Multiple choice

Which of the following is the smallest number, which when divided by 20, 25, 35 and 40, leaves the remainders as 12, 17, 27 and 32 respectively?

  1. 1200

  2. 1400

  3. 1408

  4. 1392
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Divisors: 20, 25, 35, 40. Remainders: 12, 17, 27, 32. Differences: 20-12=8, 25-17=8, 35-27=8, 40-32=8. The number is LCM(20, 25, 35, 40) - 8. LCM(20, 25, 35, 40) = 1400. 1400 - 8 = 1392.

AI explanation

We observe a constant difference between each divisor and its corresponding remainder, specifically 20 minus 12 equals 8, 25 minus 17 equals 8, and so on. We find the least common multiple of 20, 25, 35, and 40, which is 1400. Subtracting the constant difference of 8 from this multiple gives 1392.

Keep practicing — related questions