OE


Given that the natural number 𝑁 is a multiple of 5, thus 𝑁 = 5𝐼1
Also, when 𝑁 is divided by 6, the quotient is same as the remainder,
Thus 𝑁 = 6𝐼2 + 𝐼2 = 7𝐼2
Since, 𝑁 is divisible 5 and 7, thus it must be divisible by 𝐿𝐶𝑀 𝑜𝑓 (5,7) = 35
Thus, 𝑁 is a multiple of 35
As 𝑁 is a natural number less than 100, therefore the possible values 𝑁 will have will
be 35 and 70
But 70 will not be the value of 𝑁 as when we divide 70 by 6 we get quotient as 11
and remainder as 4
As, 70 = 6 × 11 + 4
Thus for 70, we do not get the remainder same as the quotient when divided by 6.
Ans. (A)