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Perimeter

by goyalsau » Tue Dec 07, 2010 3:30 am
What is the percentage increase/decrease in the perimeter of the rectangle?

(A) The length of the rectangle is increased by 19% and its breadth is decreased by 26%.

(B) If the length of the rectangle is increased by 26% and its breadth is decreased by 19%, then the ratio of its length and breadth is 7 : 3.
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by abhishekg21 » Tue Dec 07, 2010 3:41 am
should be B.

from 1
new length=119L/100
new width=74W/100

so ratio of perimeter chnage=2(119L+74W)/2(L+W)=insufficient

from 2) 119L/74W=7/3

so you can represent L in terms of W and hence you can find out % change
ratio of perimeter chnage=2(119L+74W)/2(L+W)=sufficient
so B
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by goyalsau » Tue Dec 07, 2010 3:47 am
abhishekg21 wrote:should be B.

from 1
new length=119L/100
new width=74W/100

so ratio of perimeter chnage=2(119L+74W)/2(L+W)=insufficient

from 2) 119L/74W=7/3

so you can represent L in terms of W and hence you can find out % change
ratio of perimeter chnage=2(119L+74W)/2(L+W)=sufficient
so B
Even i marked B, But OA is C
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by goyalsau » Tue Dec 07, 2010 6:22 am
goyalsau wrote:
abhishekg21 wrote:should be B.

from 1
new length=119L/100
new width=74W/100

so ratio of perimeter chnage=2(119L+74W)/2(L+W)=insufficient

from 2) 119L/74W=7/3

so you can represent L in terms of W and hence you can find out % change
ratio of perimeter chnage=2(119L+74W)/2(L+W)=sufficient
so B
Even i marked B, But OA is C
Guys Please share your views on this one too.
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by tomada » Tue Dec 07, 2010 8:40 am
On one hand, you said so ratio of perimeter change = 2(119L+74W)/2(L+W)=insufficient

Below that, you expressed the ratio of perimeter change the same way as above - 2(119L+74W)/2(L+W) - but indicated this ratio as sufficient.

Not sure how it went from being insufficient to sufficient
abhishekg21 wrote:should be B.

from 1
new length=119L/100
new width=74W/100

so ratio of perimeter chnage=2(119L+74W)/2(L+W)=insufficient

from 2) 119L/74W=7/3

so you can represent L in terms of W and hence you can find out % change
ratio of perimeter chnage=2(119L+74W)/2(L+W)=sufficient
so B
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by tomada » Tue Dec 07, 2010 9:03 am
Anyway...I think Statement (2) is necessary, but not sufficient by itself.

Statement (2) gives the following relationship:

(1.26L)/(0.81W) = 7/3.

Doing a tad of cross-multiplying and simplifying, this yields the following.

L = 1.5W

Now we have the relationship between the length and the width of the rectangle, but I can't see how this, in of itself, yields enough information to solve the problem.

Statement (1) would be sufficient to determine the % change in area, but not in perimeter.

If the original perimeter = 2L + 2W, Statement (1) tells us the perimeter is changed to 1.19L + 1.19L + 0.74W + 0.74W = 2.38L + 1.48W.

The % change will vary with the original values of L and W, which are both unknown.

Now, let's combine the two statements...

Statement (2) enables us to establish the relationship L=1.5W. Thus, the original perimeter can be rewritten as:

1.5W + 1.5W + W + W = 5W.

The revised perimeter from Statement (1) can now be rewritten as:

2.38(1.5W) + 1.48W = 5.05W.

The point is that we can express the perimeter in terms of one dimension, both initially and after the perimeter is changed.

Answer: C
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by Night reader » Tue Dec 07, 2010 9:17 am
tomada wrote:Anyway...I think Statement (2) is necessary, but not sufficient by itself.

Statement (2) gives the following relationship:

(1.26L)/(0.81W) = 7/3.

Doing a tad of cross-multiplying and simplifying, this yields the following.

L = 1.5W

Now we have the relationship between the length and the width of the rectangle, but I can't see how this, in of itself, yields enough information to solve the problem.

Statement (1) would be sufficient to determine the % change in area, but not in perimeter.

If the original perimeter = 2L + 2W, Statement (1) tells us the perimeter is changed to 1.19L + 1.19L + 0.74W + 0.74W = 2.38L + 1.48W.

The % change will vary with the original values of L and W, which are both unknown.

Now, let's combine the two statements...

Statement (2) enables us to establish the relationship L=1.5W. Thus, the original perimeter can be rewritten as:

1.5W + 1.5W + W + W = 5W.

The revised perimeter from Statement (1) can now be rewritten as:

2.38(1.5W) + 1.48W = 5.05W.

The point is that we can express the perimeter in terms of one dimension, both initially and after the perimeter is changed.

Answer: C
Tomada are sure about your calc?

126L/81W=7/3 => 126*3L=81*7W => 18L=17W => L=(17/18)*W
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by tomada » Tue Dec 07, 2010 10:23 am
Yes, I'm sure about my calculations. Speaking of which, how did you get 18L = 17W from 378L = 567W ?

Night reader wrote:
tomada wrote:Anyway...I think Statement (2) is necessary, but not sufficient by itself.

Statement (2) gives the following relationship:

(1.26L)/(0.81W) = 7/3.

Doing a tad of cross-multiplying and simplifying, this yields the following.

L = 1.5W

Now we have the relationship between the length and the width of the rectangle, but I can't see how this, in of itself, yields enough information to solve the problem.

Statement (1) would be sufficient to determine the % change in area, but not in perimeter.

If the original perimeter = 2L + 2W, Statement (1) tells us the perimeter is changed to 1.19L + 1.19L + 0.74W + 0.74W = 2.38L + 1.48W.

The % change will vary with the original values of L and W, which are both unknown.

Now, let's combine the two statements...

Statement (2) enables us to establish the relationship L=1.5W. Thus, the original perimeter can be rewritten as:

1.5W + 1.5W + W + W = 5W.

The revised perimeter from Statement (1) can now be rewritten as:

2.38(1.5W) + 1.48W = 5.05W.

The point is that we can express the perimeter in terms of one dimension, both initially and after the perimeter is changed.

Answer: C
Tomada are sure about your calc?

126L/81W=7/3 => 126*3L=81*7W => 18L=17W => L=(17/18)*W
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by Rahul@gurome » Tue Dec 07, 2010 10:23 am
goyalsau wrote:What is the percentage increase/decrease in the perimeter of the rectangle?
(A) The length of the rectangle is increased by 19% and its breadth is decreased by 26%
(B) If the length of the rectangle is increased by 26% and its breadth is decreased by 19%, then the ratio of its length and breadth is 7 : 3
Say, length = L and breadth = B
Perimeter = 2(L + B)

Statement 1: Length is increased by 19% and breadth is decreased by 26%
New length = (1.19)L
New breadth = (0.74)B
New perimeter = 2(1.19L + 0.74B)

Percentage change in perimeter = 100*[(1.19L + 0.74B) - (L + B)]/(L + B) = 100*(0.19L - 0.26B)/(L + B)
We don't know anything about L and B.

Not sufficient.

Statement 2: L is increased by 26% and B is decreased by 19% and new L : new B = 7 : 3
New length = 1.26L
New breadth = 0.81B
(1.26L)/(0.81B) = 7/3 => 3*126*L = 7*81*B => 2L = 3B => L = 1.5B

New perimeter = 2(1.26L + 0.81B)

Percentage change in perimeter = 100*[(1.26L + 0.81B) - (L + B)]/(L + B) = 100*(0.26L - 0.19B)/(L + B)

Replacing L = 1.5b, we can easily get the percentage change.

The correct answer is B.
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by tomada » Tue Dec 07, 2010 10:37 am
Thanks, Rahul. I knew that the relationship L=1.5W was correct, and then substitute one into the other to get a relationship with one variable, but mistakenly thought I needed to tie in back to the first equation.

Rahul@gurome wrote:
goyalsau wrote:What is the percentage increase/decrease in the perimeter of the rectangle?
(A) The length of the rectangle is increased by 19% and its breadth is decreased by 26%
(B) If the length of the rectangle is increased by 26% and its breadth is decreased by 19%, then the ratio of its length and breadth is 7 : 3
Say, length = L and breadth = B
Perimeter = 2(L + B)

Statement 1: Length is increased by 19% and breadth is decreased by 26%
New length = (1.19)L
New breadth = (0.74)B
New perimeter = 2(1.19L + 0.74B)

Percentage change in perimeter = 100*[(1.19L + 0.74B) - (L + B)]/(L + B) = 100*(0.19L - 0.26B)/(L + B)
We don't know anything about L and B.

Not sufficient.

Statement 2: L is increased by 26% and B is decreased by 19% and new L : new B = 7 : 3
New length = 1.26L
New breadth = 0.81B
(1.26L)/(0.81B) = 7/3 => 3*126*L = 7*81*B => 2L = 3B => L = 1.5B

New perimeter = 2(1.26L + 0.81B)

Percentage change in perimeter = 100*[(1.26L + 0.81B) - (L + B)]/(L + B) = 100*(0.26L - 0.19B)/(L + B)

Replacing L = 1.5b, we can easily get the percentage change.

The correct answer is B.
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