Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Jun 2016, 10:49

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Thanks All of the coffee mixtures sold in a certain store

Author Message
Manager
Joined: 15 Mar 2004
Posts: 155
Location: New York
Followers: 1

Kudos [?]: 2 [0], given: 0

Thanks All of the coffee mixtures sold in a certain store [#permalink]

### Show Tags

22 Mar 2004, 18:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

All of the coffee mixtures sold in a certain store contain either Columbian (C), Jamaican (J), or Brazilian coffee, or some combination of those. Of all the coffee mixtures 33 contain C, 43 contain J, and 42 contain B. Of those, 16 contain at least C & J, 18 at least J & B, and 8 contain at least B & C, and 5 contain all three. How many different mixtures are sold at the store?
_________________

---------------------------------------------------
The more I learn, the more I realize I know nothing!
----------------------------------------------------

Manager
Joined: 15 Mar 2004
Posts: 155
Location: New York
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

22 Mar 2004, 18:44
Halle,

_________________

---------------------------------------------------
The more I learn, the more I realize I know nothing!
----------------------------------------------------

Senior Manager
Joined: 30 Aug 2003
Posts: 324
Location: dallas , tx
Followers: 1

Kudos [?]: 26 [0], given: 0

### Show Tags

22 Mar 2004, 18:45
is it 56 ..if right... will explain
_________________

shubhangi

Senior Manager
Joined: 02 Mar 2004
Posts: 327
Location: There
Followers: 1

Kudos [?]: 0 [0], given: 0

### Show Tags

22 Mar 2004, 18:51
CJ, CB, JB, CJB

Just 4 mixtures.
Manager
Joined: 15 Mar 2004
Posts: 155
Location: New York
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

22 Mar 2004, 18:56
81? How?
Also, even if there are four mixtures Halle, the answer is off. I was pretty confused by this problem, thats why I think its important to see how any of us would approach this problem.
_________________

---------------------------------------------------
The more I learn, the more I realize I know nothing!
----------------------------------------------------

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4302
Followers: 34

Kudos [?]: 335 [0], given: 0

### Show Tags

22 Mar 2004, 19:09
CJB+CJ+BJ+CB+C+J+B = X

CJB = 5
CJ = 16 - 5 = 11
BJ = 18 - 5 = 13
CB = 8 - 5 = 3
C = 33 - 11 - 5 - 3 = 14
J = 43 - 13 - 5 - 11 = 14
B = 42 - 3 - 5 - 13 = 21

X = 5 + 11 + 13 + 3 + 14 + 14 + 21 = 81

It is much easier to show with a Venn Diagram but I don't know how to do it. Maybe Gmatblast can. Also, I don't like the wording of the question too much. ie. "16 contain at least C & J" Why "at least"? Why not just "16 contain C & J"
_________________

Best Regards,

Paul

Manager
Joined: 15 Mar 2004
Posts: 155
Location: New York
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

22 Mar 2004, 20:17
Paul wrote:
CJB+CJ+BJ+CB+C+J+B = X

CJB = 5
CJ = 16 - 5 = 11
BJ = 18 - 5 = 13
CB = 8 - 5 = 3
C = 33 - 11 - 5 - 3 = 14
J = 43 - 13 - 5 - 11 = 14
B = 42 - 3 - 5 - 13 = 21

X = 5 + 11 + 13 + 3 + 14 + 14 + 21 = 81

It is much easier to show with a Venn Diagram but I don't know how to do it. Maybe Gmatblast can. Also, I don't like the wording of the question too much. ie. "16 contain at least C & J" Why "at least"? Why not just "16 contain C & J"

Paul, your approach is absolutely correct. The reason it states at least is to show that some of those 16 can contain more then just two blends. If the problem stated "16 contain C & J" then C & J is not =16-5, but rather 21-5. In other words, the area of two circles in Venn digram that contains C & J only would be 16 and not 11, and the total would change.
_________________

---------------------------------------------------
The more I learn, the more I realize I know nothing!
----------------------------------------------------

Senior Manager
Joined: 06 Dec 2003
Posts: 366
Location: India
Followers: 1

Kudos [?]: 7 [0], given: 0

### Show Tags

22 Mar 2004, 20:24
Paul wrote:
CJB+CJ+BJ+CB+C+J+B = X

CJB = 5
CJ = 16 - 5 = 11
BJ = 18 - 5 = 13
CB = 8 - 5 = 3
C = 33 - 11 - 5 - 3 = 14
J = 43 - 13 - 5 - 11 = 14
B = 42 - 3 - 5 - 13 = 21

X = 5 + 11 + 13 + 3 + 14 + 14 + 21 = 81

It is much easier to show with a Venn Diagram but I don't know how to do it. Maybe Gmatblast can. Also, I don't like the wording of the question too much. ie. "16 contain at least C & J" Why "at least"? Why not just "16 contain C & J"

Paul, i accord your solution, I arrived at the same juncture using Ven Diagram.
BUT, the stem asks for "MIOXTURES OF COFFEES" and not toal no of coffee brands.
CJB + CJ + BJ + CB = 5 + 11 + 13 + 3 = 32.

PAUL, the word ATLEST has a subtle difference, it can't be ignored. ATLEAST tells you to, subtract n(J n B n C) from n(J n B) to count the no of coffee blends available with EXACT 2 Flavors in it.
I hope i am clear enough.

Dharmin
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4302
Followers: 34

Kudos [?]: 335 [0], given: 0

### Show Tags

22 Mar 2004, 20:36
Dharmin wrote:
Paul wrote:
CJB+CJ+BJ+CB+C+J+B = X

CJB = 5
CJ = 16 - 5 = 11
BJ = 18 - 5 = 13
CB = 8 - 5 = 3
C = 33 - 11 - 5 - 3 = 14
J = 43 - 13 - 5 - 11 = 14
B = 42 - 3 - 5 - 13 = 21

X = 5 + 11 + 13 + 3 + 14 + 14 + 21 = 81

It is much easier to show with a Venn Diagram but I don't know how to do it. Maybe Gmatblast can. Also, I don't like the wording of the question too much. ie. "16 contain at least C & J" Why "at least"? Why not just "16 contain C & J"

Paul, i accord your solution, I arrived at the same juncture using Ven Diagram.
BUT, the stem asks for "MIOXTURES OF COFFEES" and not toal no of coffee brands.
CJB + CJ + BJ + CB = 5 + 11 + 13 + 3 = 32.

PAUL, the word ATLEST has a subtle difference, it can't be ignored. ATLEAST tells you to, subtract n(J n B n C) from n(J n B) to count the no of coffee blends available with EXACT 2 Flavors in it.
I hope i am clear enough.

Dharmin

I refer you to the problem: All of the coffee mixtures sold in a certain store contain either Columbian (C), Jamaican (J), or Brazilian coffee, or some combination of those.
This means that any of C, J or B alone will be considered a mixture.

And yes guys, "at least" is crucial. Just figured it out
_________________

Best Regards,

Paul

Manager
Joined: 15 Mar 2004
Posts: 155
Location: New York
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

22 Mar 2004, 20:45
Dharmin,

Pauls answer is BEST. I also agree with you that the question stem is phrased incorrectly. But, the main issue here is to recognize the AT LEAST part and arrive at the right conclusion. If in fact we ignored the at least part, we would've arrived at the wrong answer. The most important fact is, that the wrong answer might be included in the real GMAT.
_________________

---------------------------------------------------
The more I learn, the more I realize I know nothing!
----------------------------------------------------

Senior Manager
Joined: 23 Aug 2003
Posts: 461
Location: In the middle of nowhere
Followers: 1

Kudos [?]: 16 [0], given: 0

### Show Tags

23 Mar 2004, 10:27
Thats was excellent Paul...If I recall it correctly...this is a Kaplan problem...and one of the hardest...you solved it very well...way to go Paul..!

And yeah... I think sometime back even Anand had suggested to change ur signature to 750+ quest...I guess it time you do that.

Vivek.
_________________

"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

Senior Manager
Joined: 30 Aug 2003
Posts: 324
Location: dallas , tx
Followers: 1

Kudos [?]: 26 [0], given: 0

### Show Tags

24 Mar 2004, 02:38
shubhangi wrote:
is it 56 ..if right... will explain

_________________

shubhangi

Display posts from previous: Sort by