This document contains a GMAT quantitative reasoning question about inequalities and data sufficiency. It asks whether the statement "m n > n n" is true given non-zero integers m and n. Statement 1 provides that the absolute value of m equals n. Statement 2 provides that m is less than n. The document analyzes both statements and determines that Statement 1 alone is sufficient to answer the question with a definite yes or no, while Statement 2 is not sufficient as counter examples can be found for both yes and no. Therefore, the answer is A - Statement 1 alone is sufficient.

1. GMAT QUANTITATIVE REASONING
INEQUALITIES – DATA SUFFICIENCY
QUESTION 3
Q-51 Series

2. Question
If m and n are non-zero integers, is 𝑚 𝑛
> 𝑛 𝑛
?
1. |m| = n
2. m < n

3. Spend a few seconds answering the following questions
Before going to the statements

4. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient?

5. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient?
It is an “is” question

6. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.

7. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.

8. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”

9. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”
If 𝑚 𝑛
< 𝑛 𝑛
then “No”

10. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”
If 𝑚 𝑛
< 𝑛 𝑛
then “No”
If 𝑚 𝑛
= 𝑛 𝑛
then “No”

11. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”
If 𝑚 𝑛
< 𝑛 𝑛
then “No”
If 𝑚 𝑛
= 𝑛 𝑛
then “No”
Do not forget this possibility

12. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no? What do we know about m & n?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”
If 𝑚 𝑛
< 𝑛 𝑛
then “No”
If 𝑚 𝑛
= 𝑛 𝑛
then “No”
Do not forget this possibility

13. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no? What do we know about m & n?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”
If 𝑚 𝑛
< 𝑛 𝑛
then “No”
If 𝑚 𝑛
= 𝑛 𝑛
then “No”
Do not forget this possibility
Both m and n are integers

14. Spend a few seconds answering the following questions
Before going to the statements
When is the data sufficient? When is it an yes & when no? What do we know about m & n?
It is an “is” question
Data is sufficient when you
answer the question with
a definite “Yes” or a
definite “No”.
If 𝑚 𝑛
> 𝑛 𝑛
then “Yes”
If 𝑚 𝑛
< 𝑛 𝑛
then “No”
If 𝑚 𝑛
= 𝑛 𝑛
then “No”
Do not forget this possibility
Both m and n are integers
Neither m nor n is zero

15. Let’s evaluate statement 1
|m| = n

16. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|1

17. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
1

18. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1

19. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2

20. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n

21. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n
mn = nn
The answer to the question is
NO.

22. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n
mn = nn
The answer to the question is
NO.
3 If m is negative

23. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n
mn = nn
The answer to the question is
NO.
3 If m is negative
m may be odd or even

24. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n
mn = nn
The answer to the question is
NO.
3 If m is negative
m may be odd or even
If m is odd, so will n be
A negative number raised to an
odd power is negative. So, mn < nn

25. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n
mn = nn
The answer to the question is
NO.
3 If m is negative
m may be odd or even
If m is odd, so will n be
A negative number raised to an
odd power is negative. So, mn < nn
If m is even, so will n be
A negative number raised to an
even power is positive. So, mn = nn
Either way, the answer is NO.

26. 1
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 1 : |m| = n
Yes
If n = |m|
n is always positive
The magnitude of m and n is the
same. ’m’ may be positive or
negative.
1 If m is positive2
m = n
mn = nn
The answer to the question is
NO.
3 If m is negative
m may be odd or even
If m is odd, so will n be
A negative number raised to an
odd power is negative. So, mn < nn
A uniform NO. So,
Statement 1is sufficient.
Answer choice A or D.
If m is even, so will n be
A negative number raised to an
even power is positive. So, mn = nn
Either way, the answer is NO.

27. Let’s evaluate statement 2
m < n

28. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n
Look for counter examples
Yes

29. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n
Look for counter examples
Identify one example that satisfies the condition that
m < n for which mn > nn. So, your answer to the question
will be yes.
Yes

30. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n
Look for counter examples
Identify one example that satisfies the condition that
m < n for which mn > nn. So, your answer to the question
will be yes.
No
Identify another set of values for m and n that satisfy the
condition m < n for which mn < nn or mn = nn. So, your
answer will be no.
Yes

31. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n
How to infer the result?
If you manage to find a pair of counter examples, one that answers
yes and another that answers no, the given statement does not give a
uniform answer. So, the statement will NOT be sufficient.
Yes

32. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n
How to infer the result?
If you manage to find a pair of counter examples, one that answers
yes and another that answers no, the given statement does not give a
uniform answer. So, the statement will NOT be sufficient.
Conversely, if you are not able to find a counter example, do not
conclude immediately that the statement is sufficient. Reason out
why it works. Use algebra, number properties, logic to justify your
conclusion.
Yes

33. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n. Finding counter examples
Yes
Example for mn < nn

34. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n. Finding counter examples
Yes
Example for mn < nn
Easy to find an example to
prove mn < nn
If |m| < |n|, then mn < nn
e.g., m = 2 and n = 4
24 < 44
Answer NO

35. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n. Finding counter examples
Yes
Example for mn < nn
Easy to find an example to
prove mn < nn
If |m| < |n|, then mn < nn
e.g., m = 2 and n = 4
24 < 44
Answer NO
Example for mn > nn

36. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n. Finding counter examples
Yes
Example for mn < nn
Easy to find an example to
prove mn < nn
If |m| < |n|, then mn < nn
e.g., m = 2 and n = 4
24 < 44
Answer NO
Example for mn > nn
Not so obvious.
To prove mn > nn when m <
n, pick m and n such that
|m| > |n|
e.g., m = -4 and n = 2
(-4)2 > 22
Answer YES

37. 2
Is 𝑚 𝑛 > 𝑛 𝑛?
Lets evaluate statement 2 : m < n. Finding counter examples
Yes
Example for mn < nn
Easy to find an example to
prove mn < nn
If |m| < |n|, then mn < nn
e.g., m = 2 and n = 4
24 < 44
Answer NO
Example for mn > nn
Not so obvious.
To prove mn > nn when m <
n, pick m and n such that
|m| > |n|
e.g., m = -4 and n = 2
(-4)2 > 22
Answer YES
We could
find a
counter
example.
So,
statement 2
is NOT
sufficient

38. Answer
Statement 1 alone is sufficient to answer the question

39. Answer
Statement 1 alone is sufficient to answer the question
Statement 2 alone is NOT sufficient

40. Answer
Choice A is the answer
Statement 1 alone is sufficient to answer the question
Statement 2 alone is NOT sufficient

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