Multiple choice

What is the largest two digit number which when divided by 6 and 5 leaves remainder 1 in each case ?

  1. 61

  2. 93

  3. 91

  4. 97
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A number leaving remainder 1 when divided by both 5 and 6 must be of form 30k + 1 (LCM of 5 and 6 is 30). For two-digit numbers: k=0 gives 1 (not two-digit), k=1 gives 31, k=2 gives 61, k=3 gives 91. Checking: 91 ÷ 5 = 18 remainder 1, 91 ÷ 6 = 15 remainder 1. 91 is the largest such two-digit number.

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