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DS exercise

by SFtraveler » Sun Feb 13, 2011 3:30 pm
Does the following statement provide sufficient information to answer the question? Show how if it does.

Question: What was the percent increase in profits for Company X between 1991 and 1993?

Statement: The average of the annual profits of 1991 and 1993 was 12.5% higher than the profit in 1991.
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Source: — Data Sufficiency |
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by Night reader » Sun Feb 13, 2011 5:49 pm
SFtraveler wrote:Does the following statement provide sufficient information to answer the question? Show how if it does.

Question: What was the percent increase in profits for Company X between 1991 and 1993?

Statement: The average of the annual profits of 1991 and 1993 was 12.5% higher than the profit in 1991.
Q: (%1993 - %1991)/ %1991 ? Call %1991=X and %1993=Y --> (X-Y)/Y
st: (X+Y)/2 = X +0,125 (12.5%) --> (X+Y) = 2*X +0,25 --> Y = X +0,25; [X -(X+0,25)]/ X = 0,25/ X; suppose X=100% OR 1, then change --> 0,25/1=0,25 OR 25% Sufficient.
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by Anurag@Gurome » Sun Feb 13, 2011 6:52 pm
SFtraveler wrote:Does the following statement provide sufficient information to answer the question? Show how if it does.

Question: What was the percent increase in profits for Company X between 1991 and 1993?

Statement: The average of the annual profits of 1991 and 1993 was 12.5% higher than the profit in 1991.

Let the annual profits of 1991 be x and the annual profits of 1993 be y.
So the average of their profits is (x+y)/2.
We need to evaluate {(y-x)/x}*100.
This is 12.5% higher than the profit in 1991 which is x.
Or (x+y)/2 = {(100 + 12.5)/100}*x
Or (x+y)/2 = x+ x/8 = 9x/8.
Or 4x + 4y = 9x.
Or 4y = 5x.
So {(y-x)/x}*100 =(5x/4 - x)/x * 100 = ¼ * 100 = 25%.
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by SFtraveler » Tue Feb 22, 2011 11:33 pm
Night reader wrote:
SFtraveler wrote:Does the following statement provide sufficient information to answer the question? Show how if it does.

Question: What was the percent increase in profits for Company X between 1991 and 1993?

Statement: The average of the annual profits of 1991 and 1993 was 12.5% higher than the profit in 1991.
Q: (%1993 - %1991)/ %1991 ? Call %1991=X and %1993=Y --> (X-Y)/Y
st: (X+Y)/2 = X +0,125 (12.5%) --> (X+Y) = 2*X +0,25 --> Y = X +0,25; [X -(X+0,25)]/ X = 0,25/ X; suppose X=100% OR 1, then change --> 0,25/1=0,25 OR 25% Sufficient.
Nightreader, why would it be (X-Y)/Y?
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by sanju09 » Wed Feb 23, 2011 2:43 am
SFtraveler wrote:Does the following statement provide sufficient information to answer the question? Show how if it does.

Question: What was the percent increase in profits for Company X between 1991 and 1993?

Statement: The average of the annual profits of 1991 and 1993 was 12.5% higher than the profit in 1991.

Let's rephrase...

If a is the profits for Company X in 1991 and b is the profits for Company X in 1993, such that a < b, then what is (b - a)/a × 100 = {(b/a) - 1} × 100? All we need to do is to find b/a only.

Statement adds...

½ (a + b) = 1.125 a

Or a + b = 2.25 a

Or b = 1.25 a

Or b/a = 1.25


Hence the given statement is sufficient to answer the stem.
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