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Gmat prep Question

by rakaisraka » Tue Sep 01, 2015 3:06 pm
The measurements obtained for the interior dimensions of a rectangular box are 200 cms by 200cms by 300 cms. If each of three measurements has an error of atmost 1cm , which of the folowing is the closest to the maximum possible difference , in cubic cms , between the actual capacity of the box and capacity computed using these measurements.
a) 100,000
b) 120,000
c) 160,000
d) 240,000
e) 320,000
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by GMATGuruNY » Tue Sep 01, 2015 3:12 pm
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200cm 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
Let L = 200, W = 200, and H = 300.
When each dimension changes by 1cm, the result is the following:

The LENGTH changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- W*H -- will change by 1cm:
1 * 200 * 300 = 60000.

The WIDTH changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- L*H -- will change by 1cm:
1 * 200 * 300 = 60000.

The HEIGHT changes by 1cm, implying that the product of the OTHER TWO DIMENSIONS -- L*W -- will change by 1cm:
1 * 200 * 200 = 40000.

Note:
Because each dimension is included in 2 of the 3 products above, there is some OVERLAP among the 3 changes in volume.
Thus:
Approximate total change in volume = 60000 + 60000 + 40000 = 160000.

The correct answer is C.
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by MartyMurray » Tue Sep 01, 2015 8:47 pm
rakaisraka wrote:The measurements obtained for the interior dimensions of a rectangular box are 200 cms by 200cms by 300 cms. If each of three measurements has an error of atmost 1cm , which of the folowing is the closest to the maximum possible difference , in cubic cms , between the actual capacity of the box and capacity computed using these measurements.
a) 100,000
b) 120,000
c) 160,000
d) 240,000
e) 320,000
The measurements are off by at most one cm. We could go with all of them actually being one cm smaller, one or two being actually 1 cm smaller and one or two being 1 cm bigger, or all of them being actually one cm bigger than the measurements. Since making them all bigger will give us the biggest difference in volume, add 1 cm to each and multiply.

Note: For all I know the other ways of changing them will generate answers that are close to what is generated by making them all bigger, but we have about two minutes to do this, and so why even bother thinking for a second about that.

The measurements give us 200 x 200 x 300 = 40,000 x 300 = 12,000,000

Adding one cm to each gives us 201 x 201 X 301 = 40,401 X 301 That looks like a lot of multiplying, but the difference between this product and 12,000,000 will come down to (300 x 401) + (1 x 40,000) = approximately 120,000 + 40,000 = 160,000.

Choose C.
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by rakaisraka » Wed Sep 02, 2015 4:00 pm
Hi, I could not understand this one. How come diff of 201 *201 * 301 and 200*200*300 is 160,000?
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by MartyMurray » Wed Sep 02, 2015 4:25 pm
rakaisraka wrote:Hi, I could not understand this one. How come diff of 201 *201 * 301 and 200*200*300 is 160,000?
200 x 200 x 300 = 12,000,000

201 x 201 x 301 = 12,160,701

When I did it I didn't want to bother calculating that second number.

So I looked at what changed.

200 x 200 = 40,000

201 x 201 = 40,401.

So the 401 makes a difference.

We also have 301 instead of 300. So the 1 makes a difference.

So first I approximated the difference that the 401 makes, by multiplying 401 by 300 to get 120,000 (well actually it's 120,300).

The I approximated the difference the 1 makes by multiplying 40,000 by 1, to get 40,000.

Then I added the differences, 120,000 + 40,000 = 160,000 for the total difference.
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by Max@Math Revolution » Wed Sep 02, 2015 9:27 pm
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


The measurements obtained for the interior dimensions of a rectangular box are 200 cms by 200cms by 300 cms. If each of three measurements has an error of atmost 1cm , which of the folowing is the closest to the maximum possible difference , in cubic cms , between the actual capacity of the box and capacity computed using these measurements.
a) 100,000
b) 120,000
c) 160,000
d) 240,000
e) 320,000

Since the error is 1 and the question asks for maximum volume difference, 201*201*301-200*200*300=160,701 approxiamtely gives us 160,000. Therefore C is the answer.


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by [email protected] » Thu Sep 03, 2015 9:22 am
Hi rakaisraka,

Mitch's approach is the most efficient way to solve this problem (without doing lots of calculations). The process of "estimating" is the key here. Look to take advantage of this option whenever:

1) The answer choices are 'spread out'
2) The word "approximation" (or similar) is used in the question

In this question, the phrase "closest maximum....difference" is a wordy way of say "approximate."

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