Directions for Quantitative Comparison Questions: Some of the following questions give you two quantities, one in Column A and one in Column B, Compare the two quantities and choose one of the following answer choices:

A．if the quantity in Column A is greater;

B．if the quantity in column B is greater;

C．if the two quantities are equal;

D．if you cannot determine the relationship based on the given information

【正确答案】

【答案解析】

【正确答案】 A

【答案解析】
To determine a relationship, recognize that y⁴-1 is equal to (y²)²-1. Therefore, you can substitute y²=x²+1 into (y²)²-1 to get (x²+1)²-1, which is equivalent to (x²+1)(x²+1)-1. Use the FOIL method to simplify:
Multiply the First terms: x⁴
Multiply the Outside terms: x²
Multiply the Inside terms: x²
Multiply the Last terms: 1
Now add the terms together: x⁴+2x²+1-1.
The quantity in Column A is x⁴+2x², and the quantity in Column B is x⁴. Because any number other than 0 raised to the second or fourth power yields a positive number, the quantity in Column A must be greater than the quantity in Column B.

【正确答案】 A

【答案解析】To solve this problem, recognize that the percentages are the percent of interest the investment will make each year. Assign x as the amount of the inheritance invested at 5% and assign the amount of inheritance invested at 6% as (15,000-x). Because the total interest earned is the sum of the interest from the two investments, it can be expressed as 0.05x+0.06(15,000-x)=800. Solve for x: 0.05x+0.06(15,000)-0.06x=800 -0.01x+900=800 -0.01x=-100 x=10,000 Thus the quantity in Column A ($10,000) is greater than the quantity in Column B ($15,000-$10,000).

【正确答案】 C

【答案解析】To solve this problem, first convert the mixed numbers into improper fractions: Column A:

Column B:

Next, recall that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, the quantity in Column

and the quantity in Column