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Question 70
Let x be the least number which when divided by 10, 12, 14 and 16 leaves the remainders 2, 4, 6 and 8, respectively, but x is divisible by 17. When x is divided by 52, the quotient is:
Solution
The given number leaves the same negative remainder when divided by 2,4,6 and 8 i.e 2-10,4-12,6-14,8-16=-8
So the given number will be in the form of LCM(10,12,14,16)k-8
=1680k-8
for k=1,2 the number obtained is not divisible by 17
for k=3 we have 1680*3-8
=5040-8
=5032
Required number is 5032/52=96.76Â
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