Is x divisible by 30?
(1) x = k*(m^3 - m), where m and k are both integers > 9
(2) x = n^5 - n, where n is an integer > 9
What's the best way to determine whether statement 1 is sufficient?
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Is x divisible by 30?
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The best way to start out is by asking ourselves: What do I need? For x to be divisible by 30, it must be divisible by 2, 3, and 5.
Statement 1 offers us: x = k*(m^3 - m), where m and k are both integers > 9
Since k could be a prime number, such as 13, or a slam dunk number, such as 30, k is only relevant if m does not provide a the necessary factors. The question becomes whether m definitely gives us the factors of 2, 3, and 5. If m is a prime number, such as 13, then you will get 13(168). Since neither 168 nor 13 contains a factor of 5, x would not be divisible by 30. So it is possible to set k=13 and m=13 and get an answer of no whereas all one need do is set k=30 to get an answer of yes.
So statement 1 is not sufficient.
Statement 1 offers us: x = k*(m^3 - m), where m and k are both integers > 9
Since k could be a prime number, such as 13, or a slam dunk number, such as 30, k is only relevant if m does not provide a the necessary factors. The question becomes whether m definitely gives us the factors of 2, 3, and 5. If m is a prime number, such as 13, then you will get 13(168). Since neither 168 nor 13 contains a factor of 5, x would not be divisible by 30. So it is possible to set k=13 and m=13 and get an answer of no whereas all one need do is set k=30 to get an answer of yes.
So statement 1 is not sufficient.
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
