I need help about this question in GMAT number properties

[ahm]

Hi,
I got Manhattan GMAT prep 2007 edition Number properties.

I feel that there is an error in question number 5, page 17.
The answer is " Cannot be determined" while I think that it should be "yes"
Can you help me more in this.

The question is ----
if "j" is divisible by 12 and 10, is "j" divisible by 24?

I answered it in this way:
j prime box contains 12, and 10
12(2,2,3) and 10(2,5)
so prime factors for j (2,2,3,2,5)
so we can multiply any of these factors and any integer result from this will also be a factor of "j" so
2*2*2*3=24

in answer they tell that we have only two 2's and I see that we have 3.
can you help me in this?!!

AHM

[Stacey Koprince]

Please make sure to read (and follow!) the forum guidelines. Problems should be posted in the relevant problem folder (Math, Verbal) on the site. This folder isn't for test questions / problems. I'll answer this question but please make sure to follow the guidelines for the future. Thanks!

The strategy guide is correct. When combining the prime boxes, we are allowed to take only the MINIMUM information that MUST be true. The two prime boxes have information that potentially overlaps, so we have to strip out that overlap before we combine them.

To see the overlap, imagine this scenario. You, Meryl Streep, and I are sitting in a room. I go into the next room (you can't see into this room) and I come back and tell you there's an orange sitting on the table in the next room. Then, Meryl Streep goes into the next room, comes back, and tells you there are two oranges sitting on the table in the next room.

What's the minimum number of oranges that MUST be on that table? Three? There might be three, but there don't have to be three. There might only be two - because the orange I told you about might be the same as one of the oranges that Meryl told you about. You know there are at least two, because Meryl reported two. But you don't know whether there's a third.

Same thing with the prime boxes. You've got 2,2,3 in one and 2,5 in the other. What if that 2 in the second box is the SAME 2 as one of the 2's in the first box? It's possible. So we don't know that we have three 2's. We only know for sure that we have at least two 2's. We might have three 2's, but we don't know.

Make sense?