Multiple choice

The largest two digit number (N), which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when (N) is divided by 5?

  1. 1

  2. 2

  3. 4

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We need the largest two-digit N where N≡1 (mod 3), N≡2 (mod 4), and N≡4 (mod 6). Checking N≡4 (mod 6) means N=6k+4. For k=15, N=94: 94÷3=31R1 ✓, 94÷4=23R2 ✓, 94÷6=15R4 ✓. For k=16, N=100 (three digits). So N=98 is the largest two-digit number satisfying all conditions. When N=98 is divided by 5: 98÷5=19R3. Wait, let me verify: 98≡1 (mod 3): 98=3×32+2, remainder is 2, not 1. Checking 94: 94=3×31+1 ✓, 94=4×23+2 ✓, 94=6×15+4 ✓. For N=98: 98=3×32+2 ✗. Let me find the correct N: N≡1 (mod 3), N≡2 (mod 4), N≡4 (mod 6). From N≡4 (mod 6): N=6k+4. This gives N≡1 (mod 3) automatically since 6k is divisible by 3 and 4≡1 (mod 3). For N≡2 (mod 4): 6k+4≡2 (mod 4) → 2k≡2 (mod 4) → k=1,3,5,... For largest two-digit: k=15 gives N=94, k=16 gives N=100 (3 digits). So N=94. 94÷5=18R4. Option C is correct.

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