Question

How many numbers are there between 100 and 300 which are multiples of 7?

• A. 28
• B. 29
• C. 27
• D. 10

Answer 1

Answer:

A. 28

There are 28 numbers between 100 and 300 that are multiples of 7.

• First multiple after 100: 105 (7 × 15)

• Last multiple before 300: 294 (7 × 42)

Arithmetic Progression Method

• Formula: $a_n = a_1 + (n - 1)d$

• First term ($a_1$): 105

• Last term ($a_n$): 294

• Common difference ($d$): 7

• Calculation: $294 = 105 + (n - 1) \times 7$

• Step 1: $189 = (n - 1) \times 7$

• Step 2: $27 = n - 1$

• Final Count ($n$): 28