How many 2-digit natural numbers are divisible by 4?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 22
The two-digit multiples of 4 run from 12 to 96 and go up by 4 each time, so they form an arithmetic progression; the number of terms is \(\displaystyle \frac{\text{last}-\text{first}}{\text{common difference}}+1\).
Smallest two-digit multiple of 4: 12; largest: 96
Number of terms \(\displaystyle =\frac{96-12}{4}+1=21+1=22\)
Shortcut: Count the multiples of 4 up to 99 and take away those below 10.
Up to 99: \(99\div4=24\) (whole part); up to 9: 2 (4 and 8)
\(24-2=22\)