GMAT data sufficiency strategy - assume,check and adjust

Stumped with data sufficiency...

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

Let’s take a question

Is the product abcd = 1?        

Statement 1: ab/cd=1

Statement 2: a,b,c,d are integers

Strategy:

Take a statement. Substitute different sets of numbers and check for consistency. If the results are inconsistent, when different sets of number are substituted, the given statement is insufficient. 

Lets solve this question with this approach

Is the product abcd = 1?        

Statement 1: ab/cd=1

Statement 2: a,b,c,d are integers

Consider statement 1

Substitute numbers which satisfy statement 1

a=2,b=3,c=6 and d=1 satisfy statement 1. But is the product abcd= 1. The answer is “no”

Plug in a different set of numbers to check consistency

a=4,b=3,c=6 and d=2 satisfy statement 1. Is the product abcd= 1. The answer is “no”

But

a=2,b=1/2,c=3 and d=1/3 satisfy statement 1. Is the product abcd= 1. The answer is “Yes”.

As the result is inconsistent, sometimes the answer is “yes” other times it is “no”. The given statement is insufficient.

Similarly analyse statement 2

Plug in numbers which satisfy statement2

a=2,b=3,c=6 and d=1 satisfy statement 1. But is the product abcd= 1. The answer is “no”

a=1,b=1,c=1 and d=1 satisfy statement 1. But is the product abcd= 1. The answer is “yes”

Thus statement 2 is insufficient, since, for certain numbers “yes” is arrived and for others “no” is arrived

Even when both statements are combined, for certain numbers “The product abcd is equal to 1” is arrived and for others “The product abcd is not equal to 1” is arrived

It is necessary to arrive at consistent result before marking an answer.

The answer is E.

Try another question with the same approach

Is (a/b)>(c/d)?

1.a>c

2.b>d

Answer is E.