GMAT Tip of the Week: Spend Your Labor Day Making Quant Problems Less Labor-Intensive

GMAT Tip of the WeekSo it’s Labor Day weekend, and hopefully you’ll celebrate by relaxing. But wait – Harvard’s admissions deadline is only about two weeks away, and Stanford’s is soon to follow, and within the next six weeks most top 20 programs will begin reviewing Round One applications.

So maybe you can’t afford to put your feet up just yet – maybe you do have to use your day off on Labor Day to start working toward your next career. But if you do decide to do some GMAT labor on Labor Day, keep in mind that you can still honor the spirit of the holiday, a day for the working man to celebrate the fruits of his labor by resting. You can practice GMAT math in the least labor-intensive way possible.

Two of the most common ways to reduce your workload on GMAT quant problems are:

  • Recognize “number properties”. If you can note that the correct answer must be negative (vs. positive) or odd (vs. even) or end in a certain digit, often you can avoid doing all the math and just follow the pattern to the correct answer.
  • Use the answer choices. If you can get away with an estimate, or eliminate certain answer choices for not having the right characteristics, or plug answer choices back into the problem (“backsolve”) to avoid doing the algebra, you can let the answer choices guide you away from hard labor.

So let’s look at an example of a problem for which the two above strategies can help us avoid some excess workload:

What is the square root of (x^2 * y^2) if x < 0 and y > 0?

(A) -xy
(B) xy
(C) -(absolute value of (xy))
(D) (absolute value of y)(x)
(E) Cannot be determined

Now, this problem can be solved using algebra but it may look a little intimidating that way, too. And algebra can lead to labor if you’re not careful. But you have clues:

*The presence of “x < 0”, “y > 0”, and two absolute value signs in the answer choices should indicate that this is a positive/negative number properties problem. The actual values of x and y don’t matter much (there are no actual values given anywhere in the problem) as long as you can figure out whether the right answer needs to be negative or positive, and whether each answer choice gives you that correctly. So in a case like this, you can avoid strange, conceptual algebra by picking numbers consistent with the stipulations in the problem:

x must be negative, so let’s call it -2
y must be positive, so let’s call it 3
Note: by avoiding 1 and -1 we avoid numbers with really unique problems, and since we’re squaring/rooting numbers by using a different base (2 vs. 3) for each we can more easily track the importance of each variable.

With x = -2 and y = 3, then inside the radical we have (-2)^2 * (3)^2 = 4 * 9 = 36. And the square root of 36 is 6, so we know that in our situation the result of that operation is 6. Now we can plug those numbers into the answer choices to see if we get 6:

(A) -(-2)(3) = 6, so A could work

(B) -2(3) = -6, so B is wrong

(C) The absolute value of -2(3) is 6, so -(6) = -6 and C is wrong

(D) The absolute value of 3 is 3, so it’s (3)(-2) = -6, so D is wrong

So of those answer choices, only A works, so A is correct.

More important is the takeaway – on this problem, if you can see that actual numbers aren’t as important as the number property, positive vs. negative, you can avoid having to do all the algebraic work in search of a solution and instead you can test numbers to see what type of positive/negative you need. Heeding these kinds of clues and using the answer choices to your advantage can help you avoid plenty of undue labor. So if you’re working on the GMAT this Labor Day, keep these strategies in mind and you’ll be able to avoid too much hard work on Test Day, a holiday that at least this year might matter all the more.

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By Brian Galvin

4 Responses

  1. Kanishk says:

    Love the blog, Brian!

    Quick question: Why couldn’t the square root of 36 also be -6?

    Hence, (-6)^2 = 36, with x=-2, y=3 – allowing us an answer of -(ABS((-2).(3))) which is answer choice (C).

    Keep up the posts. They are fantastic, and they make learning for the GMAT so much more fun! I’m a huge fan of your teaching style and blog.


    • Brian says:

      Ah, really good question – and the quick answer…getting math formatting to show up in WordPress is a little bit of a mess, so I used the text “the square root of” to replace the radical sign. The official question has that radical sign, and when *that* appears on the GMAT it’s asking for the positive square root. Really good point – just got burned a little by my own HTML shortcut in writing up that post.

  2. Vaishno says:

    Very nice post Brian! Just curious to know if one of the answer choices had |xy| as an option, then this choice would be correct, right?

    As square root of ((x)^2*(y)^2) = |xy| and it doesn’t matter what’s inside the square root as long as it’s been squared so you always get the absolute value.

    Please correct me if I am wrong. I know this question is in our Arithmetic book, but for some reason this thought never occurred to me until now. Thanks.

    P.S. I never get an email that says that I have received a reply of my message. Is this something that you guys can fix?

    • Brian says:

      Yes, you’re definitely right – as we proved in the explanation, we’re looking for a positive number that’s the multiple of x and y, so that absolute value of both of them would work. Of course, then they’d have to get rid of the current right answer since you can’t have two correct answers. But more importantly – I think you nailed the concept!

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