Multiple choice

A number when divided by $48$ leaves a remainder of $31$. Find the remainder if the same number is divided by $24$

  1. $5$
  2. $7$
  3. $9$
  4. $11$
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B Correct answer
Explanation

If a number N = 48k + 31, then N = 24(2k) + 24 + 7 = 24(2k+1) + 7. Dividing by 24 leaves a remainder of 7.

AI explanation

A number leaving a remainder of 31 when divided by 48 can be written as 48n plus 31, where n is an integer. To find the remainder when this number is divided by 24, we rewrite the expression as 24 multiplied by 2n plus 24 plus 7. This simplifies to 24 multiplied by (2n plus 1) plus 7. Since 7 is strictly less than the divisor 24, the remainder is 7.

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