Data Sufficiency

Geva@MasterGMAT wrote:

rishab1988 wrote:@Night Reader

Hope this clarifies that where you were wrong!

if you believe that Rahul too is incorrect,then you are at the wrong place.BTG is not for you..

1) Experts can be wrong too, though this is rare. (probably rarer with Rahul ).

However, I have to agree with Rahul and go for B here.
I solved it using a 3*3 table, and that is the way I recommend. When I tried in hindsight to see logically why (2) was sufficient, I tried plugging in a few numbers:

Cats = 38, so no-cat is 22.
Let's say that we have 10 with neither Cat-nor dog. This means two things:
a. stat. (2): The dog+cat is also 10 (this is taken form the 38 cats)
b. The Only-dog is the remaining 12 from the 22 no-cat families.
The total dogs will be 10+12=22.

The surprising part is that if we plug in a different number for neither cat-nor dog (say 20) we still come up with the same total dogs=22.

What happens (and this is probably what Rahul had in mind) is that
total dogs = only dog + dog-cat.
The dog-cat is taken form the 38 cats, while the only dog is taken from the 22 remaining.
If we increase the number of neither dog-nor cat (also from the 22), we "take" dogs away from the only dog component, so this component becomes smaller. BUT we simultaneously increase the "dog-cat" component by the same number, since stat. (2) tells you that the dog-cat = neither dog-nor cat. So if we increase neither/nor by 10, we decrease only dog by 10, but we increase dog-cat by the same, so the total dogs remains a constant number.

gmatmachoman wrote:@David,

I have used Matrix/Box method for this Overlapping sets questions....

I found it easier....Is there any other method easier than the other ones used here??

David@VeritasPrep wrote:OA is B.

The explanations above are correct. For those who need a little slower paced explanation as to why B works, the following gives some more detail.

Correct answer: (B)

Solution: On any Venn diagram problem it is helpful to draw out the two sets and also note the formula Total = Set 1 + Set 2 - Both + Neither. The question stem tells us that the total number of families is 60 and the total number of families with a cat is 38. The question is asking whether we can determine the total number of families who have a dog.

Statement (1) tells us that 28 families have a cat but not a dog. If there are 38 families in total that have a cat, this information tells you that 10 families (38-28) must have both a dog and a cat. It does not, however, give you any information about the number of families who have only a dog or neither a dog nor a cat. It is therefore impossible to determine how many total families have a dog. Note that because the question stem does not say that all the familes own a cat, a dog, or both, some households could own neither.

Statement (2) tells us that the number of families who have both a cat and a dog is the same as the number who have neither. This information does not appear to be sufficient at first glance but a closer look at the Venn diagram formula for two set problems shows that it is. Remember our formula from above: Total Familes = # of Families with a Cat (C) + #of Families with a Dog (D) - Families with Both (B) + Families with Neither (N). Or, with variables, T = C + D - B + N. Plug in the information from the question stem and Statement (2) to find that T = 60, C = 38, and B=N. We can then solve for D using the formula. 60 = 38 + D - B +B. D = 22. Statement (2) alone is sufficient.

So it was actually helpful that the information from the question stem gave the total families with cats and the question was asking about the total number of families with dogs. Because we are working with totals, the Both and the Neither Categories cancel out given the information in statement 2 that these two categories are equal.

Nice work guys!