LCM and prime box-Thursday with Ron June 10, 2010-

[elisabetta.portioli]

Hello,

after attending the study hall session I've become unsure about when I should use the LCM rather than the prime box -in DS on divisibility- and what is the content of a product prime box. Should I throw in the product prime box the LCM or the prime factorization of each factors contained in the product?

Also, can you elaborate my line of reasoning for the following DS and tell me whether I make any mistake or not? (taken from Ron's study hall of June 10, 2010).

What is the LCM of x and 12?
1-the LCM of x and 9 is 45.
2-the LCM of x and 4 is 20.

1-is insufficient because it doesn't say anything about 12( there isn't any overlap between 12 and 9 ). For analogy, it is the same case when we are asked in the question stem about, say, x and the statement, say, provide information about y.
2- is sufficient because 4 overlaps with 12 in 2^2, so we can deduce x=5. Hence the LCM of x and 12 is given by 5*4*3.

I appreciate your help.

[RonPurewal]

1-is insufficient because it doesn't say anything about 12 ( there isn't any overlap between 12 and 9 )

Not sure what you mean by "overlap".

12 and 9 do share a common prime factor (3). That's how I would define "overlap", so I guess I don't know what you mean.

More importantly, it's not that easy. If I took "45" out of that statement and replaced it with "135", the statement would be sufficient.

For analogy, it is the same case when we are asked in the question stem about, say, x and the statement, say, provide information about y.

I don't understand what you are saying here. Potresti scriverlo in italiano, per me fa lo stesso.

[RonPurewal]

2- is sufficient because 4 overlaps with 12 in 2^2, so we can deduce x=5.

No. In statement 2, x could be 5... but x could also be 10 or 20.

The statement is still sufficient, though, because the LCM of x and 12 is the same for all three of those values.

[elisabetta.portioli]

1-is insufficient because it doesn't say anything about 12 ( there isn't any overlap between 12 and 9 )

Not sure what you mean by "overlap".

12 and 9 do share a common prime factor (3). That's how I would define "overlap", so I guess I don't know what you mean.

More importantly, it's not that easy. If I took "45" out of that statement and replaced it with "135", the statement would be sufficient.

I express myself poorly in the above quote. I meant that there isn't any overlapping between 9 and 12 in terms of factor of 2. However, now that you brought on the table '135'(=5*3^3), I see that '2' is not the key point to prove that statement 2 is insufficient....

For analogy, it is the same case when we are asked in the question stem about, say, x and the statement, say, provide information about y.

I don't understand what you are saying here. Potresti scriverlo in italiano, per me fa lo stesso.

Statement 1 recalled me those DS statements in which the piece of info refers to something not necessary to solve the question stem. Eg: the question stem asks about the value of x, and in one of the statement is given the value of y, which is not required to solve for x.
Hence, as 9 doesn't share any 2s with 12, I thought that this piece of info was irrelevant to the question stem (somehow I saw necessary the presence of 2^2 in the number that shares the LCM with x). However, with '135' I realized that this reasoning line doesn't hold true.

[RonPurewal]

Sounds like everything is good, then. If you have further questions, please post them.

In general, you should NEVER trust your "gut instinct" on DS problems.
The official DS problems are very cleverly engineered so that the "obvious-looking" answers are just about always wrong.