Last visit was: 03 Aug 2024, 19:08 It is currently 03 Aug 2024, 19:08
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# The attendees at a certain convention purchased a total of 15,000 book

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 31 May 2006
Posts: 31
Own Kudos [?]: 47 [33]
Given Kudos: 0
Manager
Joined: 21 Jul 2006
Posts: 53
Own Kudos [?]: 76 [5]
Given Kudos: 0
General Discussion
Senior Manager
Joined: 07 Nov 2005
Posts: 354
Own Kudos [?]: 89 [0]
Given Kudos: 1
Location: India
SVP
Joined: 07 Jul 2004
Posts: 2001
Own Kudos [?]: 1925 [4]
Given Kudos: 0
Location: Singapore
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
2
Kudos
2
Bookmarks
St1:
# of male attendees = m
# of female attendees = 4000-m

But we can't work further. Insufficient.

St2:
3m + 5f = 15,000

Can't solve as there are many possibilites for (m,f) sets

Using St1 and St2:
3m + 5(4000-m) = 15,000

Can solve for m, and thus f. Sufficient.

ANS c
Senior Manager
Joined: 28 Dec 2005
Posts: 417
Own Kudos [?]: 49 [0]
Given Kudos: 0
Q49  V41
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
shehreenquayyum wrote:
Attendees at a certain convention purchased 15000 boks. How many of these attendees are females?

i) Total attendees are 4000
ii) Males purchased an average of 3 books each & females purchased an average of 5 books each.

I think we have to use the weighted average? Answer is C....

Straight C

from 1: m+f =4000
from 2: 3m+5f=15000

2 equations and 2 unknowns, 1 and 2 are insuff. but combined can give the answer.
Director
Joined: 30 Mar 2006
Posts: 894
Own Kudos [?]: 607 [0]
Given Kudos: 0
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
C

1) M + F = 4000
Not Suff

2) 3M +5F = 15000
Not Suff

Together

3(4000-F) + 5F = 15000
12000 -3F +5F = 15000
2F = 3000
F = 1500
Retired Moderator
Joined: 05 Jul 2006
Posts: 847
Own Kudos [?]: 1576 [0]
Given Kudos: 49
Re: The attendees at a certain convention purchased a total of 15,000 [#permalink]
Total attendees at a convention purchased 15000 books. How many of these were female?

1. 4000 attended the convention
2. On average men bought 3 books, females bought 5 books

My solution: 5/8 * 4000 = 2500 women. Is this correct? (even though we don't have to solve in DS). Thanks!

ONE IS OBVIOUSLY NOT SUFF

FROM TWO .......NOT SUFF

BOTH TOGETHER

TOTAL NUMBER OF BOOKS MEN PURCHASED/ TOTAL NMBER OF MEN = 3

X/Y =3

TOTAL NMBE OF BOOKS PURCHASED BY WOMEN/ NUMBER OF WOMEN =5

15000 - X / 4000- Y = 5

WE HAVE TWO EQUATIONS FOR TWO UNKNOWNS

3Y =X

15000 - 3Y = 20000 - 5Y

2Y = 5000 IE: Y = 2500 THUS ............SUFF

Senior Manager
Joined: 10 Oct 2005
Posts: 316
Own Kudos [?]: 121 [1]
Given Kudos: 0
GMAT 3: 640
Re: The attendees at a certain convention purchased a total of 15,000 [#permalink]
1
Kudos
successstory wrote:
Total attendees at a convention purchased 15000 books. How many of these were female?

1. 4000 attended the convention
2. On average men bought 3 books, females bought 5 books

My solution: 5/8 * 4000 = 2500 women. Is this correct? try to check by back solving females bought 2500*5=12500 books hence 2500 books was bought by men 2500/3=not integer and obviously can't be the number of men))) (even though we don't have to solve in DS). Thanks!

agree with yezz 1st and 2 statements insuff alone
taking both together
M+F=4000 -->M=4000-F
M*3+F*5=15000-->
3*(4000-F)+5F=15000
12000-3F+5F=15000
2F=3000
F=1500
M=2500
Director
Joined: 26 Aug 2014
Posts: 823
Own Kudos [?]: 202 [0]
Given Kudos: 98
Concentration: Marketing
GPA: 3.4
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
can someone tell me why this reasoning is wrong.

For statement B - say you take it to mean for every 8 books, 5 are bought for 1 female. So for the 15,000 books 9375 are bought by females. Average out 5 books to one female and you have 1875 females.

Where is my logic going astray?
Tutor
Joined: 16 Oct 2010
Posts: 15181
Own Kudos [?]: 67094 [2]
Given Kudos: 436
Location: Pune, India
The attendees at a certain convention purchased a total of 15,000 book [#permalink]
1
Kudos
1
Bookmarks
angelfire213 wrote:
can someone tell me why this reasoning is wrong.

For statement B - say you take it to mean for every 8 books, 5 are bought for 1 female. So for the 15,000 books 9375 are bought by females. Average out 5 books to one female and you have 1875 females.

Where is my logic going astray?

You are assuming that number of males = number of females which is not given.
You say that one male and one female buy a total of 8 books so total number of pairs = 15000/8 = 1875. So we get that there are 1875 males and 1875 females.

But isn't this possible - there are 3 females who buy 15 books and rest 14985 books are bought by 4995 males? This will give us a total of 15000 books bought such that on average males buy 3 books per person and females buy 5 books per person.

Similarly, there are many other cases possible.

We know w1/w2 = (A2 - Aavg)/(Aavg - A1)
We need to find the fraction w1/w2 = Number of males/Number of females and the total number of people to get the number of females.

i) Total attendees are 4000
This gives us Aavg = 15000/4000
We also get that w1 + w2 = 4000.
But we don't have A1, A2.

ii) Males purchased an average of 3 books each & females purchased an average of 5 books each.
This gives us A1 = 3 and A2 = 5
We don't have Aavg.

Using both, we have Aavg, A1 and A2. So we can find w1/w2 and we also know that total number of people is 4000. This is sufficient to answer the question.

Originally posted by KarishmaB on 19 Oct 2014, 20:47.
Last edited by KarishmaB on 17 Oct 2022, 01:05, edited 1 time in total.
Intern
Joined: 29 Oct 2016
Posts: 20
Own Kudos [?]: 6 [0]
Given Kudos: 19
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
Hoping someone can help me to understand what I am doing wrong:

For statement 1, I understood that M + F = 4000

But for statement 2, when I read "average" this is the type of algebraic statement I came up with:
For males, where number of total books bought by males I noted as "Bm" and overall total of males M, so equation is Bm/M =3, and similarly for females, Bf/F = 5. I then tried to set up Bm/M + BF/f = 15,000.

How come in the solution we reduce it to very simple terms as being 3M + 5F = 15,000? I'm not sure I'm quite understanding...thanks!
Tutor
Joined: 16 Oct 2010
Posts: 15181
Own Kudos [?]: 67094 [3]
Given Kudos: 436
Location: Pune, India
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
2
Kudos
1
Bookmarks
infinitemac wrote:
Hoping someone can help me to understand what I am doing wrong:

For statement 1, I understood that M + F = 4000

But for statement 2, when I read "average" this is the type of algebraic statement I came up with:
For males, where number of total books bought by males I noted as "Bm" and overall total of males M, so equation is Bm/M =3, and similarly for females, Bf/F = 5. I then tried to set up Bm/M + BF/f = 15,000.

How come in the solution we reduce it to very simple terms as being 3M + 5F = 15,000? I'm not sure I'm quite understanding...thanks!

What is 15000? The sum of the total number of books purchased.

Average number of books purchased by males = 3
Average number of books purchased by females = 5

Say there are M males and F females.

Average = Number of books purchased by males/Number of males

3 * M = Number of books purchased by males

Average = Number of books purchased by females/Number of females

5*F = Number of books purchased by females

Total number of books purchased = Number of books purchased by males + Number of books purchased by females = 3M + 5F

15000 = 3M + 5F

Note that Bm/M + Bf/F = 15,000 is wrong. You have already established that Bm/M = 3 and Bf/F = 5. These are the averages. When you add these two, you get 3 + 5 = 8.
15000 is the sum of the number of books purchased.
Intern
Joined: 29 Oct 2016
Posts: 20
Own Kudos [?]: 6 [0]
Given Kudos: 19
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
VeritasPrepKarishma wrote:
infinitemac wrote:
Hoping someone can help me to understand what I am doing wrong:

For statement 1, I understood that M + F = 4000

But for statement 2, when I read "average" this is the type of algebraic statement I came up with:
For males, where number of total books bought by males I noted as "Bm" and overall total of males M, so equation is Bm/M =3, and similarly for females, Bf/F = 5. I then tried to set up Bm/M + BF/f = 15,000.

How come in the solution we reduce it to very simple terms as being 3M + 5F = 15,000? I'm not sure I'm quite understanding...thanks!

What is 15000? The sum of the total number of books purchased.

Average number of books purchased by males = 3
Average number of books purchased by females = 5

Say there are M males and F females.

Average = Number of books purchased by males/Number of males

3 * M = Number of books purchased by males

Average = Number of books purchased by females/Number of females

5*F = Number of books purchased by females

Total number of books purchased = Number of books purchased by males + Number of books purchased by females = 3M + 5F

15000 = 3M + 5F

Note that Bm/M + Bf/F = 15,000 is wrong. You have already established that Bm/M = 3 and Bf/F = 5. These are the averages. When you add these two, you get 3 + 5 = 8.
15000 is the sum of the number of books purchased.

Thank you so much Karishma - seems like I missed out on a simple concept but you have explained it very clearly! Thanks!
Manager
Joined: 23 Dec 2013
Posts: 86
Own Kudos [?]: 83 [0]
Given Kudos: 23
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
shehreenquayyum wrote:
The attendees at a certain convention purchased a total of 15,000 books. How many of these attendees were female?

(1) There was a total of 4,000 attendees at the convention.
(2) The male attendees purchased an average (arithmetic mean) of 3 books each, and the female attendees purchased an average of 5 books each.

The goal of the problem is to find F, the number of female attendees at the convention.

Statement 1) F+M = 4000.

Insufficient. We don't know the breakdown or distribution of males or females.

Statement 2) Books bought by males / M = 3.

Books bought by females / F = 5.

5F + 3M = books bought by males and books bought by females = 15000

Insufficient because we don't know the total number of males or females.

Statements 1+2) Sufficient.

3M + 5F = 15000

M + F = 4000
Retired Moderator
Joined: 19 Mar 2014
Posts: 815
Own Kudos [?]: 983 [0]
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
The attendees at a certain convention purchased a total of 15,000 books. How many of these attendees were female?

(1) There was a total of 4,000 attendees at the convention.

Total attendees $$= 4,000$$

This does not give us any information on the number of female attendees.

Hence, (1) =====> is NOT SUFFICIENT

(2) The male attendees purchased an average (arithmetic mean) of 3 books each, and the female attendees purchased an average of 5 books each

This gives us average of Male and Female purchase of books

$$3m + 5f = 15000$$

As we are not aware of total count of the participants

Hence, (2) =====> is NOT SUFFICIENT.

Now lets combine (1) & (2)

$$m + f = 4,000$$

$$3m + 5f = 15,000$$

As you can see that with the help of these two equations we can find the total number of female attendees.

Please note that you need not do the actual calculation, only the information that we can arrive at a number should be sufficient for us.

Manager
Joined: 23 May 2017
Posts: 191
Own Kudos [?]: 361 [0]
Given Kudos: 9
Concentration: Finance, Accounting
WE:Programming (Energy and Utilities)
Re: The attendees at a certain convention purchased a total of 15,000 [#permalink]
Attachment:

FullSizeRender (9).jpg [ 65.57 KiB | Viewed 14047 times ]

Ans = C
Non-Human User
Joined: 09 Sep 2013
Posts: 34228
Own Kudos [?]: 858 [0]
Given Kudos: 0
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: The attendees at a certain convention purchased a total of 15,000 book [#permalink]
Moderator:
Math Expert
94778 posts