# Comparison Math Problems

**1. x + y = 15
x - y = 24**

**Column A - (y)
Column B - (-5)**

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 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**

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 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**

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 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**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. 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.**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. 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**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. 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**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. if it is impossible to determine which quantity is greater

**8. Column A - (x-y)
Column B - 0**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. if it is impossible to determine which quantity is greater

**9. Column A - 500% of 6
Column B - 600% of 5**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. 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**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. if it is impossible to determine which quantity is greater

**11. 5 is 2/3% of n
Column A - n
Column B - 15**

B. if the quantity in Column B is greater

C. if the two quantities are equal

D. 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 9π. The area of a semi-circle with a radius of 4 is equal to half of 16π, namely 8π. 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: 03/01/2017