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Last year in a group of 30 businesses, 21 reported a net

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Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 05 Mar 2012, 16:27
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Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.

(2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

can anybody tell the matrix approach for stmnt(2)
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 05 Mar 2012, 21:56
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Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

Given: {Total} = {Profit} + {Investment} - {Both} + {Neither} --> 30=21+15-{Both}+{Neither} --> {Neither} = {Both} - 6.
Question: {Neither} = ?

(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets --> {Both} = 12 --> {Neither}={Both}-6=12-6=6. Sufficient.

(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both --> {Profit} + {Investment} - {Both} = 24 --> 21+15-{Both}=24 --> {Both}=12 --> {Neither}={Both}-6=12-6=6. Sufficient.

Answer: D.

TomB wrote:
can anybody tell the matrix approach for stmnt(2)

As you can see the problem can be easily solved without a matrix, but anyway here you go, matrix for statement (2):
Image
(2) says that a+b+c=24, on the other hand a+b+c+d=30=Total --> 24+d=30 --> d=6. Sufficient.

Hope it's clear.
[Reveal] Spoiler:
Attachment:
30 businesses.PNG
30 businesses.PNG [ 4.79 KiB | Viewed 4397 times ]

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Re: last year [#permalink] New post 05 Mar 2012, 19:08
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TomB wrote:
Last year in a group of 30 businesses, 21 reported a net profit and
15 had investments in foreign markets. How many of the businesses
did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments
in foreign markets.

(2) last year 24 of the 30 businesses reported a net profit or invested in
foreign markets, or both.

can anybody tell the matrix approach for stmnt(2)


(A) is straight forward.

As for (B), we are told the answer straight away. If we have a total of 24 who reported Profit or invested in Foreign markets or both, then we will have 6 who did none of that and that is "did not report a net profit nor invest in foreign markets last year".
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 04 Jan 2013, 01:42
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Sachin9 wrote:
Bunuel wrote:
Sachin9 wrote:
Bunuel,
Didn't quite understand this : (2) says that a+b+c=24,

both means : b+c?
and neither means only d?


It's all in the matrix:
a = investment and profit;
b = investment and NO profit;
c = profit and NO investment;
d = NO investment and NO profit.

Hope it's clear.

Bunuel,

Do we have a similar question that tests concept that is tested in the 2nd option?


Unfortunately I don't remember any specific problem, though you can search here: search.php?search_id=tag&tag_id=45 (DS) and here: search.php?search_id=tag&tag_id=65

Hope it helps.
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Venn Diagram vs. Table Matrix [#permalink] New post 07 Nov 2012, 10:11
I am trying to figure when when I am supposed to use one over other. For example, I came across the following DS problem.

Last year in a group of 30 businesses, 21 reported a net profit and 15 had invested in the foreign markets. How many businesses did not report a net profit nor invest in the foreign markets last year?

1) Last year 12 of the 30 businesses reported a net profit and had investments in the foreign markets.
2) Last year 24 of the 30 businesses reported net profit or invested in foreign markets, or both.

Now, I am not asking anyone for a solution of this problem. I have it in front of me and it makes sense. The mistake I made is instead of using the Venn diagram (two circles that intersect a-x, x, y-x. that sort of thing), I used the matrix (net profit, no net profit, total, foreign investment, no foreign investment, total). Naturally, when I read the second statement I got confused because I did not know what to put into the table cell. I basically lost time doing the whole thing because I could not determine with matrix whether the statement 2 was sufficient or not.

Next time when I see a similar problem, I would like to know instantly which of the two approaches would bring me to the answer. What am I doing wrong?
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Re: Venn Diagram vs. Table Matrix [#permalink] New post 07 Nov 2012, 14:03
Expert's post
Baracuda123 wrote:
I am trying to figure when when I am supposed to use one over other. For example, I came across the following DS problem.

Last year in a group of 30 businesses, 21 reported a net profit and 15 had invested in the foreign markets. How many businesses did not report a net profit nor invest in the foreign markets last year?

1) Last year 12 of the 30 businesses reported a net profit and had investments in the foreign markets.
2) Last year 24 of the 30 businesses reported net profit or invested in foreign markets, or both.

Now, I am not asking anyone for a solution of this problem. I have it in front of me and it makes sense. The mistake I made is instead of using the Venn diagram (two circles that intersect a-x, x, y-x. that sort of thing), I used the matrix (net profit, no net profit, total, foreign investment, no foreign investment, total). Naturally, when I read the second statement I got confused because I did not know what to put into the table cell. I basically lost time doing the whole thing because I could not determine with matrix whether the statement 2 was sufficient or not.

Next time when I see a similar problem, I would like to know instantly which of the two approaches would bring me to the answer. What am I doing wrong?


Merging similar topics. Please refer to the solutions above and ask if anything remains unclear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 15 Nov 2012, 14:39
Thanks Bunuel and sorry for that.

It looks like I made a mistake with my matrix setup. Can you tell me though, what is the difference between Venn diagram and Matrix. I noticed that MGMAT makes distinction between the two. I cannot tell whether I make mistakes in setting up the matrix (like I did now) or Venn diagram, or there are times I can use only one of them. How can I tell?
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 22 Dec 2012, 17:36
Bunuel,
Didn't quite understand this : (2) says that a+b+c=24,

both means : b+c?
and neither means only d?
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 23 Dec 2012, 05:08
Expert's post
Sachin9 wrote:
Bunuel,
Didn't quite understand this : (2) says that a+b+c=24,

both means : b+c?
and neither means only d?


It's all in the matrix:
a = investment and profit;
b = investment and NO profit;
c = profit and NO investment;
d = NO investment and NO profit.

Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 03 Jan 2013, 21:12
Bunuel wrote:
Sachin9 wrote:
Bunuel,
Didn't quite understand this : (2) says that a+b+c=24,

both means : b+c?
and neither means only d?


It's all in the matrix:
a = investment and profit;
b = investment and NO profit;
c = profit and NO investment;
d = NO investment and NO profit.

Hope it's clear.

Bunuel,

Do we have a similar question that tests concept that is tested in the 2nd option?
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 14 Feb 2014, 04:23
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 04 Mar 2014, 21:00
I do not understand how can we say "last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both" when the question says "Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets."

Isn't B going against the question?

Statement in question : Last year in a group of 30 businesses, 21 reported a net profit
Statement B : last year 24 of the 30 businesses reported a net profit
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 04 Mar 2014, 23:59
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gauravkaushik8591 wrote:
I do not understand how can we say "last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both" when the question says "Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets."

Isn't B going against the question?

Statement in question : Last year in a group of 30 businesses, 21 reported a net profit
Statement B : last year 24 of the 30 businesses reported a net profit


Refer to the matrix:
Image
a = investment and profit;
b = investment and NO profit;
c = profit and NO investment;
d = NO investment and NO profit.

(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both --> a+b+c=24 (all groups but NO investment and NO profit.).

Hope it's clear.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 18 May 2014, 08:49
(1) is also sufficient.

The general equation for 2 overlapping groups is:

True # of entities = (total # with char 1) + (total # with char 2) + (# with neither char) - (# with both chars)

From the original info, we know that:

30 = 21 + 15 + neither - both

and we're asked to solve for "neither".

(1) gives us "both", so we can definitely solve.
Re: Last year in a group of 30 businesses, 21 reported a net   [#permalink] 18 May 2014, 08:49
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