How many numbers between 11 and 90 are divisible by 7?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11
The numbers divisible by 7 form an arithmetic progression with common difference 7, so their count is (last − first) ÷ 7 + 1.
First multiple of 7 after 11: 14
Last multiple of 7 before 90: 84
Count \(=\displaystyle\frac{84-14}{7}+1=10+1=11\)
Shortcut:
Multiples of 7 up to 90: \(90\div7\) gives 12 (whole part)
Multiples of 7 up to 11: \(11\div7\) gives 1
Between 11 and 90: \(12-1=11\)