Question

Two consecutive integers m and n are such that m > n. The difference m²- n²

A. is always an odd positive integer.

B. is always an even positive integer.

C. can be positive or negative but will be odd.

D. can be postive or negative but will be even.

( WITH EXPLANATION )
​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Two consecutive integers m and n are such that m > n. The difference m²- n²

A. is always an odd positive integer.

B. is always an even positive integer.

C. can be positive or negative but will be odd.

D. can be postive or negative but will be even.

EVALUATION

Here it is given that two consecutive integers m and n are such that m > n

Then m = n + 1

Now

$\sf{ {m}^{2} - {n}^{2} }$

$\sf{ = {(n + 1)}^{2} - {n}^{2} }$

$\sf{ = {n}^{2} + 2n + 1- {n}^{2} }$

$\sf{ = 2n + 1}$

We know that an odd integer is of the form 2n + 1 or 2n - 1

Then m² - n² will be odd

As it is not mentioned that n is positive or negative

So m² - n² can be positive or negative

FINAL ANSWER

Hence the correct option is

C. can be positive or negative but will be odd.

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