5 GMAT Math Problems You Can Solve Without Doing Any Math

gmat-math-problems-solving

What’s the point of GMAT Math? It’s often used as a proxy for testing something else entirely.

Here’s a question I love to ask at the beginning and end of the GMAT classes I teach: “What do you think the GMAT is really testing you on?”

In the first class, I tend to get a lot of responses about math and reading skills. By the last class, when I ask the exact same question, I tend to get many more responses about time-management, decision-making, pattern-recognition… and all kinds of other things that don’t really have anything to do with math or verbal skills. Sure, it’s in your interest to brush up on your quant, grammar, and all the content on the GMAT. But beneath all of that, most GMAT test-takers discover that there’s something else going on that’s more important than a content checklist.

Take math on the GMAT, for example. If the test-makers were really interested in testing your pure quant skills, they could certainly concoct a test with some calculus or advanced statistics on it. Instead, they opted to cap the content at around 10th-grade level material covered in any high school math class. I recently retook the SAT exam as an adult after years of teaching the GRE and GMAT. (Sometimes you’ve got to do strange things when you’re a test prep instructor. What can I say?) I discovered I actually had to re-learn content for that test that I’d forgotten because the GRE and GMAT don’t test it. I’m not going around doing math for fun in my spare time, so I’m honestly pretty rusty on anything beyond the GMAT and GRE.  

I don’t think that makes the GMAT an easier test than the SAT, though. As a long-time high school teacher, I’ve occasionally slipped some problems from the GMAT into my 10th-grade classroom as a thinking exercise. I found that even though my students knew the content, they were baffled about how to solve the problems.

The GMAT is hard. But it’s not hard because the level of math content is high. It’s hard because the test-makers are using high-school math as a proxy for testing all that other stuff: your pattern-recognition, your decision-making, your ability to spot easy and hard ways to do something. It’s probably a big reason why business schools want you to take the test in the first place. It’s definitely part of why my high-schoolers struggle with those questions: these are skills that don’t get fully strengthened until later in life. And it also gives us the ability to do something kind of fun: solve the problems without actually doing any of the math at all.

If you realize that “high school math” is just a disguise for all that other stuff, you can often strip away the math and do the problems without it. Below I’ve listed 5 problems that you can solve without actually doing the math.

GMAT Math-less Math Tip #1: Eliminate the crazy ones and test whatever remains.

Here’s a GMAT Problem-solving question. Glance at the answer choices. Try to find at least one crazy one that couldn’t possibly be correct.

gmat-math-problem

Answer choice E would triple the length of one side! Even without fiddling with the other side, we’d already have tripled our area, but with an increase on the width too, we’re way off the charts. Answer choice D doubles the length of the 100 foot side on the left. That alone would double the area. Increasing the other side as well just pushes this one further over the edge. Both of these answer choices can be eliminated without doing the math—just by noticing the scale of the increase.

With three answer choices remaining, here’s another tip—it’s often easiest to think about the one in the middle as a benchmark.  How about 50? Would that be too much? Too little? Or just right? If you can answer that question, you’ve solved the problem by elimination and you don’t actually need to calculate any areas.

Our original area would be 100 x 150.

If we increased each side by 50, the new area would be 150 x 200. Write that the other way around and the change is easier to see: 200 x 150

If you compare those two expressions, you’ll notice that they’re identical—except we’ve doubled the 100 portion. That should double your area. B is therefore correct and we don’t actually have to try any of the others.

Here’s the cool thing about this strategy. Compare it with what the “textbook math” would have looked like:

The initial area was 100 x 150 = 15,000. Double that and you get 30,000. Set up some algebra (100 + w)(150 +w) = 30,000… and you’re in for a world of hurt. That creates a quadratic with huge coefficients. Even with a lot of practice solving these things, it took me a while to get it this way. I’d argue that not only can we solve this problem without doing the math, but that doing the math is the trap they’ve set for us.

GMAT Math-less Math Tip #2: Leave it to the lemmings.

There’s a whole question type on the GMAT practically built upon the idea that you don’t actually have to do the math. In Data Sufficiency questions, you only have to determine: “can it be done?” Take a look at this one, for example:

gmat-math-problem-2

     A)  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

     B)  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

     C)  Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

     D)  EACH statement ALONE is sufficient

     E)  Statements (1) and (2) TOGETHER are NOT sufficient

If you hate doing algebra or solving word problems, don’t fret, you don’t actually have to do either here. Just think about what you have and what you want. We know our friend Arturo spent a total of 12,000 on his home costs. As a New Yorker, this makes me insanely jealous, by the way. That’s just a few months rent in a studio apartment in my city. 

*sigh*

Anyway, here’s the info they gave us:

12,000 = Total of Mortgage + RE Taxes + HO Insurance 

And here’s the question: how much of that was real estate taxes?  

Before you look at the statements, think about what you’d need to solve it. If we knew what part of the pie chart was made up of RE taxes, we’re golden. If we had any kind of information that could allow us to make an equation, we hypothetically could do so.  (And we actually will not, because… that’s not the point of data sufficiency.) As soon as you realize it can be solved, leave that to the underlings. You’re training for a management position, right? The goal here is to figure out whether the problem can be solved, and then pass it off to the army of calculator-wielding workers ready to do your bidding.

The first statement tells us: 

(RE taxes and HO insurance) = 33 ⅓ % of Mortgage

We might be able to set up an equation to determine how much he spent on mortgage payments, but RE taxes and HO insurance are inconveniently lumped together. Even if we could find a dollar value for how much they cost together, we wouldn’t know if that was 99% tax and 1% insurance… or vice versa.) This statement is insufficient on its own.

The second statement tells us:

RE Tax = 20% of (Mortgage + HO insurance)

This one looks like a mirror image of the first statement, but notice how the real estate tax isn’t lumped together with anything else here. We could hypothetically set up some proportions, create an equation, and solve for that piece, so this one is sufficient. The answer is B.

By the way, if you want to go one step further, that’s fine:

Mortgage insurance + HO insurance = x

RE Tax = .2x

.2x + x = 12,000

But if you are going down this road, stop there. You could solve for x. And x would give you the real estate tax. Leave it to the lemmings rather than finish the math yourself. Seconds are precious here, and we’ve got other problems to get to!

GMAT Math-less Math Tip #3: When the GMAT talks to you like a robot, restate the question like a human being would say it.

Here’s an interesting question. By the way, if the percent of test-takers who answered it correctly is an indication, it’s brutally difficult.

gmat-math-problem-3

     A)  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

     B)  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

     C)  Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

     D)  EACH statement ALONE is sufficient

     E)  Statements (1) and (2) TOGETHER are NOT sufficient

Similar to the prior two questions, this one can be done without any math. Stranger yet, I don’t think there is a way to do it that does involve math. The difficulty here is in ripping through the robotic jargon to figure out what on Earth they’re asking for in the first place. Once you understand that, the concept is simple: 

“Min” means pick the smallest. “Max” means pick the biggest.

In other words:

min(big number, small number) = small number

max(big number, small number = big number

They want to know min(10, w). There are really two scenarios here. If w is 10 or larger, our answer is 10. If w is the smaller of the two numbers, we need to know what w is.

With that in mind, take a look at each statement.

(1) w = max(20, z)  

In other words, w is the bigger out two things, 20 or z. We don’t know how big z is, but it doesn’t really matter. If it’s bigger than 20, we don’t really care. If it’s smaller than 20, then w is 20. Either way, w is bigger than 10, so we have our answer. 

Both scenarios put w at 20 or larger… so min(10, w) has got to be 10.

Now take a look at the second statement:

(2) w = max(10, w

The logic is a little strange here, but hear me out: If w was smaller than 10, then it would be the bigger out of w and 10… which would make it 10. That doesn’t make any sense. If w is the bigger out of 10 and w, it has to be at least 10. Similar to the first statement, we don’t really care exactly what w is, because the problem is already solved.

w is at least 10, so min(10, w) has got to be 10.

Because either statement is sufficient to answer the question, the answer to this question is D: EACH statement ALONE is sufficient 

Before you move on to the next question, reflect a little bit about the devious mind that wrote this question. They’re literally just asking you to identify the bigger or smaller out of two things. And yet, the question hides that behind strange notation and discussions of integers. It’s like a team of mathletes trying to exclude anyone that doesn’t understand their arcane language.  I think a big key to getting this question is refusal to be intimidated by that jargon. There’s actually not much hiding behind it.  

Speaking of what lurks behind the curtain…

GMAT Math-less Math Tip #4: Sometimes there really is no math at all behind the Wizard’s Curtain.

Here’s one that certainly looks like a math problem. The fractions and addition symbol are practically begging you to grab some paper and start finding a common denominator. But hold on one second and ask yourself whether you really need to do that.

gmat-math-problem-4

Notice the phrase “closest to.” If you ever see that (or any synonyms like “approximately”), the test makers are giving you a hint that you don’t need to solve. Estimation is fine. In fact, you probably shouldn’t actually solve it.

By the way, you need to have some math ideas in your head to be able to estimate, but you don’t necessarily need to put them into action. Here’s a quick key:

0 divided by anything is 0

As denominators get bigger, fractions get smaller.

A fraction divided by a fraction tells you to flip and multiply. In other words, dividing something by ⅕ is the same thing as multiplying it by 5.

Now take those ideas and jump back to the question above.

Answer choice E goes out the window immediately. There’s no zero on top of this fraction.

⅞ is pretty close to 1. 1/9 is tiny. Add them together and we should get something close to 1.

1 divided by ½ means that the top of our fraction is going to get doubled. That’s pretty close to answer choice A, which ends up being correct.

Compare that with the textbook math:

⅞ + 1/9 = 63/72 + 8/72

= 71/72

Now take that and divide it by ½

71/72 ➗1/2 

= 71/72 x 2/1

= 142/72 

Reduce that by dividing top and bottom by 2:

= 71/36

And we’re at a dead end. We could pull out long division and start getting into decimals, or we could revert to what we should have done in the first place: estimate. The top of the fraction is pretty much double the bottom part, so the answer is approximately 2.

It makes me sweat thinking about all of the time that could have been wasted doing arithmetic here. Notice the theme? If they give you some annoying math to do, find a way to do anything else instead.

GMAT Math-less Math Tip #5: Each elimination earns you a fraction of a point.

Check this one out:

gmat-math-problem-5

The strategies discussed in this article don’t just apply to the easy question on the test. In fact, this one is a doozy. That said, I think we can still spot at least two answers to rule out immediately.

There is a lot of hot garbage thrown at you in this question, meant to distract you from the issue at hand: we’re mixing two mixes together, each one with a certain amount of ryegrass, and we’re given the overall percent of ryegrass that comes out.

Not that you ever did this in college, but imagine this problem was talking about mixing a vile drink—say high-proof shot and a low-proof liqueur. A shot has a much higher percent alcohol than the liqueur. When we mix the two together, the percent alcohol is somewhere between the two.  

In this problem, we’ve got a high-ryegrass mixture (X) and a low-ryegrass mixture (Y). When we mix the two together, our percent ends up somewhere in between. Just like the vile drink concoction, the end result is swayed by the strength and size of each component that goes in. Picture it on a line:

gmat-math-problem-6

Which do we have more of?  

Well, our overall mixture looks a lot more like Y, so there’s got to be more Y than X. X is less than half of the mixture, so it needs to be less than 50% of the total.

Conveniently, that eliminates two answer choices: D and E

If you want to go a little deeper in your elimination on this problem, label the gaps like so:

gmat-math-problem-7

Think about the skew here. Are we almost entirely tipped toward substance Y? No, it’s more like ⅔ the way over. So X has got to be more than 10 percent of the mixture. And if you noticed that we’re dealing with thirds here, there’s only one answer choice it could be:

B) 33%

If that feels like a stretch, don’t worry about it. Like I mentioned before, this is a monstrously tough problem. That said, consider what happened with each elimination you made.

Each question on the GMAT has 5 answer choices. That means, of course, that a random guess has a 20% chance of being right.  You can think of guesses as earning you ⅕ of the credit of solving a problem on average. Now think about how that math changes if you’re able to eliminate some obviously wrong answers.

Eliminate one answer and you have a ¼ chance of guessing correctly—25%

Eliminate two answers and your odds are 33%

Eliminate three and you’re at 50%

In other words, you earn 20% of the credit by guessing randomly. And you earn an additional 5%, 8%, and 17% of the credit for the question with each respective elimination. 

I do think this is a problem where you can eliminate yourself all the way to the correct answer. But I also think that this level of elimination was tough to do. If you were able to figure out which substance you had more of, though, you got your odds to 33% on this question. And if you realized answer choice A was too heavily skewed, you got yourself to 50%. That last nudge is a tough one, and if you’re able to make it, great! But if not, you’ve already drastically increased your guessing odds.

To Sum it up…

In case any of you are wondering, these problems are closer to the norm than to the exception. When writing this blog entry, I opened my Official Guide and began listing out potential problems I could write about. After I filled 3-4 pages with a list of around 50 problems and the ways to do them without math, I just had to cut myself off. I’d encourage you to skim through your Official Guide and hunt for some of your own. Even if you theoretically could do the math, it’s a good exercise to think about ways you could avoid it. And if I do see you in the first session of a trial GMAT class, I’ll be sure to ask you what problems you found and what you think they’re really testing you on.

Now get out there and avoid some math!

Don’t forget that you can attend the first session of any of our online GRE courses absolutely free. We’re not kidding! Check out our upcoming courses here.


tom anderson gre hacks

Tom Anderson is a Manhattan Prep instructor based in New York, NY. He has a B.A. in English and an M.S. in education. Tom started his teaching career as a  New York City Teaching Fellow and is currently a Math for America Fellow. Outside of teaching the GRE and the GMAT, he is an avid runner who once (very unexpectedly) won a marathon. Check our Tom’s upcoming GRE prep offerings here.

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5 GMAT Math Problems You Can Solve Without Doing Any Math