Is the positive integer x prime?

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.