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Using Double Matrix method--Felixity, a musician, never sing

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Using Double Matrix method--Felixity, a musician, never sing

by Mo2men » Mon Mar 05, 2018 2:14 pm
Felixity, a musician, never sings sad rock songs. Of the songs on Felixity's new album, 20 songs are not sad, and 25 songs are not rock songs. How many of the songs in Felixity's new album are neither sad nor rock songs?

(1) Of the songs on Felixity's new album, the number of rock songs that are not sad is 5 less than the number of sad songs that are not rock songs.

(2) There are 30 songs on Felixity's new album.

OA: B
Source: Economist

I used the double matrix method, but why is statement 1 insufficient? I do not understand.
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Source: — Data Sufficiency |
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felixity

by GMATGuruNY » Mon Mar 05, 2018 2:55 pm
Mo2men wrote:Felixity, a musician, never sings sad rock songs. Of the songs on Felixity's new album, 20 songs are not sad, and 25 songs are not rock songs. How many of the songs in Felixity's new album are neither sad nor rock songs?

(1) Of the songs on Felixity's new album, the number of rock songs that are not sad is 5 less than the number of sad songs that are not rock songs.

(2) There are 30 songs on Felixity's new album.
Use a DOUBLE-MATRIX to organize the data.
Every song is either ROCK or NOT ROCK.
Every song is either SAD or NOT SAD.
According to the prompt:
Total not sad = 20.
Total not rock = 25.
Since Felixity never sings sad rock songs, both sad and rock = 0.
The following matrix is yielded:
Image

The question asks for the value of the CENTER BOX (neither rock nor sad).

Statement 1: Of the songs on Felixity's new album, the number of rock songs that are not sad is 5 less than the number of sad songs that are not rock songs.

Case 1: Rock but not sad = 5, sad but not rock = 10
The following matrix is yielded:
Image

Case 2: Rock but not sad = 10. sad but not rock = 15
The following matrix is yielded:
Image

Since the center box can be different values, INSUFFICIENT.

Statement 2: There are 30 songs on Felixity's new album.
The following matrix is yielded:
Image
Thus, the center box = 15.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Mon Mar 05, 2018 3:14 pm
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 songs, and the two characteristics are:
- sad or not sad
- rock or not rock

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 Mo2men » Tue Mar 06, 2018 12:50 am
GMATGuruNY wrote: Use a DOUBLE-MATRIX to organize the data.
Every song is either ROCK or NOT ROCK.
Every song is either SAD or NOT SAD.
According to the prompt:
Total not sad = 20.
Total not rock = 25.
Since Felixity never sings sad rock songs, both sad and rock = 0.
The following matrix is yielded:
Image

The question asks for the value of the CENTER BOX (neither rock nor sad).

Statement 1: Of the songs on Felixity's new album, the number of rock songs that are not sad is 5 less than the number of sad songs that are not rock songs.

Case 1: Rock but not sad = 5, sad but not rock = 10
The following matrix is yielded:
Image

Case 2: Rock but not sad = 10. sad but not rock = 15
The following matrix is yielded:
Image

Since the center box can be different values, INSUFFICIENT.
Thanks Mitch and Brent for your support.

Dear Mitch,

I have question regarding Statement 1. While you proved by plugging numbers that St 1 is insufficient, why did the algebraic solution provide otherwise as follows:
Let Rock but not sad = x
Let sad but not rock = x+5

I construct the double matrix

Image

From the row the required box is intersection between a row and column so i can establish an equation :
20 - x = 25 - x -5........X =0 .....the required box = 20

In some question, the required box could be obtained by this method.

Where did I go wrong? What did I miss here???

Thanks
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by GMATGuruNY » Tue Mar 06, 2018 2:51 am
Mo2men wrote:Dear Mitch,

I have question regarding Statement 1. While you proved by plugging numbers that St 1 is insufficient, why did the algebraic solution provide otherwise as follows:
Let Rock but not sad = x
Let sad but not rock = x+5

I construct the double matrix

Image

From the row the required box is intersection between a row and column so i can establish an equation :
20 - x = 25 - x -5........X =0 .....the required box = 20

In some question, the required box could be obtained by this method.

Where did I go wrong? What did I miss here???

Thanks
The conclusion in red is not justified.
If we solve the equation for the center box, we get:
20 - x = 25 - (x+5)
20 - x = 25 - x - 5
20 - x = 20 - x
0 = 0.

The resulting equation in blue tells us nothing about the value of x.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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by Mo2men » Tue Mar 06, 2018 2:54 am
GMATGuruNY wrote:
Mo2men wrote:Dear Mitch,

I have question regarding Statement 1. While you proved by plugging numbers that St 1 is insufficient, why did the algebraic solution provide otherwise as follows:
Let Rock but not sad = x
Let sad but not rock = x+5

I construct the double matrix

Image

From the row the required box is intersection between a row and column so i can establish an equation :
20 - x = 25 - x -5........X =0 .....the required box = 20

In some question, the required box could be obtained by this method.

Where did I go wrong? What did I miss here???

Thanks
The conclusion in red is not justified.
If we solve the equation for the center box, we get:
20 - x = 25 - (x+5)
20 - x = 25 - x - 5
20 - x = 20 - x
0 = 0.

The resulting equation in blue tells us nothing about the value of x.
Thanks Mitch.

It seems I was solving the question while sleeping <i class="em em-anguished"></i><i class="em em-grimacing"></i>
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