Multiple choice

The number lying between 900 and 1000 which when divided by 38 and 57 leaves in each case the remainder 23 is

  1. $954$
  2. $945$
  3. $953$
  4. $935$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A number N that leaves remainder 23 when divided by both 38 and 57 must satisfy N - 23 being divisible by LCM(38,57). Since 38 = 2×19 and 57 = 3×19, LCM = 2×3×19 = 114. So N - 23 = 114k, meaning N = 114k + 23. For k = 8, N = 912 + 23 = 935, which lies between 900 and 1000. Checking: 935 ÷ 38 = 24 remainder 23, and 935 ÷ 57 = 16 remainder 23.

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