Multiple choice

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

  1. $1394$
  2. $1404$
  3. $1664$
  4. $1406$
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A Correct answer
Explanation

Divisors are 20, 25, 35, 40. Remainders are 14, 19, 29, 34. The difference between divisor and remainder is constant: 6. N = LCM(20, 25, 35, 40) - 6. LCM = 1400. N = 1400 - 6 = 1394.

AI explanation

Notice that the difference between each divisor and its corresponding remainder is 6, since 20 minus 14 is 6, 25 minus 19 is 6, 35 minus 29 is 6, and 40 minus 34 is 6. First find the least common multiple of 20, 25, 35, and 40, which is 1400. Subtract the common difference of 6 from this least common multiple to get the required number, which is 1394.

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