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Here’s a careless error that any of us might make:
x – 7 – 2x + 4 = 3x
-x – 3 = 3x
-3 = 2x
x = -1.5
Did you spot the error? If yes, give yourself a pat on the back and keep reading. If not, go back and review each step. This time, as you think through it, you can only use the terms added , subtracted , multiplied , and divided . On each line, identify which of those operations we used, and how we used it.
Why? Because there’s a common pattern in careless GMAT Quant errors. If you talk about the math you’re doing in vague, non-mathematical terms—saying things like “moved x to the other side” or “crossed off the terms”—your thinking becomes vague and non-mathematical as well. If you think and speak about GMAT Quant problems precisely and clearly, your work will be clearer and more precise. And clarity and precision keep you from making careless GMAT Quant errors.
Don’t say this: “Moved to the other side of the equation”
Say this instead: “Added to (or subtracted from) both sides”
Here’s the reasoning behind the careless error we looked at earlier. The second line looked like this:
-x – 3 = 3x
What next? You could think to yourself: “Let’s move the -x term to the right side of the equation.” That leads to the next line:
-3 = 2x
But that’s where the mistake happened! We weren’t supposed to subtract x from 3x; we were actually supposed to add it. But phrasing it as “move the term to the right side” doesn’t make that clear. If you stop and think about it, you’ll probably catch yourself and avoid making a mistake. But on the GMAT, you won’t have a lot of time to stop and check every step. You’ll be tired, and you might be anxious. Make things easier on yourself!
Instead of saying “move the term to the other side,” be precise about what you’re doing. Let’s start with that second line again:
-x – 3 = 3x
Next, think this: add x to both sides of the equation .
-x – 3 + x = 3x + x
-3 = 4x
By phrasing it like that, you totally avoid the careless GMAT Quant errors that come from “moving the term to the other side.” You don’t have to worry about whether to make x negative or positive—it doesn’t even enter into your thinking.
Don’t say this: “Crossed off the terms”
Say this instead: “Subtracted (or divided)”
Here’s another type of careless error. Imagine that you’re simplifying this equation:
2x² – 3y + 4 = y – 2 – 2x²
Cross off the 2x² on both sides to get -3y + 4 = y – 2, right? No. If you think in terms of “crossing off like terms,” you also need to double-check every single time to make sure that the signs match up, or else you’ll make a careless error. Instead, think this: subtract 2x² from both sides of the equation . That gives you the correct next step:
2x² – 3y + 4 – 2x² = y – 2 – 2x² – 2x²
-3y + 4 = y – 2 – 4x²
This error shows up even more frequently when working with fractions. Check out this fraction, for example:
If you say to yourself “let’s cross off like terms,” you might quickly simplify the equation like this:
Don’t make that mistake! Instead, every time you simplify a fraction, remember that you’re dividing or multiplying the entire numerator and denominator by the same value. Here, if we tried to divide by x² , we’d end up with a total mess:
Instead of doing that, identify something you can divide the entire numerator and denominator by evenly. For instance, you could divide both by 5.
Don’t say this: “Cross-multiplied”
Say this instead : “Found a common denominator,” “multiplied,” or “divided,” depending on what math you’re doing!
There’s nothing wrong with cross-multiplication. In fact, it’s a useful tool for one situation: when you want to determine which fraction is bigger. For instance, if you want to compare 3/11 and 4/17, you could cross-multiply:
This shows that 3/11 is bigger.
However, it’s easy to fall back on the term “cross-multiplying” to talk about situations it doesn’t actually apply to. This makes your work less clear. For example, if you’re just multiplying two fractions, you don’t want to accidentally cross-multiply! Instead, think to yourself: multiply the two numerators, and multiply the two denominators. If you’re adding two fractions together, don’t use the term “cross-multiplying”! Instead, think through the actual math you’re doing, which will include multiplication and addition. Here’s an example:
First, multiply both the numerator and denominator of the first fraction by 4 :
Next, multiply both the numerator and denominator of the second fraction by 7:
Finally, you have a common denominator, so you can add the two fractions together. The answer is 15/28.
It’s okay to use the term “cross-multiply” when you want to figure out which of two fractions is larger. If you’re doing anything else, it’s safer to think about the specific math steps that you’re taking. That will keep you from accidentally cross-multiplying without thinking it through first.
In short, the language that you use when you think about math problems is important! A lot of careless GMAT Quant errors come from not being very clear and specific about what math you’re doing. If you use phrases like “crossed off the terms” as a shortcut, you might save a few seconds on some problems, but you’re also risking careless mistakes. If you challenge yourself to articulate exactly what math you’re doing at every step, you’ll not only avoid mistakes, you’ll also have a deeper understanding of how GMAT Quant works.