jjjinapinch wrote:Of a group of 50 households, how many have at least one cat or at least one dog, but not both?
(1) The number of households that have at least one cat and at least one dog is 4.
(2) The number of households that have no cats and no dogs is 14.

Official Guide question
Answer: C

We have a group of 50 households and need to determine how many of those households have at least one cat or at least one dog, but not both.

We can use the following formula:

total = # with at least one dog + # with at least one cat - # with both + # with neither

50 = # with at least one dog + # with at least one cat - # with both + # with neither

So, we need to determine # with at least one dog ONLY + # with at least one cat ONLY

or

(# with at least one dog - # with both) + (# with at least one cat - # with both)

Statement One Alone:

The number of households that have at least one cat and at least one dog is 4.

So, we have:

50 = # with at least one dog + # with at least one cat - 4 + # with neither

54 = # with at least one dog + # with at least one cat + # with neither

We can not determine (# with at least one dog - # with both) + (# with at least one cat - # with both). Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The number of households that have no cats and no dogs is 14.

So, we have:

50 = # with at least one dog + # with at least one cat - # with both + 14

36 = # with at least one dog + # with at least one cat

We cannot determine (# with at least one dog - # with both) + (# with at least one cat - # with both)

Statements One and Two Together:

Using statements one and two, we have:

50 = # with at least one dog + # with at least one cat - 4 + 14

50 = # with at least one dog + # with at least one cat + 10

40 = # with at least one dog + # with at least one cat

Thus, (# with at least one dog - # with both) + (# with at least one cat - # with both) = # with at least one dog + # with at least one cat - (2)(# with both) = 40 - 2(4) = 32.

Answer: C

[email protected] wrote:Hi jjjinapinch,

We're told that there are 50 households. We're asked how many have at least one cat OR at least one dog, but NOT both. This question is a standard example of an Overlapping Sets question - and it can be solved in a couple of different ways, including the Overlapping Sets Formula and the Tic-Tac-Toe/Matrix grid. Here's how you can use the Formula to get to the correct answer:

Total = (Group 1) + (Group 2) - (Both) + (Neither)

The question asks us for the value of (Group 1) + (Group 2)....

1) The number of households that have at least one cat AND at least one dog is 4.

With this Fact, the above formula now becomes:

50 = (Group 1) + (Group 2) - (4) + (Neither)
54 = (Group 1) + (Group 2) + (Neither)

Since we don't know the value of the "Neither" group, the answer to the question will vary.
Fact 1 is INSUFFICIENT

2) The number of households that have NO cats and NO dogs is 14.

The information in Fact 2 allows us to do the same general work that we did in Fact 1, but here we end up with...

50 = (Group 1) + (Group 2) - (Both) + (14)
36 = (Group 1) + (Group 2) - (Both)

Since we don't know the value of the "Both" group, the answer to the question will vary.
Fact 2 is INSUFFICIENT

Combined, the end calculation would be...
50 = (Group 1) + (Group 2) - (4) + (14)
40 = (Group 1) + (Group 2)

We now know the answer to the question (it's 40)
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

BUT ACCORDING TO OG 2019, ANSWER IS 32. I CAN'T UNDERSTAND WHY? EVERYONE IS ADDING BOTH. BUT WHY ? $$$$ $$$$