Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Magoosh is excited to offer you a free GRE practice test with video answers and explanations. If you’re thinking about taking the GRE or want to see how effective your GRE test prep has been, pinpoint your strengths and weaknesses with this quiz!

This webinar will focus on evaluating reading comprehension questions on the GRE and GMAT. This 60 minute class will be a mix of "presentation" and Q&A where students can get specific questions answered.

This admissions guide will help you plan your best route to a PhD by helping you choose the best programs your goals, secure strong letters of recommendation, strengthen your candidacy, and apply successfully.

In a group of 100 homeowners [#permalink]
25 Sep 2017, 13:53

2

This post received KUDOS

00:00

Question Stats:

47% (01:59) correct
52% (00:54) wrong based on 34 sessions

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

Re: In a group of 100 homeowners [#permalink]
16 May 2018, 09:24

1

This post received KUDOS

Expert's post

pranab01 wrote:

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

Re: In a group of 100 homeowners [#permalink]
19 Oct 2019, 13:09

I was trying to solve the problem using matrix method but I got 100-x-z-y which is wrong. Can anyone show me how to solve this problem using the table matrix method? Thank you

Re: In a group of 100 homeowners [#permalink]
20 Oct 2019, 05:52

1

This post received KUDOS

Expert's post

pranab01 wrote:

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

a) 100 – x – y – z

b) 100 – x – y + z

c) x – y – z + 100

d) x + y + z + 100

e) x + y + z – 100

Let's use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..

Here, we have a population of homeowners, and the two characteristics are: - has alarm security system or does NOT have alarm security system - has deadbolt locks or does NOT have deadbolt locks

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. We can set up our matrix as follows:

z homeowners had neither an alarm security system nor deadbolt locks We get:

Since the two boxes in the BOTTOM ROW must add to 100-y, we know that the missing box must be 100-y-z, since 100-y-z + z = 100-y

Finally, the two boxes in the LEFT-SIDE column must add to x In other words, ? + (100-y-z) = x Subtract (100-y-z) from both sides to get: ? = x - (100-y-z)

Take: x - (100-y-z) Simplify to get: x - 100 + y + z Rearrange to get: x + y + z - 100

Answer: E

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

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for GRE Question of the Dayemails