In a certain rural town, 250 households contain...

[BTGmoderatorLU]

In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

(1) 150 of the 250 households do not contain a cat.
(2) The total number of households that contain a cat is 100.

The OA is D.

Can any expert assist me with this DS question, please? I don't understand it. Thanks.

[DavidG@VeritasPrep]

In a certain rural town, 250 households contain a dog or a cat or both. How many of these households contain both a dog and a cat if 75 of 250 households do not contain a dog?

(1) 150 of the 250 households do not contain a cat.
(2) The total number of households that contain a cat is 100.

The OA is D.

Can any expert assist me with this DS question, please? I don't understand it. Thanks.

Matrix! Notice that within this population of 250, everyone has a pet - either they've got a dog or a cat or both. So the No Cat/No Dog cell will be '0.' We're also told that 75 homes don't have a dog, so we know that all 75 of those homes must have a cat. Our initial matrix:


Statement 1: If 150 of the households don't own a cat, we know that those 150 households all own a dog, as we've already established that within this population we don't have any petless homes. Now our Matrix looks like this:


We know that there are 25 homes that have both pets, so sufficient.


Statement 2: If 100 homes have a cat and 75 of those homes don't have a dog, well, again, we'd have to have 25 homes with both pets. Sufficient.



Either statement alone is sufficient. The answer is D

[Brent@GMATPrepNow]

I thought I'd point out that David's Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of households, and the two characteristics are:
- has dog or does NOT have dog
- has cat or does NOT have cat

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent