Question of the Week: Supplying Numbers

GRE prep | GRE Challenge | question of the week


Algebra or Arithmetic?abacus-mathematics-addition-subtraction-1019470

Math on GRE Quant can be broken down into four categories:

  • Arithmetic and Number Properties
  • Algebra
  • Geometry
  • Data Interpretation and Statistics

While algebra may be a distinct topic on the GRE, there is considerable overlap between algebra and the other areas tested, and incorporating algebra into geometry or data interpretation questions is a common way to make these questions more difficult. 

In a previous post we discussed how to try out the answers to find one that satisfied the conditions in the problem. In this post, we'll discuss how to turn even complicated algebra into more straightforward arithmetic: Supplying Numbers™. There are two benefits to this strategy:

  1. Eliminate common algebraic errors and increase accuracy
  2. Work through complicated problems quickly

While it is possible to supply numbers in different ways depending on the problem, the basic process is as follows:

  1. Evaluate the problem to identify whether it involves algebra, either explicit (as formulas, etc.) or implicit (as a word problem that needs to be converted to an expression).
  2. Determine whether you may supply any missing values. Pick appropriate, easy numbers. Look at the rest of the problem to see what numbers might work best.
  3. Work through the problem with your numbers to determine the answer.
  4. Test out the answer choices to see which one works.

Read below to see an example of this process at work.


Question of the Week

pluggingin (1)

1. Evaluate the problem.

We have algebra here in the form of two equations. We also have the variable in the answer choices. The variables m, n, and are present in the question stem. The question is asking us to determine the value of p.

2. Can we supply any missing values? What value should we choose?

Hypothetically, we could try out values for any of the variables. They are all linked together in the question stem. However, since appears in the answer choices, that's usually a pretty safe bet for a variable to try out. 

Next we ask ourselves what value might work well for m. Let's take a look at the numbers that appear in the problem. We have 2, 3, 5, and 7. We are multiplying and dividing. How could we make these calculations as simple as possible. We could try to find a common multiple of all of these, but since they are all prime, that would mean we use = 210. Let's keep things a big smaller and use = 35. This is a multiple of 5 and 7 and should keep any weirdness to a minimum. 

CodeCogsEqn (10)

3. Work through the problem with our number.

Now that we've supplied 35 for m, let's step through the problem using 35 wherever appears.

CodeCogsEqn

CodeCogsEqn (1)CodeCogsEqn (2)CodeCogsEqn (3)

Now that we have determined that = 42, we can use this value in the next equation to figure out what must equal. 

CodeCogsEqn (11)CodeCogsEqn (12)CodeCogsEqn (13)CodeCogsEqn (14)

CodeCogsEqn (15)We have now solved the problem. We've figured out that = 36. The question is asking for the value of p, so now we have to find out which answer choice gives us this value, 36. Remember that wherever we see an m, we swap in 35. Let's take another look at the answers:

pluggingin (1)Start by labeling the answers. Can we tell which one might give us 36? If m = 35, it looks like answer choice D will work. We can try out a couple other ones to make sure, but D is the only answer that checks out:

pluggingin2 (1)That's it! D is the answer! Interested in the algebraic solution? Check it out:

CodeCogsEqn (4)CodeCogsEqn2CodeCogsEqn

CodeCogsEqn (4)CodeCogsEqn (5)CodeCogsEqn (6)As long as we keep our algebra straight, we're in business. The trouble comes if we get something mixed up in one of our steps above. 


Use Any Tool that Works

As part of your GRE preparation, you must practice algebra and get comfortable manipulating equations. As part of your practice, for any problem such as the one above you should attempt it multiple ways:

  1. Solve the problem using a conventional math approach.
  2. Solve the problem using problem-solving skills and shortcuts. 

When you're taking the actual test, one key to success is not to get stuck. If something is not working out for you, consider trying something else. Any approach that produces the correct answer quickly is the best approach for you. 

Practice problem-solving skills such as Supplying Numbers, and when you have questions, jump over to our free GRE and Grad School Admissions Forums to ask questions and get expert help. We look forward to seeing you there!

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