One of the reasons why the GMAT is my favourite test of all is that it is so well defined in terms of the skills tested and consistently so. One of the things that is absolutely essential to remember on the GMAT Problem Solving (PS) is that the test-setters do not want you to do donkey work with respect to calculation. The leading companies in the world are not paying thousands of dollars to hire graduates from premier b-schools to do what a calculator can do!
This knowledge goes a great way in helping you overcome potential speed-breakers when you are suddenly faced with a problem that on the face of it looks as if it would need heavy calculation to unlock.
I have always stressed the same when I take classes. A few months back, a student who had prior experience with the GMAT and had joined for a quick retake, brought a problem along and told me that it definitely needed calculation, there was no way it could be done without it.
A question I hadn’t seen before, it was from the GMAT Test Pack 1 that is available for purchase from the GMAT Prep Software.
Here is a paraphrased version of the question.
A box measures 200 cm, 200 cm and 300 cm in length, breadth and height of respectively as per the measurements given on it. The actual measurements of each side can vary upto a maximum of 1 cm. Which of the following is closest to the maximum possible difference between the volume given as per the measurements and the actual volume?
As per the given measurement, the volume is 200*200*300. The actual measurements can vary to a maximum of 1 cm on either side so they can be 199, 199 & 299 or 201, 201 & 301.
If the difference between the given and actual volumes and has to be maximum then the actual volume can be 199*199*299 or 201*201*301.
On the face of it looks like a heavy calculation problem. Under test-taking conditions aspirants might either go ahead and grind out the calculation manually or skip the question to save time.
Such questions are question of a slightly higher-level that you will encounter after you have done the initial questions correctly. So it can come at a stage that can affect both your score as well your confidence and momentum.
Knowing that the test does not want to make you do donkey-work, is something that you should absolutely rely on to find a way out and that is what I did.
So I wrote down the numbers on the board and looked at the answer options.
All options were approximations and had a lot of zeroes, so there had to be an easy way to approximate this. Also since the last 4 digits are all zeroes it must not matter whether one takes 199*199*299 or 201*201*301!
I started thinking what if there is a pattern and the moment one thinks pattern, one thinks algebra.
So we can take x,y,z and (x+1), (y+1) & (z+1) as the two set of measurements. We would need to do get the difference between (x+1)(y+1)(z+1) and xyz and ignore the smaller-valued terms since they do not matter.
Even so we should not expand (x+1)(y+1)(z+1):
- There will be an xyz, which will get cancelled in subtraction with xyz
- There will be a 1 right at the end, which will not matter
- There will be an x, a y and a z, which will total up to x + y + z which will not matter since it will only be 200 + 200 + 300 and hence too small
- So the only terms of consequence are xy, yz & zx that are nothing but 200*200* + 200*300* + 200*300* or 40K, 40K and 60K, which will total to 160K or option C.
- This whole process can and should be mental, no writing is required!
This is why I always believe that taking the GMAT is like batting on a pitch that stays true throughout the match — there will never be variable bounce at any stage of the game; if one’s technique is correct one can trust the pitch and hit through the line!
You can now see what they truly want to test. They want to see how well you can estimate stuff, how well you can model situations and whether you can do something the smart way!
You need to show that you have the potential to become a successfully business management professional be it in consulting or any other field.
So you should stop wearing the worker-bee hat and start wearing the CEO when you are looking at GMAT Quant.
fantastic….this is what I have to learn for all problems.
And on the GMAT it’s definitely possible.
why don’t the smaller valued terms matter?
Because all the answer options have been rounded off to ‘000.