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quantumliner
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x is a prime number and y is a positive integer. If x and y have only 07 Jun 2017, 22:14
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x is a prime number and y is a positive integer. If x and y have only two common factors, what is the numerical value obtained when the least common multiple of x and y is divided by the greatest common divisor of x and y?

(1) y is divisible by 4 positive integers and has 2 prime factors, one of which is 5.
(2) y is equal to 3 times the highest number that divides both x and y.



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x is a prime number and y is a positive integer. If x and y have only 08 Jun 2017, 00:39
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quantumliner
x is a prime number and y is a positive integer. If x and y have only two common factors, what is the numerical value obtained when the least common multiple of x and y is divided by the greatest common divisor of x and y?

(1) y is divisible by 4 positive integers and has 2 prime factors, one of which is 5.
(2) y is equal to 3 times the highest number that divides both x and y.
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Hi

That’s a mouthful so let’s walk through step by step.

“x is a prime number and y is a positive integer. If x and y have only two common factors” – that just means that GCD of x and y is x (two common factors are 1 and prime x).

“numerical value obtained when the least common multiple of x and y is divided by the greatest common divisor of x and y”. LCM of x and y is y, so our problem boils down to finding out the value of \(\frac{y}{x}\).

(1) y is divisible by 4 positive integers and has 2 prime factors, one of which is 5.

\(y = p^1*q^1\), where p and q are primes, one of which is equal to x. But we don’t know the value of x.

If x=5 then we have \(\frac{y}{x} = \frac{5*q}{5} = q\) (unknown second prime).

If x=q then \(\frac{y}{x} = \frac{5*q}{q} = 5\)

We can’t get exact value. Insufficient.

(2) y is equal to 3 times the highest number that divides both x and y.

That give us directly that \(y=3*x\). Hence \(\frac{y}{x} = \frac{3*x}{x} = 3\). Sufficient.

B



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Hi there,
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Thank you for understanding, and happy exploring!
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