*Note: the scores discussed in this post refer to the old (pre-August 2011) GRE
Meet the Word Problem
The GRE Math contains a medley of word problems. You can see probability, interest, rates, combinations and even geometry problems. In general, the problems are worded in such a way that they can be vague or even downright confusing. To add to all that, some of the more difficult word problems have a little twist, in which if you’re not reading carefully you’ll get trapped.
One strategy students employ when dealing with word problems is to read the question over and over again, until their heads begin spinning. Inducing vertigo, however, is never a good strategy, especially in the test center. That’s why you want to prepare yourself for even the most convoluted and diabolical of word problems by following the steps below.
Breaking it Down
After reading the problem, you want to break the problem apart into manageable pieces. For instance, if a word problem is comprised of three sentences, make sure to understand a sentence at a time, instead of trying to “get it” all in one reading. Following this process is much like eating—you wouldn’t try to down a whole meal in one swallow. Likewise, you don’t want to try to understand the entire problem, with all its different parts, in one read (refer to vertigo in preceding paragraph).
Put in to Your Own Words
When breaking down a problem into its various parts, another effective strategy is putting the problem into your own words. Doing so will help you break a word problem down to its essence and basic meaning. Note: The longer the problem is, the more applicable this strategy tends to be.
You may notice that breaking down a complex sentence is a strategy very similar to that employed on Text Completion or Sentence Equivalence Questions. Again, throughout the GRE, a great strategy is thinking through a problem by breaking it up in your own words (versus staring at the screen and trying to read through the same turgid verbiage over and over again).
Even if you follow all the above steps, you can still get a word problem wrong if you do not do the following: always remember what is being asked. It is very easy to lose sight of the forest and get lost in the trees, so to speak, and forget what the question was originally asking for. A good idea is to write down on scratch paper what the question is. That way, after you’re done interpreting the word problem and calculating an answer, you’ll remember what the original goal was.
Finally, watch out for any twists in the way the question is worded. Many times a question will throw in one twist—such as the word approximate—so that if you are not careful you will either choose the wrong answer, or wonder why your answer choice is not there (the latter is often an indication that you missed the twist).
To see an example of convoluted word problems with a twist, as well as to practice the strategies above, try the following five word problems. These word problems are mostly in the 600 – 700 range and, just like the real GRE, cover a range of topics.
So get ready, set your timers and let’s see if you can finish these word problems in 10 minutes or less!
1. Positive integer n is equal to the difference of the squares of x and y, where x and y are integers. If n is equal to 21, then which of the following could be the sum of x and y?
2. Bikesville is 200 miles from Restsville. Jasmine can complete the entire trip in 8 hours, and Monte takes two hours longer than Jasmine to complete the entire trip. If one begins in Bikesville and the other in Restville, then approximately how long will it take them to meet?
(A) 2 hrs
(B) 2.5 hrs
(C) 4 hrs
(D) 5 hrs
(E) 8 hrs
3. A lottery game consists of the host removing one ball at a time from an opaque jar. Each ball has one of the digits (0 – 9) written on it, and no two have the same number on them. If the host removes three balls without replacement, what is the probability that the sum of the numbers written on the balls equals 24?
4. The area of isosceles right triangle XYZ equals 9. Which of the following could be the perimeter?
II. 13 + √145
III. 6√2 + 6
(A) I only
(B) I and III
(C) III only
(D) I and II
(E) All of the above
5. A brown flask contains a concoction that is 20% alcohol. A red flask contains a concoction with an unknown amount of alcohol. An equal amount of both flasks is poured into an empty jug. If the resulting mixture has an alcohol concentration that is 30% greater than the alcohol concentration of the brown flask, what percent alcohol did the red flask originally contain?
1. C Hint: Don’t forget negative numbers. Also note use of phrase “could be”.
2. C Hint: It’s asking for an approximation
3. D Hint: Don’t forget: there are 10 balls.
4. C Hint: III is 45:45:90. You can solve for x.
5. C Hint: The empty jug does not contain 30%
How Did You Do?
5: You are well on your way to the 800-level. Definitely spend your time prepping with the more challenging material. In fact, you may want to take a look at some of the previous challenge problems on Magoosh.
4: Not bad at all! You may have missed one through a careless oversight. Regardless, with a little more practice you can ace word-problems and be on your way to an impressive GRE quant score.
3: Pretty good. These questions can be confusing, and as long as you review your basic concepts and continue prepping assiduously you should do well.
2: Don’t fret. Learning to decipher these types of problems takes time. The more you practice, the more confident you’ll become!
0-1: Word problems are the bane of many students. The good news is I’ve seen students go from fear and trembling to uber-confident when it comes to longer word problems. The key is to learn your fundamentals and then do problems to help reinforce concepts. When you begin to get questions right, step up the level of difficulty just enough so that you are being challenged, but not intimidated.
1. We can rewrite the information as x^2 – y^2 = 21 = n. A good little trick to know regarding the difference of squares is that the difference of squares of consecutive integers will always be x + x + 1, where x is the lesser of the two integers. To illustrate:
5^2 – 4^2 = 9, x = 4 and 4 + 4 + 1 = 9
So what two integers, when summed, equal 21?
x + x + 1 = 21, 2x = 20, x = 10 (10, 11).
We are looking for the sum, which would be 21. However this is not an answer choice. Do not despair: we can also use -10 and -11, because each number squared will yield the same number as its positive counterpart.Playing around with these numbers we get -11 and 10. The sum of -11 and 10 is -1, answer (C).
5^2 – 2^2 would also yield a sum of 21. But remember the question is asking for which of the following COULD be the sum. Out of the five answer choices only (C) works.
2. Jamie can finish the trip in 8 hrs: 200/8 = 25 mph. Monte takes 2 hrs longer, or 10 hrs: 200/10 = 20. We want their combined rates, since they are pedaling towards each other: 200/45 = 4 4/9 , which is a little less than 4.5. The question is asking for an approximation, so that gives us: (C) 4hrs.
3. For this question, we have determine how many ways we can use three distinct numbers (0 – 9) to sum to 24. 7, 8, 9 is the only way we can do so, but remember we can rearrange those three balls in 3! = 6 ways. (8,9,7, etc.).
The next step is to determine how many total ways can we choose from 10 balls (don’t get tricked by thinking there are nine balls!). 10 x 9 x 8 = 720.
Using probability we want to divide the total number of ways by desired outcomes: 6/720, 1/120, which is (D).
4. A 45:45:90 triangle gives us x^2 = 18, x = 3√2. Solving for the perimeter we get III. Notice that answer (C).
5. The brown flask has 20% alcohol. The combined (brown + red) has 30% more than 20% (26%). We mixed equal parts so we can reason that the red flask had to have 6% more than the mixed (remember the brown flask has 6% less). This gives us 32%, or (C).
To find out where word problems sit in the “big picture” of GRE Quant, and what other Quant concepts you should study, check out our post entitled:
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