`(33)1/2%of (33)1/3%of 8979=?`

Options

A. 1000
B. 1100
C. 900
D. 2200

Answer

To solve the expression \( (33)^{1/2}\% \text{ of } (33)^{1/3}\% \text{ of } 8979 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For \( 33 \frac{1}{2} \):
\[ 33 \frac{1}{2} = \frac{33 \times 2 + 1}{2} = \frac{66 + 1}{2} = \frac{67}{2} \]

- For \( 33 \frac{1}{3} \):
\[ 33 \frac{1}{3} = \frac{33 \times 3 + 1}{3} = \frac{99 + 1}{3} = \frac{100}{3} \]

### Step 2: Write the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{67}{2}\% \text{ of } \frac{100}{3}\% \text{ of } 8979 \]

### Step 3: Convert Percentages to Fractions
Next, we convert the percentages to fractions:
- \( \frac{67}{2}\% = \frac{67}{2} \times \frac{1}{100} = \frac{67}{200} \)
- \( \frac{100}{3}\% = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3} \)

### Step 4: Substitute Back into the Expression
Now substitute these values back into the expression:
\[ \frac{67}{200} \text{ of } \frac{1}{3} \text{ of } 8979 \]

### Step 5: Calculate \( \frac{1}{3} \text{ of } 8979 \)
Calculate \( \frac{1}{3} \) of 8979:
\[ \frac{1}{3} \times 8979 = \frac{8979}{3} = 2993 \]

### Step 6: Calculate \( \frac{67}{200} \text{ of } 2993 \)
Now calculate \( \frac{67}{200} \) of 2993:
\[ \frac{67}{200} \times 2993 = \frac{67 \times 2993}{200} \]

### Step 7: Perform the Multiplication
Calculate \( 67 \times 2993 \):
\[ 67 \times 2993 = 200021 \]

### Step 8: Divide by 200
Now divide by 200:
\[ \frac{200021}{200} = 1000.105 \]

### Step 9: Round to the Nearest Whole Number
Since the question asks for a final answer, we can round \( 1000.105 \) to \( 1000 \).

### Final Answer
Thus, the final answer is:
\[ \boxed{1000} \]