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Joined: 18 Feb 2019
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GMAT 1: 460 Q42 V13
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x is a prime number and y is a positive integer. If x and y have only
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06 Jun 2019, 09:28
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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.
(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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Joined: 24 Jun 2008
Posts: 4128
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Q51 V47
Re: x is a prime number and y is a positive integer. If x and y have only
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06 Jun 2019, 10:24
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x is prime, so x only has two factors, 1 and x. So if x and y share only two factors, 1 and x must be those two factors, and y is divisible by x.
So the GCD of x and y is just x, and since y is a multiple of both y and x, the LCM of x and y is just y (or you could use the the relationship xy = LCM(x,y) * GCD(x, y) to reach that conclusion).
So the question is just "what is y/x?" Statement 1 is not sufficient, since it only tells us that y = 5p, where p is some prime different from 5. If x = 5, then y/x = p, and can thus equal any prime at all besides 5, and if x = p, then y/x = 5. So any prime value is possible for x/y.
Statement 2 tells us that y is 3 times the GCD of x and y, so it is equal to 3x. So y/x = 3x/x = 3, and Statement 2 is sufficient.
So the GCD of x and y is just x, and since y is a multiple of both y and x, the LCM of x and y is just y (or you could use the the relationship xy = LCM(x,y) * GCD(x, y) to reach that conclusion).
So the question is just "what is y/x?" Statement 1 is not sufficient, since it only tells us that y = 5p, where p is some prime different from 5. If x = 5, then y/x = p, and can thus equal any prime at all besides 5, and if x = p, then y/x = 5. So any prime value is possible for x/y.
Statement 2 tells us that y is 3 times the GCD of x and y, so it is equal to 3x. So y/x = 3x/x = 3, and Statement 2 is sufficient.
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Re: x is a prime number and y is a positive integer. If x and y have only
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18 Oct 2022, 23:09
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