Understanding Inequalities and Averages

The video tutorial covers two problems. Problem 119 involves determining if 2x - 3y is less than x squared, with two statements provided to assess sufficiency. Statement 1 alone is sufficient as x squared is always non-negative. Statement 2 is also sufficient, as 2x is always less than x squared when x is greater than 2. Problem 120 involves calculating the average number of words per paragraph in a report. The analysis of two statements reveals that statement 2 alone is sufficient to determine the average is less than 120 words per paragraph.

What is the main question being addressed in problem 119?

• Is 2x - 3y equal to x squared?

• Is 2x - 3y greater than x squared?

• Is 2x - 3y less than x squared?

• Is 2x - 3y not equal to x squared?

Why is statement 1 alone sufficient to solve problem 119?

• Because x squared is always negative.

• Because x squared is always less than zero.

• Because x squared is always equal to zero.

• Because x squared is always positive or zero.

What does statement 2 tell us about x and y in problem 119?

• x is less than 2 and y is less than 0.

• x is greater than 2 and y is less than 0.

• x is greater than 2 and y is greater than 0.

• x is less than 2 and y is greater than 0.

How does statement 2 alone help in solving problem 119?

• It shows that 2x is always equal to x squared.

• It shows that 2x is always greater than x squared.

• It shows that 2x is always less than x squared.

• It shows that 2x is always not equal to x squared.

What is the main question being addressed in problem 120?

• Is the average number of words per paragraph more than 120?

• Is the average number of words per paragraph less than 120?

• Is the average number of words per paragraph equal to 120?

• Is the average number of words per paragraph not equal to 120?

What does statement 1 tell us about the preface in problem 120?

• Each paragraph has no words.

• Each paragraph has exactly 100 words.

• Each paragraph has more than 100 words.

• Each paragraph has less than 100 words.

Why is statement 1 alone not sufficient for problem 120?

• It only tells us the average is less than 112.

• It only tells us the average is not equal to 112.

• It only tells us the average is equal to 112.

• It only tells us the average is greater than 112.

What does statement 2 tell us about the preface in problem 120?

• Each paragraph has more than 150 words.

• Each paragraph has no words.

• Each paragraph has fewer than 150 words.

• Each paragraph has exactly 150 words.

How does statement 2 alone help in solving problem 120?

• It shows the average is equal to 116.

• It shows the average is not equal to 116.

• It shows the average is less than 116.

• It shows the average is more than 116.

What conclusion can be drawn from both statements in problem 120?

• Statement 1 is sufficient, but statement 2 is not.

• Statement 2 is sufficient, but statement 1 is not.

• Both statements are insufficient.

• Both statements are sufficient.