De-Tangling Difficult Word Problems on the GRE
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Let’s start with a problem that’s been giving my students trouble recently. Read it through, but don’t try to solve it—yet.
Yikes! That’s complicated. This is what we sometimes refer to as a “story” problem or an “algebraic translation” problem. I get a big block of text, and I have to sort through that somehow to set up equations that I can solve.
When I teach problems like this, the most common mistakes students make come from trying to do too many things at once. Students will then either miss small but crucial details OR get overwhelmed and give up.
For this reason, there are two really important things to keep in mind when you encounter difficult word problems on the GRE like this:
1. Don’t expect that you’ll see the entire path to the solution right from the start.
Even though I’ve spent A LOT of time on the GRE, when I encounter a hard problem for the first time, I seldom see the entire solution path upfront. Instead, I get a broad sense of what kind of problem it is, and that helps me decide where to start—as long as I can get some foothold in the problem, I trust that I’ll be able to work through it from there.
2. Never try to do more than one thing at a time.
Once I’ve decided how to start, I move through the problem at a steady, measured pace, taking it apart piece by piece. I’m very deliberate about each step, and I write everything down.
Now, let me show you how I’d apply these two ideas to solving the problem above.
First, I read through the problem. It’s a story problem, so I decide that, to start, I’m going to go back to the first sentence and translate the question into algebra one phrase at a time.
Ravi and Brynn have won prize tickets.
Okay, so I have two unknown quantities: the number of tickets Ravi has, and the number of tickets Brynn has. I can establish my variables:
R = Ravi’s tickets currently
B = Brynn’s tickets currently
On to the next sentence:
Brynn currently has 16 more tickets than Ravi does.
Cool, this describes the relationship between my two variables, so I can set up an equation:
B = R + 16
At this point, I might do a quick common-sense check to make sure I’ve set up my equation correctly. Who has more tickets? Brynn. Is that what my equation is saying? Yup. Onward.
If she gives Ravi 6 of her tickets…
Okay, so now I have a new situation. I could use new variables to represent the new number of tickets, but then I’m going to have four variables going, and that seems complicated. Instead, I’ll stick with my original variables and use those to write expressions for the number of tickets they have after the exchange:
R + 6 = Ravi’s tickets post-exchange
B – 6 = Brynn’s tickets post-exchange
Now I’m ready to tackle the final piece:
She will then have 22 less than twice the number of tickets that Ravi will have.
There’s a lot of information here, so I translate it piece by piece:
She will have → Brynn’s new tickets equal → B – 6 =
22 less than → -22
Twice the number → 2 x
Number of tickets that Ravi will have → R + 6
I put these pieces together to get:
B – 6 = 2 (R + 6) – 22 → B – 6 = 2R -10
Now, I have two equations with two variables:
B – 6 = 2R – 10
B = R + 16
I can then solve this system of equations and get to my answer. I subtract the bottom equation from the top one to get:
-6 = R – 26
I solve for R:
20 = R
Before I fill that in, though, I’m going to double check that I’m entering the right thing. I note what I’m looking for—Brynn’s current number of tickets. Okay, so I plug R into my original equation and get:
B = 20 + 16 = 36
And that’s my answer!
While this problem looks complex at the start, if I take it apart piece by piece it becomes a fairly straightforward process. Note that I didn’t try to deal with that second sentence all at once—that’s when I’d be likely to make a mistake. I broke it down into smaller and smaller pieces until it felt manageable. Applying this idea—turning complex tasks into series of simpler ones—throughout the Quant section improves both efficiency and accuracy. ?
Were you able to solve the problem using Cat’s tactics? Let us know in the comments!
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Cat Powell
is a Manhattan Prep instructor based in New York, NY. She spent her undergraduate years at Harvard studying music and English and is now pursuing an MFA in fiction writing at Columbia University. Her affinity for standardized tests led her to a 169Q/170V score on the GRE. Check out Cat’s upcoming GRE courses here.