Re: A natural number N is a multiple of 5. If N is divided by 6, the quoti
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07 Aug 2023, 22:31
OE
Given that the natural number ๐ is a multiple of 5, thus ๐ = 5๐ผ1
Also, when ๐ is divided by 6, the quotient is same as the remainder,
Thus ๐ = 6๐ผ2 + ๐ผ2 = 7๐ผ2
Since, ๐ is divisible 5 and 7, thus it must be divisible by ๐ฟ๐ถ๐ ๐๐ (5,7) = 35
Thus, ๐ is a multiple of 35
As ๐ is a natural number less than 100, therefore the possible values ๐ will have will
be 35 and 70
But 70 will not be the value of ๐ as when we divide 70 by 6 we get quotient as 11
and remainder as 4
As, 70 = 6 ร 11 + 4
Thus for 70, we do not get the remainder same as the quotient when divided by 6.
Ans. (A)