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

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

Answer: C.


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

Answer: C.


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

thanks in advance
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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]
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.
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Re: The measurements obtained for the interior dimensions of a [#permalink]
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?

So the answer is 201*201*301-199*199*299?

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

Answer: C.



Bunuel,

I don't understand why the have you taken only 1 cm change in the three dimensions provided. Can you explain this process in a detailed way? I am missing some key concept here in the solution provided by you
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Re: The measurements obtained for the interior dimensions of a [#permalink]
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This problem is simple once a visual is formed. Refer to the image below, with each 1cm increase comes an increase in 200 x 200 cm^2 or 200 x 300 cm^2.

Summing 1cm slabs gives 200 x 200 + 200 x 300 + 200 x 300 = 160,000.
Attachments

Screen Shot 2020-06-27 at 6.13.07 pm.png
Screen Shot 2020-06-27 at 6.13.07 pm.png [ 88.53 KiB | Viewed 5911 times ]

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


Solution:

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

201 x 201 x 301 - 200 x 200 x 300

However, this can be approximated by the total volume of the 6 sides of the box with each side having a thickness of 0.5 cm. Therefore, the approximation is:

2(200 x 300 x 0.5) + 2(200 x 300 x 0.5) + 2(200 x 200 x 0.5)

60,000 + 60,000 + 40,000

160,000

Answer: C
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Re: The measurements obtained for the interior dimensions of a [#permalink]
Could you please explain this step further? "However, this can be approximated by the total volume of the 6 sides of the box with each side having a thickness of 0.5 cm."

Also could the dimensions be 199*199*299?

Thank you.

ScottTargetTestPrep 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 closest 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


Solution:

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

201 x 201 x 301 - 200 x 200 x 300

However, this can be approximated by the total volume of the 6 sides of the box with each side having a thickness of 0.5 cm. Therefore, the approximation is:

2(200 x 300 x 0.5) + 2(200 x 300 x 0.5) + 2(200 x 200 x 0.5)

60,000 + 60,000 + 40,000

160,000

Answer: C
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