# Comparison Math Problems

##### 1. x + y = 15  x – y = 24Column A – (y) Column B – (-5)
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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 1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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 1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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.
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if it is impossible to determine which quantity is greater
##### 8. Column A – (x-y)  Column B – 0 1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if it is impossible to determine which quantity is greater
##### 9. Column A – 500% of 6  Column B – 600% of 5
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. 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
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if it is impossible to determine which quantity is greater
##### 11. 5 is 2/3% of n  Column A – n  Column B – 15
1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if it is impossible to determine which quantity is greater

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) = 0.075h. 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 0.96n, which is greater than 0.95n. Thus, the quantity for Column A is greater.

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