The Art of the GRE Sanity Check

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You know what’s really frustrating? Making a ridiculous math mistake on a GRE Quant problem, totally by accident, and never noticing it. Add a three-second sanity check to your GRE Quant routine, and you’ll be more likely to catch small mistakes before they turn into huge disasters.

A “sanity check” is what you do whenever you make a mathematical move that might lead to a mistake. For instance, suppose you’re solving a GRE Quant problem that asks you to convert from dollars to cents. Perform a sanity check by asking yourself whether the result, logically, should be larger or smaller than the initial number. In this case, the result should be larger — if you end up with a smaller value, that means you divided where you should have multiplied, and you need to back up one step and try again. Do this every time you perform a unit conversion.

You can also check whether your answer is sane compared to the other numbers in the problem. Especially in problems with two variables, it’s often clear which number should be larger, and by approximately how much. If you’re solving for the weight of the larger of two rhinoceroses, and their combined weight is 7,000 lbs, a result of 3,000 lbs should fail your sanity check. It’s illogical, since it can’t possibly be the larger of the two weights.

Whenever you turn a word problem into an equation, sanity check it by plugging in small numbers. It’s easy to switch two variables around, or place a number on the wrong side of the equals sign. So, try some numbers that make sense and check that the everything comes out correctly. One common mistake I see my students make involves translating a sentence like this:

There are three fewer apples than pears.

into an equation like this:

a – 3 = p

That isn’t obviously incorrect at a glance, especially when you’re stressed out and working quickly. But quickly check whether it’s sane before you move on. According to the word problem, it would make sense to have 10 apples and 13 pears. But when you fit those numbers to the equation, you end up with “7 = 13”. It’s illogical, so back up and try again.

If you have time, you can also sanity check your final answer to a problem. This is especially valuable on numerical entry problems, where being off by even a tiny amount will lead to a wrong answer. In some problems, you can estimate about how large your answer ought to be, compared to the other numbers in the problem. If the problem states that the (unknown) value of a rare painting is 20% greater than the (known) value of a statue, then the result you find had better be slightly larger than the known value. The most powerful sanity check, though, is performed by plugging your answer back into the problem and making sure everything makes sense. For example:

Noel cuts a 40 foot length of rope into three pieces. The shortest piece is 17 feet shorter than the longest piece, and the longest piece is one foot greater than twice the length of the middle piece. What is the length of the shortest piece of rope?

Suppose that you’ve solved this problem and decided that the answer is 5 feet. This answer does seem sane: logically, it should be less than one third of the total length of the rope. To take your sanity check one step further, plug the answer back into the problem. If the shortest piece is 5 feet long, the longest piece must be 22 feet long. That leaves 13 feet for the middle piece. But 22 isn’t one foot greater than twice 13 feet, so your answer must have been wrong. If you have time, try again. If you don’t, pick another answer at random, or pick one that’s larger or smaller than your previous answer based on logic, and move on.

You don’t have to just use this method to sanity check your answers, either. You can use it to solve just about any word problem whose answer choices are just ordinary, single numbers. Plug in each answer choice, one by one, until everything else in the problem fits correctly. The answer that makes everything else work is the right one. (Try it out with the correct answer to the problem above, which is 6 feet.)

Don’t ever accept an answer that doesn’t make logical sense. If you’re doing a mathematical operation that often leads to silly mistakes — such as a unit conversion, translating a word problem into math, or solving a complicated system of equations — ask yourself whether what’s on your paper is sane. If it isn’t, back up and try again before you finish the entire problem incorrectly and run out of time! The more quickly you catch silly mistakes, the less likely they’ll turn into GRE Quant disasters. 📝

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Chelsey Cooley is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.