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A housing subdivision contains only two types of homes

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by BTGmoderatorDC » Sat Dec 16, 2017 1:31 am
A housing subdivision contains only two types of homes: ranch-style homes and town homes. There are twice as many town homes as ranch-style homes. There are 3 times as many town homes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a town home with a pool?

(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2

How will i find the best solution in this? Can some experts explain?

OA E
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by GMATGuruNY » Sat Dec 16, 2017 3:40 am
lheiannie07 wrote:A housing subdivision contains only two types of homes: ranch-style homes and town homes. There are twice as many town homes as ranch-style homes. There are 3 times as many town homes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a town home with a pool?

(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2
To organize the data, use the following DOUBLE-MATRIX:
Image

There are 3 times as many town homes with pools than without pools.
Let the number of town homes without no pool = 1, implying that the number of town homes with a pool = 3.
The following matrix is yielded:
Image

There are twice as many town homes as ranch-style homes.
Since the number of town homes = 4, the number of ranch-style homes = 2.
The following matrix is yielded:
Image

What is the probability that a home selected at random from the subdivision will be a town home with a pool?
(town homes with a pool)/(total homes) = 3/6 = 1/2.

The correct answer is E.
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by Brent@GMATPrepNow » Sat Dec 16, 2017 6:09 am
I thought I'd point out that Mitch's Double Matrix technique 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 homes, and the two characteristics are:
- ranch-style or townhome
- pool or no pool

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
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATWisdom » Sat Dec 16, 2017 8:40 am
lheiannie07 wrote:A housing subdivision contains only two types of homes: ranch-style homes and town homes. There are twice as many town homes as ranch-style homes. There are 3 times as many town homes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a town home with a pool?

(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2

How will i find the best solution in this? Can some experts explain?

OA E
let us do in a simple way
let number of town type houses without pool =100
then ............................................................. with pool =300
total town type houses..............................................=400
therefore number of ranch type houses =400/2=200
total number of houses in housing subdivision =400+200=600

probability of a town type houses with pool= 300/600=1/2

Hence option E
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by Scott@TargetTestPrep » Mon Sep 23, 2019 4:33 pm
BTGmoderatorDC wrote:A housing subdivision contains only two types of homes: ranch-style homes and town homes. There are twice as many town homes as ranch-style homes. There are 3 times as many town homes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a town home with a pool?

(A) 1/6
(B) 1/5
(C) 1/4
(D) 1/3
(E) 1/2

How will i find the best solution in this? Can some experts explain?

OA E
If we let the total number of homes = 12, then 4 are ranch-style homes, and 8 are townhomes, and 6 town homes have pools, and 2 do not.

Thus, P(town home with a pool) = 6/12 = 1/2

Answer: E

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