GMAT data sufficiency tip - substitute numbers wisely…HOW?

Data sufficiency is a test of mathematical reasoning.  It tests your ability to evaluate the adequacy of given data in answering a question in the mathematical setting. This involves verifying the sufficiency of data to solve a problem, distinguishing between relevant and irrelevant data, and establishing relationship between variables.

Here’s how the directions for data sufficiency problems appear in the exam

A given question is followed by two statements. You are required to determine whether the statements can be used to answer the question.

Mark (A) if statement I alone is sufficient but statement II alone is not sufficient to answer the question

Mark (B) if statement II alone is sufficient but statement I alone is not sufficient to answer the question

Mark (C) if both statements I and II together are sufficient to answer the question

Mark (D) if each statement alone is sufficient to answer the question

Mark (E) if statement I and II together are not sufficient to answer the question

Let us understand one approach to solve DS questions with lots of variables

That is substituting numbers

Here’s  a DS question

Is zp negative?

(1)pz4

(2)p+z4=14

In sums involving inequalities, substitute numbers for variables wisely. When you see the variables (i.e. a,b,c...)  you would substitute numbers. For those of you who are out of touch in math, would substitute natural numbers (1,2,3,4...).

You should realize that a number could be positive, negative, zero,  a fraction,  square root, pi or some other decimal.   The possibilities are many.

So before arriving at a conclusion check whether the inequality satisfies all the different types of number. At times the question will introduce conditions and this will limit the types of numbers which have to be substituted.

Lets take statement 1

(1)pz4

z=1 hence z4=1(positive) z=-1 hence z4=1(positive)

z=0.1 hence z4=0.0001(positive) z=-0.1 hence z4=0.0001(positive)

z cannot be 0 as the product pz4 has to be less than 0

z4 is always positive, but z can be positive or negative but not 0.

As the product pz4 has to be less than 0, p has to be a negative number.

Now lets analyze the product zp

z =positive p=negative zp =negative

z =negative p=negative zp =positive

Statement (1) is insufficient to answer the question as the answer is inconsistent.

(2)p+z4=14

Statement can be analyzed by framing a table.

Choose numbers such that p+z4=14

p=13 z=1 z4=1 product of zp = positive

p=13 z=-1 z4=1 product of zp = positive

p=14 z=0 z4=0 product of zp = 0 neither positive or negative

Statement (2) is insufficient to answer the question as the answer is inconsistent.

On combining both the statements

Lets frame a table

Choose numbers which satisfy p+z4=14

p=-2 z=-2 z4=16 product of zp = negative

p=-2 z=-2 z4=16 product of zp = positive

Statements (1) and (2) together are insufficient to answer the question as inconsistent values can be derived. Answer E

Questions based on number properties appear on the GMAT. If you are weak on number sense, you may hastily arrive at a conclusion without checking all possibilities. Be smart at picking numbers.