##### 1. x + y = 15

x – y = 24

**Column A – (y)**

**Column B – (-5)**

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**2. Column A -The average (arithmetic mean) of v,w,y,x, and z **

Column B – 70

Column B – 70

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**3. The shaded are in the below figure is 65% of the are of the entire circle, what is the value of d?**

**Column A – d **

Column B – 126 degrees

Column B – 126 degrees

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**4. Column A – The area of a circle with the radius of 3 **

Column B – The area of a semi-circle with the radius of 4

Column B – The area of a semi-circle with the radius of 4

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**5. Sarah volunteered from 9:27 A.M. until 12:45 P.M. **

Jan volunteered from 9:15 A.M. until 12:32 P.M.

**Column A – The amount of time Sarah volunteered. **

Column B – The amount of time Jan volunteered.

Jan volunteered from 9:15 A.M. until 12:32 P.M.

Column B – The amount of time Jan volunteered.

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**6. If 34% of 360 equals 7.5% of h, what is h**

**Column A – h **

Column B – 1634

Column B – 1634

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**7. Column A – The fraction of 76 hours of a week **

Column B – The fraction of 10 hours in a day

Column B – The fraction of 10 hours in a day

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**8. Column A – (x-y) **

Column B – 0

Column B – 0

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**9. Column A – 500% of 6 **

Column B – 600% of 5

Column B – 600% of 5

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**10. If n>0, **

Column A – 24/25 of n

Column B – 95% of n

Column A – 24/25 of n

Column B – 95% of n

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

**11. 5 is 2/3% of n **

Column A – n

Column B – 15

Column A – n

Column B – 15

- if the quantity in Column A is greater
- if the quantity in Column B is greater
- if the two quantities are equal
- if it is impossible to determine which quantity is greater

## Answers & Explanations

1. **A:** Solving the system of equations gives *y* = -4.5. Since -4.5 is greater than -5, the quantity in Column A is greater.

2. **A:** The average may be represented as (360°)/5, which equals 72°. Since 72° is greater than 70°, the quantity in Column A is greater.

3. **C:** The shaded area comprises a total angle measure that may be represented as 0.65(360°), or 234°. Thus, the non-shaded area, which represents the value of d, is equal to the difference of 360° and 234°, or 126°. This value is the same value given for Column B.

4. **A:** The area of a circle with a radius of 3 is equal to 9p. The area of a semi-circle with a radius of 4 is equal to half of 16p, namely 8p. Thus, the quantity in Column A is greater.

5. **A:** The amount of time Sarah volunteered was 3 hours, 18 minutes. The amount of time Jan volunteered was 3 hours, 17 minutes. Thus, Sarah’s quantity was greater.

6. **B:** The problem may be modeled as 0.34(360) = 0.075*h*. Solving for *h* gives *h* = 1632, which is less than 1634. Thus, the quantity in Column B is greater.

7. **A:** The fraction of 76 hours in a week may be represented by the ratio, 76/168, which is approximately 45%. The fraction of 10 hours in a day may be represented by the ratio, 10/24, which is approximately 42%. Thus, the quantity in Column A is greater.

8. **C:** Since the values of *x* and *y* are the same, the difference will equal 0. Thus, the quantities in Columns A and B are equal.

9. **C:** The value for Column A may be written as 5(6). The value for Column B may be written as 6(5). Both expressions equal 30, thus the quantities for Columns A and B are equal.

10. **A:** The quantity, given for Column A, may be written as 0.96*n*, which is greater than 0.95*n*. Thus, the quantity for Column A is greater.

11. **B:** The problem may be modeled as 5 = 0.667*n*, where *n* ˜ 7.5. Since 15 is greater than 7.5, the quantity in Column B is greater.

by Enoch Morrison | Last Updated: December 31, 2018