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Math Expert V
Joined: 02 Sep 2009
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Mo2men wrote:
Bunuel wrote:
imhimanshu wrote:
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000
B. 120,000
C. 160,000
D. 200,000
E. 320,000

The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*200*300 = 60,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 200*1*300 = 60,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 200*200*1 = 40,000 cubic centimeters.

So, approximate maximum possible difference is 60,000 + 60,000 + 40,000 = 160,000 cubic centimeters.

is not it kind of overlapping? each dimension is included in 2 of the 3 products above.

Check the first sentence of the solution.
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Bunuel

i took this measurement as 21 21 31 and 20 20 30 and i computed to get 1671 ,is this approximation okay??
Math Expert V
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Posts: 56244
Re: The measurements obtained for the interior dimensions of a  [#permalink]

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jayantheinstein wrote:
Bunuel

i took this measurement as 21 21 31 and 20 20 30 and i computed to get 1671 ,is this approximation okay??

Here it worked because again the options are well spread but your way has one flaw: 1 centimetre for 20 is 5% while 1 centimetre for 200 is 0.5%, so for other similar questions it could give much more skewed result.
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Hi all,

I understand Bunuel's method to the solution, but I'm wondering where my logic is off. Could someone please help here?

Largest difference between capacities = (200*200*300) - [(199*199*299)]

Solved by multiplying (200-1)*(200-1) = (some #), and then (some #)*(300-1).

However, final answer is off. Could someone please explain my gap in logic?

Thank you!
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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So I got E because I thought I had to find the difference between the max and minimum possible values and I see that some people also followed the same logic. ( 201*201*301 - 199*199*299). Was breaking my head trying to see Bunuel's point and then re-read the question only to realize the error in my understanding. :D

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The measurements obtained for the interior dimensions of a  [#permalink]

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Bunuel wrote:
imhimanshu wrote:
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000
B. 120,000
C. 160,000
D. 200,000
E. 320,000

The options are well spread so we can approximate.

Changing the length by 1 cm results in change of the volume by 1*200*300 = 60,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 200*1*300 = 60,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 200*200*1 = 40,000 cubic centimeters.

So, approximate maximum possible difference is 60,000 + 60,000 + 40,000 = 160,000 cubic centimeters.

Why is the difference not (201x201x301)-(199x199x299)? Is it because of this wording: "each of the three measurements has an error of at most 1 centimeter"? Therefore, the difference between the actual and given dimensions can be max. 1cm?

The wording is different from saying that a measurement has a margin of error of 1cm, which would mean that the difference could be +/- 1cm from the given values, correct?
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Cez005 wrote:

Why is the difference not (201x201x301)-(199x199x299)? Is it because of this wording: "each of the three measurements has an error of at most 1 centimeter"? Therefore, the difference between the actual and given dimensions can be max. 1cm?

The wording is different from saying that a measurement has a margin of error of 1cm, which would mean that the difference could be +/- 1cm from the given values, correct?

The question is:
which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements

The actual capacity will be 200*200*300. So we have to calculate the volume for two cases and determine which case will result in the maximum difference.

Posted from my mobile device
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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dina98 wrote:
Cez005 wrote:

Why is the difference not (201x201x301)-(199x199x299)? Is it because of this wording: "each of the three measurements has an error of at most 1 centimeter"? Therefore, the difference between the actual and given dimensions can be max. 1cm?

The wording is different from saying that a measurement has a margin of error of 1cm, which would mean that the difference could be +/- 1cm from the given values, correct?

The question is:
which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements

The actual capacity will be 200*200*300. So we have to calculate the volume for two cases and determine which case will result in the maximum difference.

Posted from my mobile device

You have to maximize the difference and that will be the answer. Comparing different cases isn't the correct approach...
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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300*200*200=12,000,000

299*199*199=(300-1)*(200-1)*(200-1)
Solve individually we get:
(60000-200-300+1)*(200-1)
=(60000-500)*(200-1) I have ignored the 1 above in coz we need the approx value

Solving we get 1200000-100000-60000

Total difference = 160,000 (C)
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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imhimanshu wrote:
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000
B. 120,000
C. 160,000
D. 200,000
E. 320,000

This problem can be approximated as follows:

1cm change in the length = 1*200*300 = 60,000
1cm change in width = 200*1*300 = 60,000
1cm change in height = 200:200*1 = 40,000

2*60,000 + 40,000 = 160,000.
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The measurements obtained for the interior dimensions of a  [#permalink]

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Bunuel wrote:
imhimanshu wrote:
Hello Bunuel,
Sorry, but I dont understand the solution.
I thought,since it is given that the dimensions have at most an error of 1 cm. So maximum possible difference in volume would be: (201* 201 * 301) - (200 *200*300). Pls suggest what i am doing wrong.

Posted from my mobile device

Yes, that's correct. But the way I suggested gives and approximate answer which is much easier to calculate than (201*201*301) - (200*200*300)= 160,701.

Yep. The numbers themselves and "closest to maximum" suggest finding a simple way and approximation does just that.
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Bunuel wrote:
imhimanshu wrote:
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000
B. 120,000
C. 160,000
D. 200,000
E. 320,000

The options are well spread so we can approximate.

Changing the length by 1 cm results in change of the volume by 1*200*300 = 60,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 200*1*300 = 60,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 200*200*1 = 40,000 cubic centimeters.

So, approximate maximum possible difference is 60,000 + 60,000 + 40,000 = 160,000 cubic centimeters.

hi

for the ease of calculation, you have set the numbers this way, I understand

but, for the sake of clarity, please do let me know whether I am okay

1 * 200 * 300 + 201 * 1 * 300 + 201 * 201 * 1

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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Just to clarify - the logic here is that:

If by changing dimension h to h+1, volume will change from lbh to (h+1)lb = lbh + lb. Since we know lbh (200X200X300), for each change in value, we are just calculating the change (lb - similarly for b+1 it is lh, and for l+1 it'll be bh).

This is a good question!
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Are there any "similar" questions? This is the first I've found after doing 6 Manhattan CATS, 3 Official Guide CATs and my real GMAT. Just asking to know if I should practice more or where to excercise this topic-approach.
Thanks
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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imhimanshu wrote:
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?

A. 100,000
B. 120,000
C. 160,000
D. 200,000
E. 320,000

Here we have two options , one is subtracting dimensions by 1 or adding 1 to them. Since we are multiplying adding 1 gives maximum difference.

So Answer will be 201*201*301 - 200*200*300 = 160000.

Computational tips :

201 * 201 = (200 + 1)^2 = 4*10^4 + 1 + 400 = 40400(approx)

201^2 * 301 = 404 * 10^2 *301 = 1204
0000
1204
=121604 * 10^2

So difference will be 160000
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Re: The measurements obtained for the interior dimensions of a  [#permalink]

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Danuthan wrote:
Hi there,

The questions states that there is a 1 cm error to each of the measurements.

So can we assume that the error is +-1cm?

Thanks,

the question clearly states that we need to find the approximate difference between the error value i.e +-1 and value computed by sides 200,200 and 300 respectively

If the question would've asked the maximum possible difference between error values then your solution would've been correct.

furthermore, if you consider (200*200*300)-(199*199*299)
the difference turns out to be 159301 which is approximately option (C)

and if you consider, (201*201*301)-(200*200*300)
the difference turns out approximately option (c)

HTH Re: The measurements obtained for the interior dimensions of a   [#permalink] 27 Mar 2019, 01:43

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