Estimations

The SBC GMAT Files

General Strategies For Quant: Estimations: Why An MBA Is Not An MSc. Part II

In my last article, I addressed the importance of estimation in the GMAT, and discussed the common tendency to mistakenly approach GMAT quant questions as problems in formal mathematics. My main point could be summed up as follows:

Estimation is a central part of test, which can and should be applied in many situations. Not only is this an effective way to bypass lengthy calculations – it is what we are actually expected to do by the question writers.

The following Official Guide problem serves as a prime example of the benefits of applying efficient problem solving techniques in the GMAT:
If 1 kilometer is approximately 0.6 miles, which of the following best approximates the number of kilometers in 2 miles?

(A) 10/3Ӭ(B) 3Ӭ(C) 6/5Ӭ(D) 1/3Ӭ(E) 3/10

Alright, simple enough. One kilometer is equivalent to 0.6 mile: let K be kilometers and M be miles, then:
K = 0.6M

Now, the ”˜proper’ mathematical solution to this problem would involve isolating M so as to express the value of one mile in kilometers, and then multiplying by 2 to reach the value of 2 miles. This is probably what we would have done had we encountered this problem in a junior high math exam:
Turn 0.6 into a fraction: 0.6 = 6/10, which can be reduced to 3/5.
K =3/5M
5K = 3M
M = 5/3K

Multiply by 2 to reach the required 2 miles:
2M = 10/3K

So the correct answer is A.
Sure enough, the problem is solvable with proper algebra. But was all this math really necessary? Is this problem really here just to test our ability to form equations and isolate a variable? Although these are indeed important skills that are tested frequently in the GMAT, I argue that the answer is ”˜no’. This problem isn’t supposed to just differentiate between those who can and those who cannot solve it – it’s supposed to differentiate between those who can’t solve it, those who can, and those who can solve it quickly and efficiently. What the question writer actually had in mind was discerning whether or not the test-taker applies the following, much more efficient logical path:

If one kilometer is 0.6 miles, then the required “two miles” should equal slightly more than 3 kilometers, since 0.6 goes a little more than 3 times into 2: 0.6 multiplied by 3 is 1.8 – just a little shy of the required 2. In other words, if one kilometer is 0.6 miles, then 3 kilometers equal exactly 1.8 miles, so 2 miles should equal “slightly more” than 3 kilometers.

This estimation, although resulting in nothing more than a rough ballpark, is completely sufficient in order to solve the problem. Take a look at the answer choices: only two of them are even close to 3; answer choices A and B – the other options are too small to even be considered. Between A and B, eliminate B because we know the answer is a little more than 3, not exactly equal to 3. A, at 10/3, fits that description: 9/3 is exactly 3, so 10/3 is slightly more than 3.

Thus, a 10 second estimation was sufficient to solve the problem. The process, in a nutshell:
1. If 0.6 miles equals 1 kilometer, then two miles should equal slightly more than 3 kilometers: Eliminate answers C, D and E, as they’re too small.”¨2. We need more than 3: eliminate B.”¨3. Win!

Although the proper mathematical solution here is far from being especially complicated, the solution outlined above can take mere seconds, thus saving precious time. When looking at the big picture, it is exactly those few seconds saved on each problem that make the difference between good and great. More importantly, it is an efficient and elegant solution method, leaving your mind fresh to tackle the next problem, and the one after that. Part of your job in the quantitative section is not JUST to get a good score here – you also want to do so while conserving enough mental energy and focus to overcome the following verbal section. Being good at math definitely gives one an advantage in the GMAT- but reaching a top score demands more than that – it demands being logical and efficient, and knowing when NOT to show off your algebra.

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