4GMAT Diagnostic Test Q5 - Data Sufficiency : Algebra, equations

GMAT QUANTITATIVE REASONING

NUMBER PROPERTIES

DATA SUFFICIENCY

Diagnostic Test

Question

What is the value of x ?

Statement 1: x + 3y = 18

Statement 2: x3 = -16

Step 1

Jot down answers to these 2 questions

before looking at the statements

What is the value of x?We will not even look at the statements while answering the following questions


When is the data sufficient?



For DS questions that ask for the value of x




Data is sufficient when we can get a uniquevalue for x


When is the data sufficient? When is it not sufficient?







If the statement(s) provide more than one value for x






Data is NOT sufficient







What is the approach?








Evaluate each statement independently first








Evaluate each statement independently first

If solving the equation results in a unique value for x, data is sufficient. Else no.

Step 2

Let’s evaluate statement 1 alone

What is the value of x?Statement 1: x + 3y = 18


x + 3y = 18


x + 3y = 18

The given equation is a linear equation in two variables.


x + 3y = 18


The value of x will be different for different values of y.


x + 3y = 18



For e.g., if y = 0, x = 18. If y = 1, x = 15.


x + 3y = 18



For e.g., if y = 0, x = 18. If y = 1, x = 15.

So, we will not get a unique value for x from statement 1.


Statement 1 alone is NOT sufficient

x + 3y = 18



For e.g., if y = 0, x = 18. If y = 1, x = 15.



Eliminate choices A and DStatement 1 alone is NOT sufficient

x + 3y = 18



For e.g., if y = 0, x = 18. If y = 1, x = 15.



Choices narrow down to B, C or E.


x + 3y = 18



For e.g., if y = 0, x = 18. If y = 1, x = 15.



Choices narrow down to B, C or E.


x + 3y = 18



For e.g., if y = 0, x = 18. If y = 1, x = 15.


For linear equations, the necessary condition to get a unique value for the unknowns is to have as many equations as the number of unknowns.

Step 3

Let’s evaluate statement 2 alone

Is x > y?Statement 2 : x3 = -16


x3 = -16


x3 = -16

x = 3−16. The result is unique


x3 = -16


Odd roots such as cube root, fifth root will result in a unique value for x.


Statement 2 alone is SUFFICIENT

x3 = -16




Eliminate choices C and EStatement 2 alone is SUFFICIENT

x3 = -16




Correct Answer choice B.


x3 = -16




Correct Answer choice B.


x3 = -16



The value of 3−16 is not

positive. It is not an integer.

It does not matter. It only has to be unique.

Points to Remember

Useful points

Useful points

Equations : Unique solution

Useful points


For Linear Equations: Number of equations should be as many as number of variables

Useful points



Note : The above is a necessary but not sufficient condition

Useful points


Odd and even roots



Useful points


Odd and even roots


Odd roots unique solution

Even roots NO unique solution


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4GMAT Diagnostic Test Q5 - Data Sufficiency : Algebra, equations

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