Problem Solving

Guys,

I asked this question to the MGMAT staff, but guess they are inundated by other posts.

I always use the 2 set matrix method for solving set questions. however, i feel it does not work always. I am posting the below question.

Can some of you experts pls help me? I need to get this funda cleared. My GMAT is next Thursday.

I am copy pasting the question asked in that forum here.
------------------------------------------------------
Ron,

You say that always use the 2 set matrix and not the venn unless you want to make life harder.

I am attaching below 3 problems. All of them are from the GMAT Prep software. I have tried using the 2 set matrix but it does not work (at least for me). I also tried 'googling' these questions and the solutions are either the venn diagram or the T = A+B-Both+Neither formula, which i understand is nothing but the venn diagram algebraic representation.

If you could please throw some light, I will indeed be glad. Perhaps i am missing the concept or doing something wrong, but this if you reply, it will indeed help.


1) A seminar consisted of morning session and afternoon session. If each of the 128 people attending attended at least one of the two sessions, how many of the people attended the morning session only?
a. ¾ attended both sessions
b. 7/8 attended the afternoon session

----------------

2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.

---------------


3) 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.
--------------------

I'll take the first one.

1) A seminar consisted of morning session and afternoon session. If each of the 128 people attending attended at least one of the two sessions, how many of the people attended the morning session only?
a. ¾ attended both sessions
b. 7/8 attended the afternoon session

Set up a venn diagram. Let x equal the people who went only to the morning. let y equal the people who went to both. Let z equal the people who only went to evening. Then from the question stem you know that x + y + z = 128.

(1) then y = 3/4 of (x + y + z) so that gives you a value of y (if you calculated it'd be 96 but you don't really need to bother, it's DS). But you can't solve for x (which is what you're asked for.)
(2) then y + z = 7/8 (x + y + z). So y + z = 7/8 (128). So that gives you a value of y + z, which means that you'd be able to subtract that value from 128.

The Venn diagram wasn't necessary here really but it helps you organize what you know and what you don't know.

2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


I would mark E for this.
Because it's not necessary that the guest will order either coffee or desert.
If the guest will order either coffee or desert then 1) would have been sufficient
I tried calculating taking two statements into consideration,but then the we get percentage which results into decimals.
But it has to be a whole no.since we are talking about the guests.

Experts plz revert.

Got redirect from Venn digram post-

x=Total number of guests
D=0.75x
C=?
Formula : T = D + C - Both + Neither
There is no information about Neither part, it isn't given that all had something ( Dessert or Coffee) or certain number had nothing.
So neither= Not known.

Statement 1:
D & C = 0.6*0.75x

Use formula x = 0.75x + C - Both + Neither
0.25x = C - (0.75*0.6x) + Neither
Do we know neither ? No ! Not sufficient.

Statement 2:
C & D= 90% of Coffee

Use formula
x = 0.7x + C -(0.9C) + Neither
Do we know neither ? No ! Not sufficient.

Combine 1 & 2 : 0.9C = 0.6*0.75x
Can we get value of c in terms of x ? Yes. Sufficient.
C.

In this case, My choice is "Both statement together is sufficient to answer"
FROM (1) 60 percent of the guests who ordered dessert also ordered coffee.

75 x 60/100 = 75-x , so x = 30

FROM (2) 90 percent of the guests who ordered coffee also ordered dessert.

(75-x+y) x 90/100 = 75-x , so using 1, y can be evaluated.

So solving, x = 30, y = 5

Please let me know, if i am right.

prachich1987 wrote:2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


I would mark E for this.
Because it's not necessary that the guest will order either coffee or desert.
If the guest will order either coffee or desert then 1) would have been sufficient
I tried calculating taking two statements into consideration,but then the we get percentage which results into decimals.
But it has to be a whole no.since we are talking about the guests.

Experts plz revert.

sachin2411 wrote:In this case, My choice is "Both statement together is sufficient to answer"
FROM (1) 60 percent of the guests who ordered dessert also ordered coffee.

75 x 60/100 = 75-x , so x = 30

FROM (2) 90 percent of the guests who ordered coffee also ordered dessert.

(75-x+y) x 90/100 = 75-x , so using 1, y can be evaluated.

So solving, x = 30, y = 5

Please let me know, if i am right.

prachich1987 wrote:2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


I would mark E for this.
Because it's not necessary that the guest will order either coffee or desert.
If the guest will order either coffee or desert then 1) would have been sufficient
I tried calculating taking two statements into consideration,but then the we get percentage which results into decimals.
But it has to be a whole no.since we are talking about the guests.

Experts plz revert.

I think the way it has been solved is not right.
You have not taken into consideration the fact that "there might be some people who will order nothing" or "there might be some people who might order something else"
I would be grateful if rahulk can advise OA
Thanks

beat_gmat_09 wrote:Got redirect from Venn digram post-

x=Total number of guests
D=0.75x
C=?
Formula : T = D + C - Both + Neither
There is no information about Neither part, it isn't given that all had something ( Dessert or Coffee) or certain number had nothing.
So neither= Not known.

Statement 1:
D & C = 0.6*0.75x

Use formula x = 0.75x + C - Both + Neither
0.25x = C - (0.75*0.6x) + Neither
Do we know neither ? No ! Not sufficient.

Statement 2:
C & D= 90% of Coffee

Use formula
x = 0.7x + C -(0.9C) + Neither
Do we know neither ? No ! Not sufficient.

Combine 1 & 2 : 0.9C = 0.6*0.75x
Can we get value of c in terms of x ? Yes. Sufficient.
C.

thanks beat_gmat_o9..i think this should be the correct way off solving it.

if you will add

(x) + (y) + (75-x) = 30 + 5 + 45 = 80%

that means 20 % might have ordered something else or have not ordered anything.

Let me know, where i am wrong in my logic.

prachich1987 wrote:

sachin2411 wrote:In this case, My choice is "Both statement together is sufficient to answer"
FROM (1) 60 percent of the guests who ordered dessert also ordered coffee.

75 x 60/100 = 75-x , so x = 30

FROM (2) 90 percent of the guests who ordered coffee also ordered dessert.

(75-x+y) x 90/100 = 75-x , so using 1, y can be evaluated.

So solving, x = 30, y = 5

Please let me know, if i am right.

prachich1987 wrote:2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


I would mark E for this.
Because it's not necessary that the guest will order either coffee or desert.
If the guest will order either coffee or desert then 1) would have been sufficient
I tried calculating taking two statements into consideration,but then the we get percentage which results into decimals.
But it has to be a whole no.since we are talking about the guests.

Experts plz revert.

I think the way it has been solved is not right.
You have not taken into consideration the fact that "there might be some people who will order nothing" or "there might be some people who might order something else"
I would be grateful if rahulk can advise OA
Thanks

sachin2411 wrote:if you will add

(x) + (y) + (75-x) = 30 + 5 + 45 = 80%

that means 20 % might have ordered something else or have not ordered anything.

Let me know, where i am wrong in my logic.

prachich1987 wrote:

sachin2411 wrote:In this case, My choice is "Both statement together is sufficient to answer"
FROM (1) 60 percent of the guests who ordered dessert also ordered coffee.

75 x 60/100 = 75-x , so x = 30

FROM (2) 90 percent of the guests who ordered coffee also ordered dessert.

(75-x+y) x 90/100 = 75-x , so using 1, y can be evaluated.

So solving, x = 30, y = 5

Please let me know, if i am right.

prachich1987 wrote:2]If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?
(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.


I would mark E for this.
Because it's not necessary that the guest will order either coffee or desert.
If the guest will order either coffee or desert then 1) would have been sufficient
I tried calculating taking two statements into consideration,but then the we get percentage which results into decimals.
But it has to be a whole no.since we are talking about the guests.

Experts plz revert.

I think the way it has been solved is not right.
You have not taken into consideration the fact that "there might be some people who will order nothing" or "there might be some people who might order something else"
I would be grateful if rahulk can advise OA
Thanks

Oh I aplogize

Thanks to those who helped.

The OA's are

1. B
2. C
3. D

Hi there, rahulku.

rahulku wrote: If you could please throw some light, I will indeed be glad.

That´s what I intend to do below, because the problems you´ve asked were already solved!

rahulku wrote:Ron,
You say that always use the 2 set matrix and not the venn unless you want to make life harder.

Ron´s gave you an opinion, and in my opinion he is simply wrong.

I suggest you use "matrix" (ONLY) when you are dealing with MUTUALLY EXCLUSIVE properties, 2 examples:

> When you are a man, you are not a woman and reciprocally.

That means "be a man" is mutually exclusive with "be a woman". (Yes, I know nowadays we have 22 different kinds of GMAT orientations, but I am not dealing with this sort of "social phenomena here", LOL.)

> When you are "20 years or older", you are not "less than 20 years", and reciprocally.

That means... well, you know what I mean.

As far as

rahulku wrote:T = A+B-Both+Neither formula, which i understand is nothing but the venn diagram algebraic representation.

you are right, but it is a very important one! Have a look at both pictures I´ve attached here for you.






Best Regards and success in your exam!
Fabio.

Fabio,

Thanks for those diagrams.

However, I am still not able to understand in detail the concept of at least and exactly 2 in a 3 set venn.

I am listing a problem below. Perhaps you can explain that.

At a certain school, each of the 150 students,takes between 1 and 3 classes.The 3 classes available are maths, Chemistry and English. 53 study math, 88 study chemistry and 58 study english.if 6 students take all 3 classes.
How many take
1. EXACTLY 2 classes.
2. AT LEAST 2 classes.

How should we solve this using the diagrams?

rahulku wrote:Fabio,

Thanks for those diagrams.

However, I am still not able to understand in detail the concept of at least and exactly 2 in a 3 set venn.

I am listing a problem below. Perhaps you can explain that.

At a certain school, each of the 150 students,takes between 1 and 3 classes.The 3 classes available are maths, Chemistry and English. 53 study math, 88 study chemistry and 58 study english.if 6 students take all 3 classes.
How many take
1. EXACTLY 2 classes.
2. AT LEAST 2 classes.

How should we solve this using the diagrams?

Sure!

At least two characteristics means two or more of them, exactly two means EXACTLY two, not more, not less...

Your problem: from the question stem, 150 is the total number AND is also M union C union Q, because the remainder is ZERO.

53 is M, because 53 study AT LEAST Math, may be some of them are studying also C and/or also Q...
The same for the other numbers... plug them in the proper places in "my 3-Sets diagram" before continue reading...

(1) From our formula and the details above:

150 = M union C union Q = 53 + 88 + 58 - (Sum of Exactly 2) - 2. 6 DONE!

(2) The answer will be (Sum of Exactly 2) + (Exactly 3) , the former is calculated in (1), the last parcel is of course 6.

Got it?

Regards,
Fabio.