Multiple choice

Find the least number which when divided by $15$, leaves a remainder of $5$, when divided by $25$, leaves a remainder of $15$ and when divided by $35$ leaves a remainder of $25$.

  1. $515$
  2. $525$
  3. $1040$
  4. $1050$
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A Correct answer
Explanation

The difference between divisor and remainder is constant: 15-5=10, 25-15=10, 35-25=10. The number is LCM(15, 25, 35) - 10. LCM(15, 25, 35) = 525. 525 - 10 = 515.

AI explanation

Notice the common difference between the divisors and remainders: (15 minus 5) is 10, (25 minus 15) is 10, and (35 minus 25) is 10. This means the required number is 10 less than a multiple of the least common multiple of 15, 25 and 35. The LCM is 525, so subtracting 10 gives 515.

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