There’s an old saying that says, “Almost only counts in horseshoes and hand grenades.” In grade school and high school, you were probably taught that math had to be precise; maybe you even had that unforgivingly drilled into you. Well, now you’re preparing for the GMAT, and the rules are different. On GMAT Math, “almost” can be good enough to count.

It’s a fact that you cannot use a calculator on the GMAT. Therefore, it’s also a fact that the writers of the GMAT can’t expect you do long calculator-type calculations on the GMAT. They can’t expect you to multiply & divide ugly four-digit numbers and get an exact answer – but they can, and will, expect you to estimate.

## When should I estimate on GMAT math?

The short answer is: whenever you would have to be a Will-Hunting-type savant to figure out the exact result in your head, that’s a clue that you should ditch the exact answer altogether and try estimating. The GMAT may give you the green light by using the words “the estimated value of” or “approximately.” Another clue is the spread of the answer choices. If the answer choices are all very close together, well, then it’s going to take some precision to distinguish among them. But, if the answer choices are widely spaced, estimating will get you close enough to the right answer.

## What the GMAT will and won’t ask

Here is an example of a question that will not appear on the GMAT Math: “Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Figure out the exact amount she has after two years.” True, that might have been a question in high school math, but definitely not on the GMAT. First of all, it’s not Problem Solving or Data Sufficiency, so it’s not the right question type. Moreover, nobody short of a savant-sadist is going to expect you come up to the exact answer that question without a calculator. You will absolutely not have to do a problem like that.

Here, though, is a suspiciously similar question, and one that the GMAT *could* pose:

1. Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?

- (A) $10079.44

(B) $10815.83

(C) $12652.61

(D) $14232.14

(E) $20598.11

**Solution**: first of all, notice the magic word “approximately” — the test-writer is letting us know estimation is perfectly fine. Furthermore, the answer choices are nicely spread out, which will facilitate estimating.

OK, get ready for some fast & furious estimation. The interest rate 3.96% is an ugly number, so I’m going to approximate that as 4%. It compounds semiannually, so that means that there’s 2% every six months, and that happens four times in two years. Well, 2% of $10000 is $200. If you get $200, or a little more, on four occasions, that’s a little more than $800 in interest. We expect an answer slightly higher than $10800, so of course **(B)** is just right.

Notice, I estimated so that everything up until the last sum was single-digit math. Single-digit calculations are a good standard for which to strive when you are practicing estimation.

By the way, if you find the bank that will do answer (E), *double your money in only two years*, that’s terrific, but it probably is something wildly illegal, a Ponzi scheme or worse! In the real world, that just doesn’t happen. On word problems, especially in financial situations, you should always have your antenna up for what’s realistic or unrealistic.

## Practice Question

2. ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets for $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces and sells 987 sets of horseshoes, what was their profit?

- (A) $20,874.25

(B) $30,943.25

(C) $41,308.50

(D) $51,817.50

(E) $53,624.25

## Answer and Explanation

The numbers are ugly, and the answer choices are widely spread out. This problem is absolutely screaming for estimation!

So here’s some more fast and furious estimation. Initial manufacturing outlay: round that from $11450 to $10000. Cost per set: round to $20. Sales revenue per set: $50. Number produced & sold: 1000. OK, now we’re in business.

Cost equals 10000 + 20*1000 = 10000 + 20000 = $30000. Sales revenue = 50*1000 = $50000. Profit = (Sales Revenue) – (Cost) =$50000 – $30000 = $20000. Answer choice **(A)** is the only answer even close to that. Single digit calculations all the way, and it was enough to get the answer!

If you would like to share your thoughts on this or ask a question, please let us know in the Comments section below! 🙂

Hi Mike,

Though I agree with your approach to question number 2, my approach is to estimate as little as 1 or 2 quantities, when dealing with problems involving substitution.

Also, I tend to substitute only in one direction, as opposed to going up and down on the estimation scale.

For example, if I choose to estimate 981 to 1000 (that is, on an increasing side): in case I need to estimate quantities further, I would choose to round off or estimate towards the higher side itself. This would ultimately help me in determining whether the correct option choice would DEFINITELY be on the higher side as compared to my estimated answer, or DEFINITELY on the lower side as compared to my answer.

The way you’ve done it in example 2: 987 estimated to 1000 (this is fine!), whereas 11450 has been estimated to 10000 (I beg to differ here- I’d rather round it off to 12000).

Hope you get my intent! 🙂

On a side note, kudos to you & the team’s hard work! Great lectures, and questions. Hope I’ll crack my GMAT this time round! 🙂

Hi Varun. Thanks for sharing your thinking! The thing about estimating is that it’s not a perfect science. It sounds like you have a plan of attack that helps you tackle questions like this and account for potential issues with your estimated answer. Great job!

On behalf of all of us here at Magoosh, thank you for your kind words and we sincerely hope that your GMAT went well! 🙂

Hi Mike,

I am a certified public accountant by profession and I am used to calculating numbers up to the last cent. The GMAT often requires estimation, different strategy from what I have been trained to do. Your video lessons and your blog posts are really useful. Thank you for the tips!

Hi Mike,

Firstly, thanks a ton for helping the students so generously and treating us friends (I feel honored).

When I came across example no. 2, what I did was: 52.5 – 20 = 32.5

32.5*1000 = 32500 and 32500 – 11450 ~ 21000. So, answer (A). My question is can’t we expect a problem with answer choices actually ranging from 15000 to 25000 (as suggested by Ms. Liz) where test takers expect us to estimate more closely?

Dear Binit,

You are quite welcome! I am glad you found all this helpful! 🙂

Could we have a problem such as this with answer closer together, that make us estimate more closely? Think about the test writer, the folks who write these questions. From their point of view, one of the “traps” of the question is to get bogged down in a detailed precise calculation: some folks will not realize that they can estimate, and will waste tons of time doing an exact 5-digit calculation. That’s the trap, and those folks will waste tons of time, which will

hurtthem on the Q section as a whole even if they get this question correct. The question in its current form also distinguishes those “trapped” test takers from folks who realize we can use very rough estimates and get the answer in 10-20 seconds, thushelpingus on the rest of the Q section. Now, if the test required more detailed estimation, essentially, they would be closing the time gap between the folks who estimate and the folks who do a long exact calculation — in other words, they would make the question less discriminating, less discerning.If this were a test of mathematical ability itself, then yes, the test would reasonably measure all kinds of precise and not-so-precise estimation. But, the folks who write the GMAT Quant section are NOT primarily interested in measuring how much math people know — that is secondary. Almost every who takes the GMAT knows most of the math. The folks who write the GMAT Quant section are interested in separating those who thinking critically and creatively from those who don’t. If you think of the GMAT Quant section as a math test, then you really miss the point. Yes, you have to be sharp with math, but that’s not the real point — the real point is that you need to be able to think critically and creatively, to look at problems with intellectual agility and see unique shortcuts that will speed you to a solution. That’s what they are testing, not the math itself.

Does all this make sense?

Mike 🙂

Absolutely !!! Thanks again for making things more clearer to me (new for GMAT).

Dear Binit:

You are quite welcome, my friend. 🙂 Best of luck to you in your studies!

Mike 🙂

Hi,

This is an amazing article!!!

I’m a GRE test taker and it helped me a lot :).

Thanks for sharing it with us

Dear Anurag,

You are more than welcome, my friend. 🙂 I’m very glad you found this helpful! 🙂 Best of luck to you in all your studies!

Mike 🙂

Test taker ability to estimate in Quant and IR helps in time management. The practice problem given in the post is an excellent example. I request more practice questions that may include more mathematical operations.

Thanks.

Dear Arun

First of all, I am very glad you found this blog helpful! 🙂 You are quite welcome! 🙂

As to your request, do you understand the time and effort it takes for us to write GMAT practice questions? Do you understand how much specialized work you are requesting when you casually ask for more practice questions? This is like asking any professional to do their professional work for you for free — doctor, please heal me; construction worker, please build me a house. I recognized that it probably is not your intention, but this request communicated tremendous disrespect: it is as if you take all my efforts for granted, and expect me to do a large amount of work simply because you asked. The casualness of the request implies a total disregard for the time and energy I would have to expend in order to create new questions. If you made a request in similar fashion of someone at a business school, that person might well make a negative recommendation to the admission committee at that school. A lack of perceived courtesy can thwart you more than you know.

If I may give you advice, whenever you ask someone for something, always make sure to communicate your respect and appreciation and gratitude for the efforts that they will have to expend on your behalf. Ask with humility, not with entitlement.

As to your specific request: look through the Quant articles on this blog. All of the practice problems were written to be done without a calculator. You will find several examples in which estimation would be appropriate. Part of the skill you need to develop is recognizing for yourself, in a pro-active way, when estimation would be an appropriate approach to a problem.

Does all this make sense, my friend?

Mike 🙂

This is okay with the answer choices so far apart.

What if the ans. choices were all between 15,000 & 25,000???

Liz,

Then it wouldn’t be an estimation problem, but a problem for which almost everybody would need a calculator, which means it would be absolutely inappropriate as a GMAT Quant question. You have to appreciate: the “no calculator” rule of course puts restrictions on students, as they are well aware, but it also puts significant restrictions on the test writers. The test writers absolutely cannot create a question for the Quant section on which a calculator is necessary: they absolutely have to create questions that reasonably could be solved without a calculator.

Does all this make sense?

Mike 🙂

Absolutely!!

Thank you Mike.

Liz,

You are quite welcome, my friend. Best of luck to you!

Mike 🙂