Discussion
What is the least number that must be added to 1,056 to make it exactly divisible by 23?
Answer: B
Correct answer: 2
Divide 1,056 by 23: \( 23 \times 45 = 1035 \), leaving a remainder of \( 1056 - 1035 = 21 \). To reach the next multiple of 23, add the difference between the divisor and the remainder: \[ 23 - 21 = 2. \] Checking, \( 1056 + 2 = 1058 = 23 \times 46 \). The distractor 21 is the remainder itself, and it is the answer to the opposite question - the least number to be subtracted to make the figure divisible. Reading which is asked is where marks are usually lost. The two rules are worth stating together. To make a number divisible by \( d \), subtract the remainder \( r \), or add \( d - r \). If the remainder is zero the number is already divisible and nothing need be added. The same reasoning extends to finding the nearest multiple in either direction.
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