Multiple choice

Find the least number which when divided by 16, 24, 32 and 40 leaves the remainder 7, 15, 23 and 31 respectively.

  1. 489

  2. 231

  3. 471

  4. 480
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C Correct answer
Explanation

The divisors are 16, 24, 32, and 40. The differences between each divisor and its respective remainder are 16-7=9, 24-15=9, 32-23=9, and 40-31=9. The required number is the Least Common Multiple (LCM) of (16, 24, 32, 40) minus the common difference 9. The LCM is 480, and 480 - 9 = 471.

AI explanation

Notice that the difference between each divisor and its corresponding remainder is 9. Therefore, if we add 9 to the unknown number, the result will be exactly divisible by 16, 24, 32, and 40. Find the least common multiple of these divisors, which is 480. Subtracting 9 from 480 gives the required number, which is 471.

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