Multiple choice

A natural number N, when divided by 5, 6 or 8, leaves a remainder of 2 in each case. Find the number of 3-digit values that N can take.

  1. 8

  2. 12

  3. 15

  4. 4
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A Correct answer
Explanation

N = LCM(5, 6, 8) * k + 2 = 120k + 2. For 3-digit values, 100 <= 120k + 2 <= 999. 98 <= 120k <= 997. k can be 1, 2, 3, 4, 5, 6, 7, 8. Total 8 values.

AI explanation

Find the least common multiple (LCM) of 5, 6 and 8 to determine the base number, which is 120. Since the number N leaves a remainder of 2, it must be in the form 120k plus 2. The three-digit values are found by substituting k from 1 to 8 (122, 242, 362, 482, 602, 722, 842, 962); therefore, there are exactly 8 such values.

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