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

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Senior Manager
Joined: 18 Sep 2009
Posts: 328
Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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05 Mar 2012, 17:27
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Difficulty:

35% (medium)

Question Stats:

72% (01:21) correct 28% (01:25) wrong based on 540 sessions

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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)
Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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05 Mar 2012, 22:56
12
6
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.

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):

(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.
Attachment:

30 businesses.PNG [ 4.79 KiB | Viewed 12603 times ]

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Manager
Joined: 08 Jun 2011
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05 Mar 2012, 20:08
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TomB wrote:
Last year in a group of 30 businesses, 21 reported a net profit and
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]

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22 Dec 2012, 18:36
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]

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23 Dec 2012, 06:08
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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Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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03 Jan 2013, 22:12
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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My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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04 Jan 2013, 02:42
1
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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Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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04 Mar 2014, 22:00
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
Math Expert
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Posts: 47157
Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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05 Mar 2014, 00:59
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:

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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GMAT Date: 07-31-2014
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Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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18 May 2014, 09:49
(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.
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Posts: 1792
Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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01 Jun 2015, 03:14
Presenting the Venn diagram approach of the solution

Interpreting the given info
We are told about 30 businesses of which 21 reported a net profit and 15 had investments in foreign markets.Refer the venn diagram below:

As the total number of businesses is 30 we can write a + b + c + d = 30

Also, 21 firms reported a net profit, that would give us a + b =21. Also, it would give us c + d = 9

Similarly, 15 firms had investments in foreign markets, that would give us b + c = 15. Also it would give us a + d = 15.
We need to find the number of businesses that did not report a net profit nor invest in foreign market i.e. d. Let's see if the statements provide us the information to find a definite value of d

Statement-I
St-I tells us that 12 businesses reported net profit and had investments in foreign markets i.e. b = 12. This would give us the value of a = 9.
We know that a + d = 15 i.e. d = 6.
Hence st-I is sufficient to answer the question.

Statement-II
St-II tells us that 24 businesses reported a net profit or invested in foreign markets or both i.e. a + b + c = 24

Since a + b + c + d = 30 we can find the value of d = 6

Hence st-II is sufficient to answer the question.

Hope this helps

Regards
Harsh
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Manager
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Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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11 Jul 2015, 05:41
Easiest for statement 2 is imho to think that there are 24 businesses that comprise the three segments "Profit / Investment", "Profit / No Investment" and "No Profit / Investment".

We are looking for the number of "Profit / Investment", as this one is not given and because this one is a combination of both the other segments it is necessary to subtract the number of businesses that had either a profit and an investment.

-> 24 = 21 + 15 -x
-> x = 12 (Profit AND Investment)

From that on we can fill out the matrix.
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Joined: 07 Jun 2017
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Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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09 Sep 2017, 01:08
Bunuel 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?

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.

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):

(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.
Attachment:

The best way is table. When you solve by table, it is really simple.

Posted from my mobile device
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Joined: 11 Feb 2018
Posts: 29
Re: Last year in a group of 30 businesses, 21 reported a net  [#permalink]

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20 Apr 2018, 12:59
Bunuel 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?

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.

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):

(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.
Attachment:

Hi Bunuel

Thanks for the great explanation as always. Is it safe to follow the Venn diagram method throughout all the questions;though in MGMAT book it is suggested that for 2 decision questions we should use matrix approach.
So, just wanted to know from your expertise which of the two - Venn diagram/Matrix approach is effective/time-saving for 2 decision questions.
Re: Last year in a group of 30 businesses, 21 reported a net &nbs [#permalink] 20 Apr 2018, 12:59
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