Multiple choice

The smallest number which when divided by 20, 25, 35 and 40 and leaves remainders as of 14, 19, 29 and 34 respectively is

  1. 1,394

  2. 1,404

  3. 1,664

  4. 1,406
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A Correct answer
Explanation

The divisors are 20, 25, 35, 40 and remainders are 14, 19, 29, 34. Note that the difference between divisor and remainder is constant: 20-14=6, 25-19=6, 35-29=6, 40-34=6. The number is LCM(20, 25, 35, 40) - 6. LCM(20, 25, 35, 40) = 1400. 1400 - 6 = 1394.

AI explanation

In each case, the difference between the divisor and the remainder is 6 (20 minus 14, 25 minus 19, 35 minus 29, and 40 minus 34). We find the least common multiple of 20, 25, 35 and 40, which is 1400. Subtracting the common difference of 6 from 1400 gives the required number, 1394.

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