This question is from Manhattan 5LB Book of GRE Practice Problem in Chapter 13:

- If x is divisible by 18 and y is divisible by 12, which of the following statements must be

true?

Indicate all such statements.

x + y is divisible by 6

xy is divisible by 48

x/y is divisible by 6

How is I the only one that is true?

got both I, II as true statements. However, the book said only I is correct

a multiple of 18 is 36 and a multiple of 12 is 24. When I plug it into statement II I get 864. I then divide by 48 giving me 18 which is an integer that means statement II is also correct. Why is that considered wrong?

I would consider 18 and 12 itself as x and y. If you do that, it is clearly not divisible by 48.

When considering multiples, you considered 18x2, that 2 is making it divisible by 48. Whenever you’re trying to consider multiples of a number, try to consider numbers like 18x13 or 18x7, basically multiply with primes which do not affect your answer.

Ahhh okay, thank you for the advice! However, I did multiply by prime numbers to both 18 and 12. I did 18x2=36 and 12x3=36. In statement II the 36x36=1296. I then divide 1296/4= 27 making statement II correct. I am still confused as to why it wouldn’t be correct since I am multiplying 18 and 12 by the prime numbers 2 and 3.

Sorry, I meant primes in the sense that the numbers which might not alter your answer. Like 2 and 3 will clearly do. Because 48 is a multiple of both 2 and 3. Whereas a number like 7,13, or 17 will be a safe bet. As you can see 18x12 is clearly not divisible by 48. So (18x7)x(12x13) will also not be divisible. But (18x2)x(12x3) will be because of that **2**. So be careful

Oh okay I see, I understand what you mean. Thank you for your help!