Lately, I’ve been speaking with a few different students who are aiming for a 750+ score – in other words, stratospheric! I’ve tried (and hope I’ve succeeded!) to impress upon these folks that getting such a score involves a lot more than studying the hardest questions.
What’s another crucial component? Finding faster / easier ways to answer questions that you can already answer now.
Why? The questions that you can do right now in the 650 or 700 range will need to turn into “very easy for you” questions in order to hit 750+. It isn’t enough that you can do them now in relatively normal time. You’ll actually need to turn these into “I can answer this very quickly without making a mistake” so that you can knock these out and have a little bit more time and mental energy to spend on the even-harder questions you’ll need to answer to hit 750+
Try this GMATPrep® question:
* ” A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?
Done? Okay, how long did it take you? More than 30 seconds? Go look at the question again and see whether you can find any shortcuts or faster ways to approach it. Take all the time you need.
When you’re done, come back here and keep reading!
Okay, let’s do the “real math” solution first. Then we’ll look at the 30-second solution.
They’re asking for an average and they actually straight out give me the numbers that I need to average. Great – I can just plug them into the average formula and crunch the numbers!
Let’s see. Average = sum / # of terms.
The sum is 14,000 + 14,000 + 16,000 + 17,000 + 17,000 + 17,000. That’s a little annoying. Oh, but I can save some time here by just adding 14 + 14 + 16 + 17 + 17 + 17 and then adding the three zeroes back in. Okay, 14 + 14 + 16 + 17 + 17 + 17 = 95. Add three zeroes to get 95,000.
There are 6 employee salaries, so the number of terms is 6. Now we’ve got 95,000 / 6 = ugh, another annoying calculation. I’m going to do 95/6… let’s see, long division, that’s 15.833 repeating. Then I have to add in the three zeroes that I chopped off, so it turns out to be 15,833.33.
Oh, I see. I should’ve watched the answers while I did that long division. As soon as I saw it was going to be 15.8, I could’ve stopped and picked the correct answer, C.
Got all that? Not too horrible as far as GMAT questions go, although there were several annoying calculations there.
Now, let’s get into the big leagues.
There are 6 salaries overall. Three of them are $17,000. What if the other three were all at the other end of the range, $14,000? What would the overall average be?
Because there would be three of each, the average would be halfway between 14,000 and 17,000, or 15,500.
What did we just learn?
(1) The answer is NOT 15,500 (answer B), because we don’t actually have three 14,000 salaries.
(2) The answer is also not A (15,200). Two of the three salaries are 14k but the third one is higher (16k), so the overall average also needs to be higher.
(3) This is a weighted average question in disguise…
That last little realization was exactly what allowed me to figure out the rest of my 30-second solution.
I’ve got three answers left. One is “prettier” than the others: 16,000. What would get me an average of 16,000?
Well, if the top 3 are still 17,000, and if the bottom three averaged to 15,000, then the overall average would be 16,000.
Do the bottom three actually average to 15k? The bottom three are 14k, 14k, and 16k.
Once again, we’ve got another mini-weighted average. 14, 14, and 16 can’t average to 15. The values are “skewed” towards 14, so the average has to be less than 15.
Bingo. Answer E is definitely wrong because that would require a “bottom three” average greater than 15.
[Note: this next bit was added after original publication because I glossed over this math.] What about D? The mini-average is not 15, it’s true… but the question asks for the “closest” answer. So is the overall average closer to 15.8 (that is, less than 15.9) or closer to 16 (that is, more than 15.9)? Estimate how great the “skew” is.
14, 15, and 16 would average to 15 (in which case the overall average would be 16 and the answer would be D). We’ve actually got 14, 14, and 15. Only that one “off” number is skewing the average down.
That 14 is one of 6 numbers, so it has a weighting of 1/6 in the overall calculation. It is 1 “off” from what it would have to be (15) in order to get an overall average of 16. So that last 14 is going to “pull” the overall average down by 1 × 1/6 = 1/6.
1/6 is larger than 1/10, so the overall average must be “pulled” from 16 to below 15.9. The correct answer has to be C.
Done – with almost no calculation at all, let alone the incredibly annoying calculations from our first solution method.
Right now, many people reading this are thinking, “Wow, I would never have thought of doing it that way.” That’s perfectly fine if you’re not going for a 750+ score (or a 95+ percentile score on quant alone). Do it the “old-fashioned math” way as we first did above.
If you are going for crazy high scores, though, then our first solution method above is not going to be sufficient. You’re going to have to take some time to figure out how to answer this one far more efficiently (without making a mistake – so you can’t just speed up!).
Finally, a word of caution and encouragement. Going for a super-high score is… let’s call it unpredictable. Most people, by definition, will never make it that high. If you’re really determined to get there, then you’re going to have to try to learn how to do what I described above, and this is going to take time, patience, and hard work. You’re going to be slow at first – that’s okay. If you stick with it and don’t try to rush things, you’ll make progress (though I can’t, of course, guarantee that you’ll progress all the way to 750+).
Key Takeaways for Figuring Out Major Shortcuts
(1) These are not just about doing the same work faster. You’re likely going to need to come at this from a completely different angle – and this will usually involve a new way of thinking through what’s going on, not just different math.
(2) If you’re going for a super-high score, it’s not enough to be able to do the lower-level problems in normal to slightly-faster-than-normal time. You’ve got to knock those problems out of the park – very quickly without reducing your accuracy.
(3) You might spend 5 or 10 minutes examining a problem (after trying it) to try to figure out better approaches. You can also google the problem to see whether someone else has come up with a great alternate method – but try yourself first. If you figure it out for yourself, you are far more likely to understand why the alternate approach works the way it does, and this means you’ll be far more likely to recognize when you can use the same approach on different, future questions.
Edited after original publication. See my comment posted 18 March (below) for more takeaways!
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.