Inequalities and Fraction Behavior

The video tutorial reviews GMAT problems 142, 143, and 144. It begins with a critique of problem 142, suggesting a possible error in the GMAT's interpretation. The instructor then analyzes problem 143, which involves comparing fractions with added values to the numerator and denominator, and concludes that both given statements are needed to solve it. Finally, problem 144 is discussed, focusing on powers of ten and inequalities, demonstrating that each statement independently suffices to answer the question.

In problem 142, what is the main issue the instructor identifies with the GMAT question?

• The GMAT question lacks sufficient information.

• The equation is incorrectly stated.

• The GMAT question is irrelevant.

• The solution provided is too complex.

Tags

CCSS.HSF-IF.C.7D

In problem 143, what happens to the fraction m/n when a large positive x is added to both the numerator and denominator?

• The fraction becomes smaller.

• The fraction becomes negative.

• The fraction remains unchanged.

• The fraction approaches 1.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

In problem 143, why is statement 1 alone not sufficient?

• It does not specify if x is positive.

• It does not consider negative values of x.

• It assumes m is greater than n.

• It only applies to fractions greater than 1.

In problem 143, what is the result when x is negative and m < n?

• The fraction becomes larger.

• The fraction becomes smaller.

• The fraction remains the same.

• The fraction becomes negative.

Tags

CCSS.7.NS.A.1B

In problem 143, what is the effect of adding a positive x to a fraction where m < n?

• The fraction remains constant.

• The fraction increases.

• The fraction becomes negative.

• The fraction decreases.

Tags

CCSS.4.NF.C.6

In problem 144, what is the equivalent expression for 0.01?

• 1/10

• 1/100

• 1/1000

• 1/10000

In problem 144, what does statement 1 imply about n?

• n must be a negative integer.

• n must be equal to 2.

• n must be greater than 2.

• n must be less than 2.

In problem 144, how does the instructor simplify the inequality 1/10^n < 0.01?

• By adding 1 to both sides.

• By rewriting 0.01 as 1/10^2.

• By dividing both sides by 10.

• By multiplying both sides by 10.

In problem 144, what is the conclusion about the sufficiency of statement 2?

• It requires additional information.

• It contradicts statement 1.

• It is equivalent to the original problem statement.

• It is not sufficient.

In problem 144, what is the result of multiplying both sides of the inequality by 1/10?

• The inequality becomes more complex.

• The inequality is simplified to 1/10^n < 0.01.

• The inequality remains unchanged.

• The inequality becomes invalid.