Question

How many numbers are there in between 55 and 3815, which are multiples of 5 and divisible by 3?

• A. \(249 \)
• B. \(250 \)
• C. \(251 \)
• D. \(252 \)
• E. \(238 \)

Hint:

To count multiples in a range: - Convert condition to a single LCM - Use formula: last index $-$ first index $+ 1$

Answer 1

The Correct Option is B

Concept: A number that is a multiple of 5 and divisible by 3 must be divisible by: \[ \text{LCM}(5, 3) = 15 \] So, we need to count multiples of 15 in the given range.
Step 1: Find first multiple of 15 greater than 55.
\[ \frac{55}{15} \approx 3.66 \Rightarrow \text{next integer} = 4 \] \[ \text{First multiple} = 15 \times 4 = 60 \]

Step 2: Find last multiple of 15 less than 3815.
\[ \frac{3815}{15} \approx 254.33 \Rightarrow 254 \] \[ \text{Last multiple} = 15 \times 254 = 3810 \]

Step 3: Count number of terms.
\[ \text{Count} = 254 - 4 + 1 = 251 \]

Step 4: Adjust for “in between”.
Since the question asks strictly between 55 and 3815, both 60 and 3810 are included, so: \[ \text{Total numbers} = 251 \]