. x-y>2 2. 0<x-y<2 3. 0<y-x<2 4. y-x>0 5. y-x = -1


PA91=1.2PA90, PA92=1.2PA91=1.44PA90
PB91=1.4PB90, PB92=1.01PB91=1.414PB90

x=(PA91+PB91-PA90-PB90)/(PA90+PB90)=(0.2PA90+0.4PB90)/(PA90+PB90)
0.2<x<0.4
y=(PA92+PB92-PA91-PB91)/(PA91+PB91)=(0.2PA91+0.01PB91)/(PA91+PB91)
0.2>y>0.01

0<x-y<0.39

I'd say 2 is right.
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 [#permalink] New post 22 May 2005, 21:37
I need a clarification. In standard English, when people say percentage does it mean 0.4 or 40 (%)?
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 [#permalink] New post 22 May 2005, 21:41
40 percent = 40%=0.4 :)
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 [#permalink] New post 22 May 2005, 22:54
Question seems fuzzy :-D , but I'll go with A.

Percentage, like in 40% ==> percentage is 40.
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Re: PS - Profit (700+ question) [#permalink] New post 23 May 2005, 09:31
HongHu wrote:
pb_india wrote:
For company A, the amount profit earned in 1991 increased by 20 percent than the year before and in 1992 increased 20 percent than the year before. For company B, the profit of 1991 increased by 40 percent than 1990 and in 1992, increased by 1 percent than 1991.If x expressed the percentage the total profit of A and B increased in 1991 and y expressed the percentage the total profit of A and B increased in the 1992. Which of the following is the relation between x and y?

1. x-y>2 2. 0<x-y<2 3. 0<y-x<2 4. y-x>0 5. y-x = -1


PA91=1.2PA90, PA92=1.2PA91=1.44PA90
PB91=1.4PB90, PB92=1.01PB91=1.414PB90

x=(PA91+PB91-PA90-PB90)/(PA90+PB90)=(0.2PA90+0.4PB90)/(PA90+PB90)
0.2<x<0.4
y=(PA92+PB92-PA91-PB91)/(PA91+PB91)=(0.2PA91+0.01PB91)/(PA91+PB91)
0.2>y>0.01

0<x-y<0.39

I'd say 2 is right.


Awesome HongHu.

Though the maxima and minima of x and y are indeed correct. Just the means are sufficient to eliminate the rest and arrive at 2.

HMTG
Re: PS - Profit (700+ question)   [#permalink] 23 May 2005, 09:31
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