If m and n are non-zero integers, is mn nn?Statement 1: |m| = nStatement 2: m

Question

If m and n are non-zero integers, is mn > nn?Statement 1: |m| = nStatement 2: m < na)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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.Correct answer is option 'D'. Can you explain this answer?

Answer

Equal to zero?

No, the product of two non-zero integers is not equal to zero.

Answer

Step 1: Decode the Question Stem and Get Clarity
Q1. What kind of an answer will the question fetch?
An "Is" question will fetch an "Yes" or a "No" as an answer.
The data provided in the statements will be considered sufficient if the question is answered with a conclusive Yes or a conclusive No.

Q2. When is the answer an "Yes"?
If mn > nn, the answer to the question is a conclusive Yes.

Q3. When is the answer a "No"?
If mn ≤ nn, the answer to the question is a conclusive No.
Note: When mn = nn, the answer is No.

Q4. What values can m and n take?
From the information available from the question stem, both m and n can take only integer values.
So, we need not worry about values such as 0.5 or 1.2.
However, both m and n can be either positive or negative. Neither can be 0.

Step 2: Evaluate Statement 1 ALONE
Statement 1: |m| = n
We can infer the following information about m and n from the statement.

The modulus of a number is always positive. n = |m|. Hence, n is positive
m can take either positive or negative values.
Example: Let m = -3 and n = 3. |m| = n holds good.
(-3)3 < 33. So, the answer to the question is NO.

Counter Example: Let m = -2 and n = 2. |m| = n still holds good.
(-2)2 = 22. So, the answer to the question is NO.

Notice that we are not able to come up with a counter example. Both examples returned NO as answer.
Not finding a counter example might be our limitation. Let us reason why we seem to be getting NO as answer and will it hold good for all values satisfying statement 1.

When a negative number is raised to an odd power, the result is negative. So, LHS < RHS. Answer is NO.
When a negative number is raised to an even power, the result is positive. So, LHS = RHS. It is still not greater. So, the answer will still be NO.

The values that m and n takes based on statement 1 gives a conclusive answer to the question.
Hence, statement 1 is sufficient.
Eliminate answer options B, C, and E.

Step 3: Evaluate Statement 2 ALONE
Statement 2: m < n
We need to check whether we get a conclusive Yes or No using this statement to determine whether statement 2 alone is sufficient.
Let us look for counter examples

Example: Let m = 2 and n = 3
23 < 33. So, the answer to the question is NO.

Counter Example: Let m = -3 and n = 2
(-3)2 > 22. So, the answer to the question is YES.

The values that m and n takes based on statement 2 do not give a conclusive answer to the question.
Hence, statement 2 is not sufficient.
Eliminate answer option D.

Choice A is the correct answer.

Answer