N is the largest two digit number, 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?
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Answered by
6
Remainder = 4 , N = 94 is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively
Step-by-step explanation:
N = 3A + 1
N = 4B + 2
N = 6C + 4
N < 100
3A + 1 = 6C + 4
3A = 6C + 3
A = 2C + 1
3A + 1 = 4B + 2
=> 3A = 4B + 1
3A + 1 < 100
=> 3A < 99
=> A < 33
A = 32 no integral value of B
A = 31 => 93 = 4B +1 => B = 23
B = 23 A = 31
3A + 1 = 94
N = 94
94 = 18 * 5 + 4
Remainder = 4
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Answered by
7
Step-by-step explanation:
Trial and error soon determines that the smallest such number is 10.
The LCM of 3, 4 and 6 is 12.
So, find the largest multiple of 12 that is still under 100 when you add 10 to it.
84 + 10 = 94
94 mod 5 = 4
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