Kaplan Problem: Don't understand solution logic

[Night reader]

To simplify conversion take 01 year (X) is 0.8 part of 03 year(Y). This makes X=0.8Y OR X=4Y/5. Now rewrite X=4Y/5 as 4Y=5X and Y=5X/4. Does it make sense?

Hi All,

There is a sample problem with explanation in the Kaplan 2010/2011 book that is confusing the hell out of me. If you refer to page 444 of the Kaplan GMAT Premier 2010-2011 guide, there is a sample problem as follows:

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

Statement 1) The company earned 20% less profit in 1991 than in 1993.

Answer:

Statement 1 is sufficient. We could reverse the math and figure out percent increase from the given decrease. Let the 1993 profit be P1993 and the 1991 profit be P1991.

The statement can be translated to:

P1991 = 0.80*P1993 OR P1991 = 4/5*P1993

That means P1993 = 5/4*P1991 OR 1.25*P1991

This is a 125% difference, or a 25% increase.


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I understand the entire problem sequence until the highlighted line in red. How did the book determine that P1993 came to be 5/4??? I have been thinking for the last 3 hours of how they acheived this and it makes no sense to me. The closest I can come is to determining that 4/5 * the 1/5 left gives me 4/25 which can be reduced to 1/4 which would give me the 25% but I don't even know if that's the correct method of going about this....please explain!

Oxford Bound

[Night reader]

1/.8 is just reciprocal of 4/5 which is 5/4 and 1.25 is decimal representation of 125%

Sort of...

1/.8 = 1.25, but the book states this is a 125% difference...what is thier base starting point? The sequence of the question's solution just seems fuzzy to me.

understood that 1.00 - .20 (20% less than 1993) = .80

But why am I taking 1/.80 to get this 125% difference, what does this mean? To my knowledge, percent difference problems are original amount - new amount / original amount, but I don't see that sort of logic in this problem. I feel like i'm missing a huge knowledge piece here that's preventing me from understanding your logic Night Reader...

To simplify conversion take 01 year (X) is 0.8 part of 03 year(Y). This makes X=0.8Y OR X=4Y/5. Now rewrite X=4Y/5 as 4Y=5X and Y=5X/4. Does it make sense?

[Stuart@KaplanGMAT]

Hi,

let's examine an analogous problem:

If y is 80% of x, then what percent greater than y is x?

We know that y = 80%(x), or y = 4/5(x).

We can now use simple algebra to solve:

1) multiply both sides by 5:

5y = 4x

2) divide both sides by 4:

(5/4)y = x

Finally, let's convert (5/4) to a percent:

(5/4) * 100% = (500/4)% = 125%

So, putting the x on the left side:

x = 125%(y)

The final step: we want to know what percent greater than y is x, so:

% change = (new - old)/(old) * 100%
% change = (125%y - 100%y)/(100%y) * 100%
% change = (25%y)/(100%y) * 100%
% change = 25%

Hope that helps!

[Night reader]

Hi Stuart, if y=(4/5)*x and x=1 then by answering 25% to what percent greater than y is x we SHOULD get (4/5)*x + 25%*x=1 while we get x(4/5 +1/4)=x*(21/20) AND here we cannot assume at one instance 4/5 of x and 25% of y.
y=80% and x=100% the difference between x and y is 20%

increase in y is 25% = change in y for x OR (4/5)*x *(1 1/4)=X and
decrease in x is 20% = change in x for y OR (x - 0.2*x)=0.8*x, 80% of x

Hi,

let's examine an analogous problem:

If y is 80% of x, then what percent greater than y is x?

We know that y = 80%(x), or y = 4/5(x).

We can now use simple algebra to solve:

1) multiply both sides by 5:

5y = 4x

2) divide both sides by 4:

(5/4)y = x

Finally, let's convert (5/4) to a percent:

(5/4) * 100% = (500/4)% = 125%

So, putting the x on the left side:

x = 125%(y)

The final step: we want to know what percent greater than y is x, so:

% change = (new - old)/(old) * 100%
% change = (125%y - 100%y)/(100%y) * 100%
% change = (25%y)/(100%y) * 100%
% change = 25%

Hope that helps!

[Stuart@KaplanGMAT]

Hi Stuart, if y=(4/5)*x and x=1 then by answering 25% to what percent greater than y is x we SHOULD get (4/5)*x + 25%*x=1 while we get x(4/5 +1/4)=x*(21/20) AND here we cannot assume at one instance 4/5 of x and 25% of y.
y=80% and x=100% the difference between x and y is 20%

increase in y is 25% = change in y for x OR (4/5)*x *(1 1/4)=X and
decrease in x is 20% = change in x for y OR (x - 0.2*x)=0.8*x, 80% of x

Hi,

the mistake in your math is:

we SHOULD get (4/5)*x + 25%*x=1

The actual equation should be:

(4/5)*x + 25%*y = 1

and since y = 4/5(x):

(4/5)x + 1/4(4/5)x = 4/5(x) + (1/5)x = 1x = 1

(since x=1)

[Night reader]

I guess confusion occurs in my interpretation I know that x is greater than y by 25%. For this I perform (x- 0.8x)=0.2x 0.2x/0.8x=0.25 OR 25%. What you specify is an amount increase of x expressed in the percentages and I meant the difference of x and y in percentages... like 5-3=2, 100%-80%=20% ... thanks anyway

Hi Stuart, if y=(4/5)*x and x=1 then by answering 25% to what percent greater than y is x we SHOULD get (4/5)*x + 25%*x=1 while we get x(4/5 +1/4)=x*(21/20) AND here we cannot assume at one instance 4/5 of x and 25% of y.
y=80% and x=100% the difference between x and y is 20%

increase in y is 25% = change in y for x OR (4/5)*x *(1 1/4)=X and
decrease in x is 20% = change in x for y OR (x - 0.2*x)=0.8*x, 80% of x

Hi,

the mistake in your math is:

we SHOULD get (4/5)*x + 25%*x=1

The actual equation should be:

(4/5)*x + 25%*y = 1

and since y = 4/5(x):

(4/5)x + 1/4(4/5)x = 4/5(x) + (1/5)x = 1x = 1

(since x=1)

[Stuart@KaplanGMAT]

I guess confusion occurs in my interpretation I know that x is greater than y by 25%.

Right - so here's the important thing to remember:

In the phrase "x is greater than y by z%", y is the whole (original amount), x is the part (new amount) and z is the percent.

So:

% change = (amount of change)/(original amount) * 100%

or

z% = (x-y)/(y) * 100%

In other words, whatever follows "than" is the "original amount" in the equation.

Similarly, in the phrase "x is z% of y", y is the whole, x is the part and z is the percent, so when we write the basic percent equation:

% = (part/whole) * 100%

we get

z% = (x/y) * 100%