If p is a positive integer, is p prime?
1. The highest common factor of P and 110 is 11.
2. The least common multiple of P and 110 is 110

IMO C

St. 1 not sufficient - HCF is 11 which means that there has to be a 11 in P so P could be 11 and the answer would be yes. But if P is 143 ( 11*13) the HCF is still 11 but here P is not a prime no.

St. 2 Not sufficient. LCM is 110. And the other number is 110 therefore we can conclude that either P is 110 or less than 110. Now LCM = 110= ( 11*5*2) . another number 110= 11*5*2. Now P could be either 11 or 2 or 5 or 55 or 22 or 110. As for LCM we only choose the highest power of prime no.s P cannot have more than 1 ( 11 5 2). There P could be just 11 or 5 or 2 ( prime no.s) or it could be 22 55 10 110 ( non primes)

St. 1 and St. 2 -- HCF * LCM= P* 110 ( standard formula)
Therefore- 11*110= P* 110
Therefore P is 11 ( prime no.) . C is the right answer

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The question says least common multiple!

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