This one is a data sufficiency question from algebraic equation and solution to equations and basic number properties. What is the value of x ? Statement 1: x + 3y = 18 Statement 2: x^3 = -16

1. GMAT QUANTITATIVE REASONING
NUMBER PROPERTIES
DATA SUFFICIENCY
Diagnostic Test

2. Question
What is the value of x ?
Statement 1: x + 3y = 18
Statement 2: x3 = -16

3. Step 1
Jot down answers to these 2 questions
before looking at the statements

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

5. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient?

6. 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

7. 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 unique
value for x

8. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it not sufficient?
For DS questions that
ask for the value of x
Data is sufficient when
we can get a unique
value for x

9. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it not sufficient?
For DS questions that
ask for the value of x
Data is sufficient when
we can get a unique
value for x
If the statement(s)
provide more than
one value for x

10. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it not sufficient?
For DS questions that
ask for the value of x
Data is sufficient when
we can get a unique
value for x
If the statement(s)
provide more than
one value for x
Data is NOT sufficient

11. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it not sufficient?
For DS questions that
ask for the value of x
Data is sufficient when
we can get a unique
value for x
If the statement(s)
provide more than
one value for x
Data is NOT sufficient
What is the approach?

12. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it not sufficient?
For DS questions that
ask for the value of x
Data is sufficient when
we can get a unique
value for x
If the statement(s)
provide more than
one value for x
Data is NOT sufficient
What is the approach?
Evaluate each
statement
independently first

13. What is the value of x?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it not sufficient?
For DS questions that
ask for the value of x
Data is sufficient when
we can get a unique
value for x
If the statement(s)
provide more than
one value for x
Data is NOT sufficient
What is the approach?
Evaluate each
statement
independently first
If solving the equation
results in a unique value
for x, data is sufficient.
Else no.

14. Step 2
Let’s evaluate statement 1 alone

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

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

17. What is the value of x?
Statement 1: x + 3y = 18
x + 3y = 18
The given equation is a linear equation in two variables.

18. What is the value of x?
Statement 1: x + 3y = 18
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.

19. What is the value of x?
Statement 1: x + 3y = 18
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.
For e.g., if y = 0, x = 18. If y = 1, x = 15.

20. What is the value of x?
Statement 1: x + 3y = 18
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.
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.

21. What is the value of x?
Statement 1: x + 3y = 18
Statement 1 alone is NOT sufficient
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.
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.

22. What is the value of x?
Statement 1: x + 3y = 18
Eliminate choices A and D
Statement 1 alone is NOT sufficient
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.
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.

23. What is the value of x?
Statement 1: x + 3y = 18
Choices narrow down to B, C or E.
Eliminate choices A and D
Statement 1 alone is NOT sufficient
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.
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.

24. What is the value of x?
Statement 1: x + 3y = 18
Choices narrow down to B, C or E.
Eliminate choices A and D
Statement 1 alone is NOT sufficient
x + 3y = 18
The given equation is a linear equation in two variables.
The value of x will be different for different values of y.
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.
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.

25. Step 3
Let’s evaluate statement 2 alone

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

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

28. Is x > y?
Statement 2 : x3 = -16
x3 = -16
x =
3
−16. The result is unique

29. Is x > y?
Statement 2 : x3 = -16
x3 = -16
x =
3
−16. The result is unique
Odd roots such as cube root, fifth root
will result in a unique value for x.

30. Is x > y?
Statement 2 : x3 = -16
Statement 2 alone is SUFFICIENT
x3 = -16
x =
3
−16. The result is unique
Odd roots such as cube root, fifth root
will result in a unique value for x.

31. Is x > y?
Statement 2 : x3 = -16
Eliminate choices C and E
Statement 2 alone is SUFFICIENT
x3 = -16
x =
3
−16. The result is unique
Odd roots such as cube root, fifth root
will result in a unique value for x.

32. Is x > y?
Statement 2 : x3 = -16
Correct Answer choice B.
Eliminate choices C and E
Statement 2 alone is SUFFICIENT
x3 = -16
x =
3
−16. The result is unique
Odd roots such as cube root, fifth root
will result in a unique value for x.

33. Is x > y?
Statement 2 : x3 = -16
Correct Answer choice B.
Eliminate choices C and E
Statement 2 alone is SUFFICIENT
x3 = -16
x =
3
−16. The result is unique
Odd roots such as cube root, fifth root
will result in a unique value for x.
The value of
3
−16 is not
positive. It is not an
integer.
It does not matter. It only
has to be unique.

34. Points to Remember

35. Useful points

36. Useful points
Equations : Unique
solution

37. Useful points
Equations : Unique
solution
For Linear Equations:
Number of equations
should be as many as
number of variables

38. Useful points
Equations : Unique
solution
For Linear Equations:
Number of equations
should be as many as
number of variables
Note : The above is a
necessary but not
sufficient condition

39. Useful points
Equations : Unique
solution
Odd and even roots
For Linear Equations:
Number of equations
should be as many as
number of variables
Note : The above is a
necessary but not
sufficient condition

40. Useful points
Equations : Unique
solution
Odd and even roots
For Linear Equations:
Number of equations
should be as many as
number of variables
Odd roots unique solution
Even roots NO unique
solution
Note : The above is a
necessary but not
sufficient condition

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