Tackling GRE Word Problems: One Thing at a Time
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“The man who moves a mountain begins by carrying away small stones.” -Confucius
Recently, one of my students emailed me the following question. I imagine at some point in your GRE practice you’ve run into the same issue:
“I’m still having a hard time tackling Quant problems. I’ll read the question and sort-of know what it’s asking me, but by the time I start figuring it out I run out of time and need to just pick something and move on. I just don’t know how/where to start or how to get quicker at it. My guess is that I just need to practice, practice, practice. But I wanted to just reach out and see what you thought and see if you had any suggestions.”
If that sounds familiar, you’re facing one of the most common problems on GRE Quant. Yes: practice, practice, practice (and learn your mechanics and times tables). However, you may also want to shift the way you look at longer Quant problems.
You, like many students, may be trying to plan your way through the whole question before you write anything on your scratch paper, trying to “set it up” entirely in your mind before you get to work. Therefore, you end up stuck, with no idea how you’re going to begin to put it all together, much less get to the end of the problem. This holistic “doing math in space” method will sometimes work with very easy one-step problems, but not with anything more complicated.
The best GRE word problems are elegant little puzzle boxes (really, I love them). You won’t even know what step two is asking until you solve step one. Therefore, relax. Just focus on the first sentence, or even just the first phrase, or one tiny piece in the middle you know you can handle.
Each step, ask yourself: What can I write down? What formulas and rules apply? What math can I do right now? What else do I know?
Take the following (made up) problem:
The area of a right triangle is 24 square inches. The base of the triangle is two inches longer than the height. What is its hypotenuse?
If you try to set up that whole problem “holistically,” you might get some awful unsolvable quadratic garbage: ½(x)(x+2) = 24??? And then maybe Pythagoras? (x)^2 + (x+2)^2 = c^2????? Ugh. No.
You barely need ANY algebra to solve GRE word problems like this. Just focus ONLY on the first bit, work out what you know, and go from there:
The area of a right triangle is 24 square inches…
STOP! Don’t read more than that! Breathe. Draw the triangle. Make sure it’s marked as a right triangle. Write down the formula you know: ½ * b * h = 24 and get to work. Oh, okay… that means b * h must be 48. What else do I know? 48 might be 1 * 48, 2 * 24, 3 *16, 4 * 12, or 6 * 8…
Stay there in the space after the period and do as much work as you can. Squeeze every drop out of the one little piece of the puzzle you CAN solve, and only then move on to the next step.
The base of the triangle is two inches longer than the height.
Now, add that to what you already know. Interesting. You already know 48 could mean 1 * 48, 2 * 24, 3 *16, 4 * 12, or 6 * 8, so… Oh, hey! The only combination that works is 6 and 8 (8 is 2 more than 6). Wait, which one is longer? The base? So that must mean the base is 8 and the height is 6. Add that info to your figure.
Then, and only then, face the final question:
What is the hypotenuse?
I could work out the Pythagorean theorem or (with practice) recognize that this is a classic 3:4:5 right triangle times 2, or 6:8:10. So the hypotenuse must be 10.
And you’re done. The answer is 10.
What’s the lesson? Take it in tiny bite-sized pieces and you will avoid all kinds of headache.
Let’s look at another one:
Yumiko spends 1/5 of her monthly income on rent. She then spends 3/8 of the remainder on food. After that, she puts 1/3 of what’s left over into a savings account. What fraction of her income does she put into savings each month?
Holistically/algebraically, this is a nightmare: Is it x – (1/5)(3/8)(1/3)(x)? Is it (1/3)(3/8)(4/5)(x)? Who knows? Who cares? (Both of those are wrong, by the way)
If the problem starts with an unknown amount, “Yumiko spends 1/5 of her monthly income on rent” (income is unknown) and only asks you for a fractional answer, the easiest thing to do is to make up your own “smart number.” [You’ll learn this and all kinds of other great techniques in our classes.]
Look at the fractions in the problem (1/5, 3/8, 1/3). I’ll start with a nice easy multiple of those denominators for Yumiko’s income (5 * 8 * 3 = $120) and get to work. But on ONLY the first bit.
Yumiko spends 1/5 of her monthly income on rent.
Don’t read further. Do your math. Okay, that means she spends 1/5 of $120, or $24 on rent. What else do I know? She must have $96 remaining.
She then spends 3/8 of the remainder on food
Okay. 3/8 of that $96 is going to be $36. So now, she has 96 – 36 = $60 left over.
After that, she puts 1/3 of what’s left over into a savings account.
What’s 1/3 of $60? $20 goes into her savings account. Then, and only then, tackle the question.
What fraction of her income does she put into savings each month?
$20 out of $120 is 20/120, which reduces to 1/6. Therefore, the answer is 1/6!
And yes: practice. Notice the real key to speed is your ability to do the little pieces quickly and accurately (factor 48, get 3/8 of 96). For now, relax. Take your time on every practice problem, but get confident that you CAN solve the little pieces. Even if you don’t know how you’re going to get there, confidently jump in anyway. Start writing and solving and tinkering. Trust that you’ll get there eventually.
And have fun. As I said, GRE word problems are often elegant little puzzles to solve, and with time you can learn to love the process of taking them apart. ?
Find Neil’s musings helpful? We all do. Don’t forget that you can join him twice monthly for a free hour and a half study session in Mondays with Neil.
When not onstage telling jokes, Neil Thornton loves teaching you to beat the GRE and GMAT. Since 1991, he’s coached thousands of students through the GRE, GMAT, LSAT, MCAT, and SAT, and trained instructors all over the United States. He scored 780 on the GMAT, a perfect 170Q/170V on the GRE, and a 99th-percentile score on the LSAT. Check out Neil’s upcoming GRE course offerings here or join him for a free online study session twice monthly in Mondays with Neil.