GMAT Tip of the Week: Million, Not Billion

GMAT prepYesterday, the world economy nearly crumpled, with the Dow losing almost a full thousand points before a late rally to close at “awful” instead of “catastrophic.” Was it the Greek/EU economic crisis? Was it oil speculation related to the Gulf spill? Was it the advertising industry’s fear of LeBron James’ elbow injury?

No, it was the kind of silly mistake that cost the Dow over 300 points and could do the same for your GMAT score if you’re not careful. Indications are that a trader accidentally submitted a trade for “billions” instead of “millions,” triggering a selling frenzy that left the world in limbo wondering what this meant for economic recovery. This simple mistake – just one letter off – caused billions (and, yes, I meant to use the ‘b’) of dollars to change hands and scores of people to lose piles of money, and hopefully serves as fair warning for future titans of industry preparing for that critical first step, the GMAT:

Make sure you use the proper units when selecting your answer.

Many a GMAT question has been missed because the examinee performed all of the calculations correctly but failed to answer properly with the correct units.

Consider the question:

A cylindrical bucket with radius r and height 10, is 3/4 filled with water. A boy is dropping marbles with volume r/10 into the bucket at a rate of 12 marbles per minute. How many seconds will it take before the water overflows from the bucket?

A) 2.1 * pi * r
B) 25 * pi * r
C) 125 * pi * r
D) 300 * pi * r
E) 375 * pi * r

There are quite a few things to tackle in this problem, but for the purposes of this demonstration follow the units closely.

The bucket’s volume can be calculated using the formula Volume = pi * r^2 * height, providing the volume 10 * pi * r^2. If 3/4 of that bucket is full, the marbles need to fill the other 1/4, or 2.5 pi * r^2, in order for the bucket to overflow.

So at this point we have the volume that we need to fill, 2.5 pi * r^2. Because we need to fill that volume, we need to set it equal to the “replacement” volume of marbles, so we can set up the next step as:

x (number of marbles) * r/10 (volume per marble) = 2.5 pi * r^2 (volume to be filled)

Divide both sides by r to get: x/10 = 2.5 pi * r

Multiply both sides by 10 to solve for x: x = 25 pi * r

This arrives at answer choice B, but just like Citibank’s rogue trader, we’d be making a colossal mistake if we incorrectly used “B” – 25 pi * r represents the number of marbles, but that’s the wrong unit for the answer. We need seconds, not marbles!

If we have 25 pi * r marbles, and drop 12 per minute, then that means that we drop one every five seconds. 25 pi * r marbles * 5 seconds / 1 marble = 125 pi * r seconds, and the correct answer is C.

Particularly when a question involves multiple steps, like the one above, the authors of the GMAT know that they can catch a fairly high percentage of test-takers by allowing them to finish their calculations and ignore the units. Be certain to double-check that you’ve used proper units – you may not cost the world billions by making the mistake, but you could cost yourself some serious points.

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