Abe's quiz scores are 62, 68, 74, and 68.
Ben's quiz scores are 66 and 70.
`{:("Quantity A","Quantity B"),("The score Abe needs on","The score Ben needs on"),("his fifth quiz to raise his","his third quiz to raise his"),("average to 70","average to 70"):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we need to determine the scores Abe and Ben need on their respective quizzes to achieve an average of 70.

### Step 1: Calculate Abe's required score
Abe's current quiz scores are 62, 68, 74, and 68. We need to find out what score (let's call it \( X \)) he needs on his fifth quiz to raise his average to 70.

1. **Sum of Abe's current scores**:
\[ 62 + 68 + 74 + 68 = 272 \]
2. **Total number of quizzes**:
\[ 5 \text{ (including the fifth quiz)} \]
3. **Average formula**:
\[ \text{Average} = \frac{\text{Sum of scores}}{\text{Total number of quizzes}} = \frac{272 + X}{5} \]
4. **Set the average equal to 70**:
\[ \frac{272 + X}{5} = 70 \]
5. **Multiply both sides by 5**:
\[ 272 + X = 350 \]
6. **Solve for \( X \)**:
\[ X = 350 - 272 = 78 \]

### Step 2: Calculate Ben's required score
Ben's current quiz scores are 66 and 70. We need to find out what score (let's call it \( Y \)) he needs on his third quiz to raise his average to 70.

1. **Sum of Ben's current scores**:
\[ 66 + 70 = 136 \]
2. **Total number of quizzes**:
\[ 3 \text{ (including the third quiz)} \]
3. **Average formula**:
\[ \text{Average} = \frac{\text{Sum of scores}}{\text{Total number of quizzes}} = \frac{136 + Y}{3} \]
4. **Set the average equal to 70**:
\[ \frac{136 + Y}{3} = 70 \]
5. **Multiply both sides by 3**:
\[ 136 + Y = 210 \]
6. **Solve for \( Y \)**:
\[ Y = 210 - 136 = 74 \]

### Conclusion
- **Abe needs a score of 78 on his fifth quiz**.
- **Ben needs a score of 74 on his third quiz**.

### Comparison of Quantities
- **Quantity A (Abe's required score)**: 78
- **Quantity B (Ben's required score)**: 74

Since 78 is greater than 74, we conclude that **Quantity A is greater than Quantity B**.

### Final Answer
**Option 1: Quantity A is greater.**

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