Arithmetic question from free official guide exam

[AlexandraO504]

Hello,

I have a question regarding a question which appeared in the free GMAT official exam we have access to through mba.com. Question copied below:

Q: The measurements obtained for the interior dimensions of a rectangular box are 200 centimeters by 200 centimeters by 300 centimeters. If each of the three measurements has an error of at most 1 centimeter, which of the following is closest to the 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. 240,000

E. 320,000

In my mind you have to work out 200 x 200 x 300 followed by 201 x 201 x 301 to get to the answer but not sure how one does this quickly. Could you shed some light?

Thanks!

[Sage Pearce-Higgins]

Thanks for posting, but please read the forum guidelines before doing so. This problem belongs in the GMAT Prep folder. But no worries for now.

I like your interpretation of the problem: you considered the biggest possible box, and then considered trying to find the difference between that and the precise dimensions of the box. To find a difference, we could do some subtraction. However, as you pointed out, calculating 201 x 201 x 301 is not really practical. So, how about using some of your algebra skills to turn it into the following calculation? Have a go at this:

(200 + 1)(200 + 1)(300 + 1) - 200 x 200 x 300 = ???

Although that's a practical way of doing it (I think you could do this in less than 2 minutes), if we notice that the answers are quite spread out we might consider estimation as a strategy. Think about it in these terms: if we take the box 200 x 200 x 300 and make it 1cm bigger in each dimension, then we add on a layer 1cm thick to the top (that would be 200 x 300), to the side (200 x 300) and the end (200 x 200). Add these up (60000 + 60000 + 40000) and it takes you to answer C.