I keep having a tough time figuring out the basics because

Question

I keep having a tough time figuring out the basics because I'm confusing it with factors.

Is x a multiple of 18?

1) x is a multiple of 6.

2) x is a multiple of 9.

Now, I know the answer is C and have seen the reasoning but still don't get it. Can someone please try to clear this up? Thanks!!

Damager · Answer

x is multiple of 6

x=m*6 where m is any integer 1,2,3,4 etc

x= m* 2*3 (1)

x=m*9 where m is any integer 1,2,3,4 etc

x= m*3*3 (2)

We can see from above that x is multiple of 3 its common b/w (1) and (2)

For both 1 and 2 to be true x should also be a multiple of common 3 as well as non common 2 and other 3

so x is multiple of 3*3*2

chile · Answer

X is a multiple of Y if there exists another integer Z such that X=Z*Y

That means : X / Y must be an integer

 1) x/6 is an integer A 
if A = 1 then X is 6 //// 6/18 is an integer ?: NO
if A = 2 then X is 12 //// 6/18 is an integer ?: NO
if A = 3 then X is 18 //// 18/18 is an integer ?: YES
if A = 4 then X is 24 //// 24/18 is an integer ?: NO
....
Statement 1) is no enough : eliminate choices A - D

 2) x/9 is an integer B 
if B = 1 then X is 9 //// 9/18 is an integer ?: NO
if B = 2 then X is 18 //// 18/18 is an integer ?: YES
if B = 3 then X is 27 //// 27/18 is an integer ?: NO
if B = 4 then X is 36 //// 36/18 is an integer ?: YES

Statement 2) is no enough : eliminate choices B

 1+2) x/(6*9) is an integer C 
The expression can write : x/(2*3 * 9) = x/(18*3)
So, x/(18*3) must be an integer C

if C = 1 then X is 18*3*1 //// (18*3*1)/18 is an integer? : YES
if C = 2 then X is 18*3*2 //// (18*3*2)/18 is an integer? : YES
if C = 3 then X is 18*3*3 //// (18*3*3)/18 is an integer? : YES
if C = 4 then X is 318*3*4 //// (18*3*4)/18 is an integer? : YES

The problema is resolved with the combination of both statement, so the answer is C

Matrix02 · Answer

The way I do these are to pick numbers. I have seen these type of problems before and you need to read them through carefully. Sometimes just one statment can lead you to the answer but not in this case.

1) Picking 36 = which is a multiple of both 6 and 18
 Picking 42 which is a multiple of 6 but NOT 18 
 NOT SUFFICIENT

2) Picking 36 which is a multiple of 9 & 18 but 27 is multiple of only 9 so again NOT SUFFICIENT

Together x Must be a multiple of both 9 and 6 and the LCM is 54 which IS a multiple of 18. You are good to go!

Fish n Chips · Answer

Thank you to everyone that responded! A huge eye opener!! :beer

I keep having a tough time figuring out the basics because

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