GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 17:04

GMAT Club Daily Prep

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

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

At the opening night performance of a new play, 5 percent of the theat

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50002
At the opening night performance of a new play, 5 percent of the theat  [#permalink]

Show Tags

25 Jul 2018, 00:23
00:00

Difficulty:

95% (hard)

Question Stats:

45% (02:05) correct 55% (01:45) wrong based on 109 sessions

HideShow timer Statistics

At the opening night performance of a new play, 5 percent of the theater patrons are late and are seated immediately, but 30 per cent of the patrons who are late are not seated until the end of the first act. Approximately what percent of the theater patrons that evening are late?

(A) 5%
(B) 7%
(C) 35%
(D) 70%
(E) 80%

_________________
Senior RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 767
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
At the opening night performance of a new play, 5 percent of the theat  [#permalink]

Show Tags

25 Jul 2018, 01:41
1
1
Lets 100 be the total number of patrons and X be the number of patrons that are late

30 percent of the patrons who are late are not seated immediately

=> 70 percent of the patrons who are late are seated immediately

=> 70 percent of the patrons who are late are seated immediately = 5 percent of the theater patrons are late and are seated immediately

=> $$\frac{70}{100} * X$$ = 5% of total patrons = $$\frac{5}{100} * 100$$ = 5

=> X = 7

percent of the theater patrons that evening are late = $$\frac{7}{100} * 100$$ = 7%

Hence option B
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Intern
Joined: 23 Aug 2017
Posts: 26
Re: At the opening night performance of a new play, 5 percent of the theat  [#permalink]

Show Tags

01 Aug 2018, 07:35
T = Theater patrons
L = Patrons who are late

If 30% of the patrons are late and did not seat immediately, then 70% of the patrons who are late DID seat immediately. So, The percentage of patrons who are late and seated immediately is 5%*T or 70%*L

then,

5/100T = 70/100L
L/T = 5/70 ≃ 0.071 ≃ 7%

Option B.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)
Re: At the opening night performance of a new play, 5 percent of the theat  [#permalink]

Show Tags

10 Aug 2018, 18:38
Bunuel wrote:
At the opening night performance of a new play, 5 percent of the theater patrons are late and are seated immediately, but 30 per cent of the patrons who are late are not seated until the end of the first act. Approximately what percent of the theater patrons that evening are late?

(A) 5%
(B) 7%
(C) 35%
(D) 70%
(E) 80%

We can let the total number of patrons = X and the number of patrons who are late = L.

Since 30% of the patrons who are late are not seated immediately, 70% of the patrons who are late are seated immediately. Since these patrons are also the 5% of the patrons who are seated immediately. Thus we have:

0.7 L = 0.05 X

L = 0.05/0.7 X= 5/70 X = 1/14 X ≈ 7/100 X

We see that the number of patrons who are late is approximately 7% of the total number of patrons.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
Joined: 12 Sep 2015
Posts: 3020
Re: At the opening night performance of a new play, 5 percent of the theat  [#permalink]

Show Tags

28 Aug 2018, 16:13
Top Contributor
Bunuel wrote:
At the opening night performance of a new play, 5 percent of the theater patrons are late and are seated immediately, but 30 per cent of the patrons who are late are not seated until the end of the first act. Approximately what percent of the theater patrons that evening are late?

(A) 5%
(B) 7%
(C) 35%
(D) 70%
(E) 80%

It may be useful to use the Double Matrix Method to help us arrange our information. This 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 theater patrons, and the two characteristics are:
- late or not late
- seated immediately or not seated immediately

So, we get the following:

Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of theater patrons in this population. Let's say there are 100 theater patrons.

5 percent of the theater patrons are late and are seated immediately
The top left box is for theater patrons who are late and are seated immediately. So, 5% of the entire population will be in this box.

30 percent of the patrons who are late are not seated immediately
The patrons referred to here are those who go in the top right box. Unfortunately, we don't know the total number of patrons who are late, so we can't find 30% of that value.
So, let's let x = the total number of patrons who are late.

Now we can deal with this: 30 percent of the patrons who are late are not seated immediately
In other words, 30% of x will go in the top right box.

At this point, we know that the two top boxes must have a sum of x.
So, we can write: 5 + 0.3x = x (now solve)
Rearrange: 5 = 0.7x
Divide: 5/0.7 = x
Or 50/7 = x
Approximate: 7.something = x

Since x represents the total number of patrons who are late, we know that about 7 out of 100 patrons are late.
In other words, about 7% of the patrons are late.

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:

_________________

Brent Hanneson – GMATPrepNow.com

Sign up for our free Question of the Day emails

Re: At the opening night performance of a new play, 5 percent of the theat &nbs [#permalink] 28 Aug 2018, 16:13
Display posts from previous: Sort by

At the opening night performance of a new play, 5 percent of the theat

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.