ریاضی ذهنی، برآورد GRE

Now we’ll talk about estimation. One of the big ideas of mental math on the GRE is estimation. Yes, you get a calculator, but you will be wasting time if you reach for it on every problem.

The GRE does not care about your ability to do precise detailed calculations. It cares about your ability to simplify problems with logic.

And estimation is a big part of that. So here’s a practice question. Pause the video and do this without a calculator. Okay, if you were trying to do that exact precise equation without a calculator, that, that would just be ridiculous.

That would be incredibly hard and unnecessary. It would be a mistake to reach for the calculator and type in these detailed cal, these numbers as well. This would be a big time sync.

For example, suppose this problem showed up on the GRE. Many, many people are gonna be typing in all these numbers into the calculator.

And that’s a huge waste of time also. And that’s actually gonna take much longer than it needs to take. Instead, we’re gonna estimate. So let’s just look at these numbers. That dollar amount, 7,935, that’s awfully close to $8,000. I’m just gonna call it $8,000.

We rounded it up a little bit. 26,3 is close to 25%. A nice round number again. We rounded down. We hope that rounding up and rounding down are gonna roughly cancel out there. So now all we need is 25% of 8,000.

Well you may remember 25% is a quarter. A quarter of 8,000 is 2,000. The answer will have to be something very close to 2,000. So we go back to here, Which answer is very close to 2,000? Well of course, answer choice B.

Notice that it was easy to estimate this problem because the answer choices were spaced well apart and that’s one of the tips. If you see a multiple choice question and the answer choices are far apart, then estimating is often a good way to do this.

Estimating is also extremely helpful on the quantitative comparison. If a GRE Quant problem seems to call for a lengthy and complicated calculation, think again.

The GRE is not interested in your ability to perform form long, detailed, intricate calculations, so if a problem appears to demand one, there must be another, shorter way to solve.

Estimation is often one of these simplifying ways to solve, especially if the answers are spaced far apart. Here’s another practice problem.

Pause the video and then we’ll talk about this. Okay. So this is a problem just screaming for estimation. Again, even if you solve this on the real GRE, it would be an absolute mistake to touch your calculator for this.

This is screaming for estimation and estimation will be much quicker. So, I’m gonna start with that amount of gallons at 10 o’clock. I’m just gonna round that down slightly. Round that down to 200,000. Nice, neat number. Increases by 30%.

Well, we will deal with percents. We’ll actually have a few videos on percents coming up. That’s coming up shortly in one of the next modules. Right now, well I’ll just say 10% of 200,000 is just a 10th of it, knock off a 0, it would be 20,000. 20,000 would be 10%, we’ll multiply that by 3.

30% would be 60,000. So if I add 30%, I’m up to 260,000 at 5 am Now, in the morning water usage, 5% of that new amount is consumed. Well 10% of 260,000, again knock off a 0, will be 26,000. And then just divide that by 2. 26,000 divided by 2 is 13,000.

And so, 13,000, remember we rounded down, so it should be something just bigger than 13,000. And of course, this would be answer choice D. The GRE is not interested in our ability to do a long, complicated, detailed calculation.

And in fact, if you find yourself doing a long, complicated, detailed calculation, chances are very good, you fell into one of their traps, and you’re doing it the long, hard way. If the answer choices are spread far apart, estimating can be a very quick and efficient way to zero in on the answer.