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.

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.

Understanding GMAT data sufficiency question

The next set of blogs will be focusing on Data sufficiency(DS). Many students feel that they make more errors in DS than problem solving. Let us understand this question type in depth.

Sample question:

What is the value of a?

(1)      3a + 2b = 15

(2)      b = (-3/2) (a – 5)

The Directions:

Each data sufficiency problem consists of a question and two statements, labeled (1) and (2), that give data. You have to decide whether the data given in the statements are sufficient for answering the question.

Use the data given in the questions plus your knowledge of mathematics and everyday fact, you must indicate whether the data given in the statements are sufficient for answering the questions and then indicate one of the following answer choices:

(A) Statement (i) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

 (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;

(D) EACH statement ALONE is sufficient to answer the question asked;

(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

NOTE: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Numbers: All numbers used are real numbers.

Figures: A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees. All figures lie in a plane unless otherwise indicated.

These questions require knowledge of the following topics: • Arithmetic • Elementary algebra • Commonly known concepts of geometry

DS problem – Approach flow chart

Next post: Strategies to tackle data sufficiency questions