When do you know to test cases (pick numbers) in DS?

Hi, If you are picking the numbers to solve DS question be cautious, look for all the possibilities. Check with integers(+,0,-), rational. at the same time check for the insufficient answers.

There are two types of questions in Data Sufficiency; (1) Value question (2) Yes/No question.

Picking numbers is a useful strategy in Yes/No questions. Generally, pick numbers to prove that the statements are not sufficient, i.e. pick a number which gives a yes answer another number to get a no answer. For proving sufficiency try to use logic rather than testing numbers.

Test numbers systematically. Use a standard set of numbers during your practice sessions so that this becomes a habit. After reading the constraints mentioned in question stem and the 2 statements, you could test for (assuming no constraints) -2,\(\frac{-3}{2}\),-1,\(\frac{-1}{2}\),0,\(\frac{1}{2}\),1,\(\frac{3}{2}\) and 2.

Hi Andi1gmat,

You ask a really interesting question. You need to be careful to not “over-pick” numbers when tackling Data Sufficiency questions. Many DS questions may be screaming at you to pick numbers (as a trap) but can actually be simplified down to a point at which you don’t need to select numbers at all. Good indications of when you can pick numbers are 1) there is nothing to simplify in the question stem and 2) there is an inequality in which you are asked to compare variables with exponents in the form of an inequality. The latter is a good indication that you should plug in numbers because different types of numbers react differently to exponents. For instance, when squaring a positive integer, the result increases; however, when squaring a positive proper fraction, the result decreases. The GMAT may test you on these types of principles, and to answer such questions, you’d want to plug in numbers. Let’s review the following example:

If m and n are greater than zero, is m^5 > n^3?

1) m > n^3

2) m - n > n – m

Since we see that we are asked to determine whether m raised to the 5th power is greater than n raised to the 3rd power, plugging in numbers will help us determine an answer. The solution is below:

Solution:

Statement One Alone:

m > n^3

If we let m = 2 and n = 1, we see that m^5 is greater than n^3, since 32 is greater than 1. However, if m = 1/2 and n = 1/3, we see that m^5 is not greater than n^3, since 1/32 is not greater than 1/27. Thus, statement one is not sufficient.

Statement Two Alone:

m - n > n – m

Simplifying statement two, we see that m > n. Let’s use the same values we used in statement one:

If we let m = 2 and n = 1, we see that m^5 is greater than n^3, since 32 is greater than 1. However, if m = 1/2 and n = 1/3, we see that m^5 is not greater than n^3, since 1/32 is not greater than 1/27. Thus, statement two is not sufficient.

Statements One and Two Together:

Since we were able to use the same values in both statements and not get a definitive answer, we see that the answer here is E.

While this is just one example, you should look out for problems that can’t be simplified and that compare variables with exponents, because in that case, it’s a pretty good bet that plugging in numbers is the way to go. Feel free to reach out with further questions.

Good luck!

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