Multiple choice

Number of two digit whole number which when divided by $2, 8, 9$ leave the remainder $1, 7, 8$ respectively is

  1. $0$
  2. $1$
  3. $2$
  4. More than $2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number x satisfies x = 2k-1, x = 8m-1, and x = 9n-1. Thus, x+1 must be a multiple of LCM(2, 8, 9) = 72. The only two-digit number satisfying x+1=72 is 71.

AI explanation

Observe the given conditions to see that the remainder is always one less than the divisor. This means if you add 1 to the unknown number, it will be perfectly divisible by 2, 8, and 9. The least common multiple of 2, 8, and 9 is 72, meaning the number must be one less than a multiple of 72, such as 71 or 143. Among the two-digit whole numbers, only 71 satisfies this rule.

Keep practicing — related questions