Hi,
Again this question, if we know the below simple properties then it’s just a 20-sec problem.
Product of two numbers = Products of their HCF and LCM
• If two numbers are m and n, then HCF of m and n cannot be larger than the difference between m and n
• Two consecutive numbers (x and x+1) can share no factors other than 1, HCF will be 1 and LCM will be x(x + 1).
Two numbers are called co-prime(relatively prime) if HCF of two numbers is 1 and LCM is product of two numbers.
For two numbers to be co-prime not necessary that numbers has to be prime.
If you don’t know the below above rule, then don’t hesitate plug in numbers.
Question is “x” prime ?
That’s is, whether x = 2,3,5,7,11, ….
Statement I is insufficient:
The Greatest Common Factor of x and y is 1.
If x = 2 and y =3 , then G.C.F is 1 and answer to the question is YES(x is prime).
But if x = 4 and y = 3, then G.C.F is 1 and answer to the question is NO(x is not prime).
Statement II is insufficient:The Least Common Multiple of x and y is xy.
We can take the same examples,
If x = 2 and y =3 , then L.C.M is 6 and answer to the question is YES(x is prime).
But if x = 4 and y = 3, then L.C.M is 12 and answer to the question is NO(x is not prime).
Together also we can use the same numbers,
So not sufficient.
Answer is E.
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