Data Sufficiency

mt10087 wrote:I'm still very confused on this really straightforward concept. Even with reduced numbers it still doesn't make sense to me.

is x divisible by 24?

If x is divisible by 6....(3, 2)...It seems divisible to 24.

24/6= 4
24/3= 8
24/2= 12

If x is divisible by 4...(2,2)...It seems divisible by 24
24/4 = 8
24/2 = 12

Could anyone explain where my thought process has gone wrong?

You're answering the opposite question to what's being asked. You're (correctly) answering the question:

Is positive integer x a divisor of 24?
1. x is a divisor of 4
2. x is a divisor of 6


In this case, each Statement is sufficient - from Statement 1, x can only be 1, 2 or 4, and from Statement 2 x can only be 1, 2, 3 or 6, all of which are divisors of 24.

In the original question, the statements tell us the opposite of what the statements tell us in the question I invented above. In the original question, Statement 1 tells us that x is divisible by 4. That means that 4 is a divisor of x, not that x is a divisor of 4. That is, x is a multiple of 4: x could be 4, 8, 12, 16, 20, 24, and so on. All we know for sure is that 2^2 is a factor of x. That's not enough to tell us if x is a multiple of 24 - it might be, because x could be equal to 24, or 48, or 72, but it might not be, because x could be equal to 8, or 28, or 100, for example.

Statement 2 is not sufficient for the same reason, and even combined, the Statements are not sufficient, since x could be equal to 12 or 36, etc, in which case x is not divisible by 24, or x could be equal to 24, or 48, etc, in which case x is divisible by 24.

mt10087 wrote:
I paid $6.00 for 12 cans of soda. How much did each can cost? I always pick a number and start dividing it. If the quotient looks strange, i swap the other number.

I was wondering if anyone knew the correct way of pulling the information from a word problem to correctly set up the equation?

You'll probably find, after doing a lot of practice in this area (which you should do - it's crucially important on the GMAT) that this becomes almost instinctual. For now, I can suggest you try two things:

* If you can rephrase what you want to find as "something per something else", that tells you what to divide by what. For example, if you want to find "cost per can", you want to divide cost by cans: find cost/cans. If you want to find speed (i.e. miles per hour) you want to divide miles by hours, or distance/time. So in your cans example, you want cost per can, so you would divide $6/12 = $0.50 per can.

* If you aren't sure, change one of your numbers to '1' and ask what you would divide by what. For example, if I pay $6 for 1 can of soda, the cost of a can is clearly 6/1 = $6, and not 1/6 = $0.166... so I want to divide the money by the number of cans, not the reverse. Then just change the '1' back to the number in the question - in your example, back to 12, to get 6/12 = $0.50 per can.