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What number divided by 5 has a remainder of 1 divided by 6 has a remainder of 4 divided by 7 has a remainder of 6?
Wiki User
∙ 11y ago
Well, we know that it's one more than a multiple of 5 and one less that a multiple of 7. Also, it's even, because it has an even remainder when divided by an even number. So far, we know:
It ends in 1 or 6 (remainder 1 when divided by 5)
It's one less than a multiple of 7, which must therefore end in a 2 or a 7
It ends with an even number, because it's even
Therefore it ends with a 6
Great so far.
Since it's one less than a multiple of 7, it has to also be one less than a multiple of 11, or 21, or 31 etc. because only numbers ending in a 1 will give 7 as a last digit when multiplied by 7.
Now that we know it's either 7*11 - 1, or 7*21 - 1, or 7*31 - 1..., we start testing.
7*11 - 1 = 76
76/7 = 11r6
76/6 = 12r4
76/5 = 15r1
All the criteria are met on the first try, therefore the number is 76.
That was fun.
Wiki User
∙ 11y ago
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