Usage of Word "Exactly" In Quant Problems

Question

I'm confused about the meaning of the word "exactly" on the GMAT Quant section. I was looking today at a problem from Jeff Sackman's problem set (DS set, question 17) and choice A for a data sufficiency question had this statement:

1. y has exactly two prime factors.

I originally understood this statement as "y has two prime factors and no more". So for instance, 4 has exactly 2 prime factors: 2 and 2. However, the author of the set treats the wording as "y has two unique prime factors", in which case "4 has exactly 1 unique primer factor". I've searched on the Internet and it looks like GmatPrep uses similar wording in one problem:

Does anybody have an idea on what the official stance on this usage is? I've seen the word "exactly" in several other DS questions as well, especially the ones related to sets.

MacFauz · Answer

y has two prime factors means that y has to unique factors. It cannot be taken to mean 2 & 2. In this instance y cannot be 4. The least possible positive value for y is 6. As far as sets are concerned, we often see something like "10 people are in exactly two groups". That means that those ten people are not in more than two groups. That is people who are in all three groups are not accounted for in this 10. The significance of this can be seen from Bunuel's explanation in the below page: https://gmatclub.com/forum/formulae-for- ... 69014.html

alexcey · Answer

But then how does one refer to the number of all prime factors in a number then?

Here is what MGMAT says on page 122 of the Number Properties guide:
1. How many different prime factors? ... maybe phrased as "different" or "unique" prime factors
2. How many total prime factors (length)?
3. How many total factors?

Another question that I have is for a statement like this one "Set A has 2 numbers". Does it mean on GMAT that set A can have 3 and more numbers?

MacFauz · Answer

As seen from your post itself, that would be the prime factor length

eg: 1080 = 2 x 2 x 2 x 3 x 3 x 3 x 5

The number of different prime factors would be 3 (2,3 and 5)
The prime factor length would be 7

And IMHO set A has two numbers means only that. i.e It has only two numbers. If it had said "at least two numbers" it would mean that set A has two or more numbers.

KarishmaB · Answer

The usage can vary a little from question to question but in most cases the intended meaning is quite clear.

y has two prime factors 
=
y has exactly two prime factors
=
y has two distinct prime factors
=
y has exactly two distinct prime factors (gives the meaning clearly so is most preferred)

'Set A has two members' means 'Set A has exactly two members and no more'

There is a source of confusion in this concept. Let's discuss that with an example.
There were 100 people at a party. The food at the party consisted of three things - cake, candy and corn.

'50 people ate cake'
This means exactly 50 people ate cake. The other 50 did not eat cake. The only thing is that of these 50 people, some or all could have eaten something else too. This statement doesn't imply that these 50 did not eat anything else. You have to remember this.

'50 people ate only cake'
This is different. This means 50 ate cake and nothing else.

50 people belong to group1 means exactly 50 belong to group1 but the point is that they could belong to other groups too.

Usage of Word "Exactly" In Quant Problems

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