Data Sufficiency

DanaJ wrote:Source: Veritas Prep

Of the 60 families in a certain neighborhood, 38 have a cat. How many of the families in this neighborhood have a dog?

(1) 28 of the families in this neighborhood have a cat but not a dog
(2) The number of families in the neighborhood who have a dog and a cat is the same as the number of families who have neither a cat nor a dog.

Experts: only Veritas Prep experts, please!

Ganesh hatwar wrote:

DanaJ wrote:Source: Veritas Prep

Of the 60 families in a certain neighborhood, 38 have a cat. How many of the families in this neighborhood have a dog?

(1) 28 of the families in this neighborhood have a cat but not a dog
(2) The number of families in the neighborhood who have a dog and a cat is the same as the number of families who have neither a cat nor a dog.

Experts: only Veritas Prep experts, please!

T-n = A+B - both

68- n= 38+B- both

From 2 we know n = both so

68 = 38 + B

so B = 30

Ans B

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!

Veera123 wrote:Thanks all for the good explanations.
What difficulty level would you rate this question?