How to Tackle Every Single GMAT Problem (Seriously!) – Part 1

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Manhattan Prep GMAT Blog - How to Tackle Every Single GMAT Problem (Seriously!) - Part 1 by Stacey Koprince

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Wouldn’t it be nice to have one common thread among every single GMAT problem you’ll ever do, something you do no matter what kind of problem or content area is being tested?

I’m here to answer your prayers. 😊

Okay, obviously, there are many things you’re going to need to learn and practice in order to get a great GMAT score — there isn’t literally just one thing to learn. But it turns out that there is one set of principles tying together everything we need to do on the GMAT.

Here it is:

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You can use this on Problem Solving (PS) and Data Sufficiency (DS) problems. It’ll work on Sentence Correction (SC), Reading Comprehension (RC), and Critical Reasoning (CR). It even works for Integrated Reasoning (IR) and the essay! And I’m going to show you how.

Try this PS problem from the GMATPrep® free exams.

“*The perimeter of a certain right isosceles triangle is 16+16sqrt{2}. What is the length of the hypotenuse of the triangle?

“(A) 8

“(B) 16

“(C) 4sqrt{2}

“(D) 8sqrt{2}

“(E) 16sqrt{2}

Ready?

glance_read_jot

 

Glance is literally what it means. Take about 1-2 seconds to just glance and see what you have.

  • Is it PS or DS?

Right now, you’re rolling your eyes at me. A fellow teacher of mine did an experiment last year. She put a math question up in class for a few seconds, then pulled it off and asked the class whether the problem was PS or DS. Fewer than half of the students were able to say! People are so anxious to start reading that they don’t even take in the whole screen to see what they’ve got.

So your first task is to notice, consciously, whether you have PS or DS. This one is PS. Next:

  • Stories / lots of words? Numbers / formulas? Graphics?

There’s a weird number in the middle there. Don’t start reading yet! One more thing:

  • What are the answers like?

Hmm. Two are nice numbers and three are like the weird number in the problem. You’re not going to do anything with that knowledge yet, but do remember it.

Okay, finally, you can go ahead and Read this thing. As you read, Jot down the major information.

Note: jot means just that—write down what’s there, but do not start solving or manipulating anything yet. Just get everything on your paper.

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They told me it’s a right triangle and it’s isosceles, so I drew a little picture. After a second of thought, I added the labels to remind myself that it’s isosceles. Then they gave me that equation and they asked me for the hypotenuse, which I’d labeled y.

I have not yet thought about how I’m going to solve this thing. I’m not at that stage yet! This is one of the big differences between someone who does really well on Quant and someone who knows a lot of stuff but is struggling to put it together: you actually want to take your time to figure out your options before you decide how to solve.

Now it’s time to solve, right?

Not so fast!

reflect-organize

Now, I reflect on what I’ve got and figure out what path I want to take. If either of these first two steps / rows fail, then I know I shouldn’t even bother to go to step 3. Instead, I should just pick my favorite letter and move on.

So what have we got here? There’s a right triangle, so I actually have a second formula: the Pythagorean Theorem. I can add that to my notes, using the variables that I chose:

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The answer choices make more sense now. At least one of the sides of the triangle should include sqrt{2} since the perimeter does. And two of the sides have to be the same…hmm. I wonder if it’s as easy as saying the sides are 8, 8, and 16sqrt{2}? (I’m spilling over into step 3, Work, here.)

Oh, no, wait, that won’t work, because 8 + 8 = 16, which is smaller than 16sqrt{2}. The sum of the other two sides can’t be smaller than the third side.

Back up: back to Reflect and Organize. That wasn’t a complete waste of time, because now I know the answer is not (E). I also wouldn’t guess (A) at this point, because 8 is part of the faulty calculation that I just did, so it’s probably not right. In fact, maybe 8 is too small in general. I could probably estimate to get rid of some of the other answers. Something to keep in mind if I can’t come up with a better plan.

I could also work backwards, just trying the answers in the problem. That’d be pretty easy for (A) and (B), but the other two remaining answers are more annoying.

Oh, back to my original idea: I first tried to split the 16 into two parts (8 and 8), but they weren’t big enough to be the legs. What if I split 16sqrt{2} into two parts? Let’s do some more Work.

In this case, the two legs would be 8sqrt{2} and the hypotenuse would be 16. Does that fit the Pythagorean theorem?

(8sqrt{2})^2+(8sqrt{2})^2=16^2

(64)(2)+(64)(2)=256

128+128=256

Bingo! This math works, so the hypotenuse equals 16.

The correct answer is (B).

Right now, you may be thinking, “Yeah, that’s okay for you; you do really well on this test. But I can’t take all that time to Reflect and Organize before I start Working!”

I know you feel that way…but you’re wrong! You’re nervous that you’ll need more time to solve, because you’re used to diving in and trying to solve without a clear plan and that approach, naturally, takes a lot of time. If you can actually come up with a clear plan, your solution process will be a lot faster—I promise.

What if you can’t come up with a clear plan? Then your best bet is to bail on this question. Don’t start writing down random numbers / formulas and seeing where they take you, using up precious time and mental energy. Get out of the problem entirely!

Let’s take a look at some of the other paths that I rejected.

Working Backwards

You can work backwards when the answer choices represent a discrete number or variable in the problem and those answers are relatively “nice” numbers. In this case, (A) and (B) are very nice. The other three aren’t quite as nice, but they may not be terrible.

We generally recommend starting with answer (B) or (D). Answer (B) is easier, so start there.

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Now, we got lucky, because the first one we tried worked. What if we’d tried answer (D) first instead?

 

300 - image 4

The math actually isn’t that horrible, after all, even though the starting number is annoying. I still like the first way I did it better, but if I hadn’t thought of that, then this is a good alternative approach.

Estimation

I also noted earlier that I might be able to eliminate some answers via estimation.

If the hypotenuse is 8, for example, then the two legs have to be smaller than 8, so the total perimeter has to be less than 24. 16+16sqrt{2} is definitely greater than 24, so 8 can’t be the hypotenuse.

What about 4sqrt{2}? The square root of 2 equals approximately 1.4. Call it 1.5, since we’re estimating. (4)(1.5) = 6, which is even smaller than 8. Answer (C) can’t be correct either!

Let’s try 8sqrt{2}. That’s about 12, so the two legs would have to be smaller, and the perimeter would have to be less than 36.

Hmm. 16+16sqrt{2} is about 16 + (16)(1.5) = 16 + 24 = 40. It can’t be answer (D) either. We’re down to 2 answer choices, just by estimating! Let’s keep going.

If the hypotenuse is 16, then the perimeter has to be less than 48. That works with the 40 figure. And if the hypotenuse is 16sqrt{2}, then the numbers could also fit.

We’re down to two answers just by estimating, and if you’d already figured out, as we did at the beginning, that (E) couldn’t be right, then you’d know the answer has to be (B)!

Keep an eye out for this series; every week, I’ll be doing a new problem type using the overall GRW approach. (GRW = the first letters of each of the three lines. Maybe you can help me come up with a better name for this…) Check out Part 2 here!

Key Takeaways for Every Single GMAT Problem You Will Ever Do:

(1) First, you have to understand what’s in front of you. Glance at the problem to pick up any clues you can about what it is, where the complexity is, and what kinds of strategies might be available to you. As you Read, Jot down the given information—but don’t try to solve yet!

(2) Next, Reflect on what you’ve been given and Organize your thoughts and your scrap paper. Notice how much thinking I did before I went ahead and solved the thing? I came up with three different approaches and then picked the one that seemed the best to me. And here’s the best part: this valuable investment of time will help you to pick the best path when you can do so and it will help you to guess and move on when that’s the best call to make.

(3) Finally, you get to do the Work to solve this thing, assuming that you actually passed the first two steps: you understand the problem and you have a plan to solve. If not, then your best move is to make an educated guess when possible (estimate, for example) or just pick your favorite letter and move on. 📝

* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.


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stacey-koprinceStacey Koprince is a Manhattan Prep instructor based in Montreal, Canada and Los Angeles, California. Stacey has been teaching the GMAT, GRE, and LSAT  for more than 15 years and is one of the most well-known instructors in the industry. Stacey loves to teach and is absolutely fascinated by standardized tests. Check out Stacey’s upcoming GMAT courses here.

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