At a certain bakery, the chocolate chip cookies are sold only in packets of three while the peanut butter cookies are sold only in packets of four. If a total of 35 chocolate chip and peanut butter cookies were sold last Tuesday, what is the maximum number of packets of chocolate chip cookies that could have been sold that day.
a. 5
b. 8
c. 9
d. 10
e. 11
Chocolate Chip
This topic has expert replies

 Master  Next Rank: 500 Posts
 Posts: 135
 Joined: 03 Oct 2011
 Followed by:4 members
points u have to note
1.there are 35 cookies sold(no more no less)
2.in packets of 3 and 4
3.maximum no. of packets
when will maximum no. of packets will occur >> when the least combination of packets is sold more(no. of choc cookies packets is sold more)
choc cookies are sold in packet of 3, now the highest possible no.(< 35) that is divisible by 3 is 33(3*11=33)
for peanut cookies >> 3533=2
as the peanut cookies are sold in packet of 4(2 is not divisible by 4)
next highest possible no. is 30,that leaves us with 5 for peanut cookies(again not possible,leaves remainder)
next highest possible no. is 27,that leaves us with 8 for peanut cookies(which is 4*2=8,no remainder)
hence 3*[9]=27 and 4*[2]=8
27+8=35
the ans is 9+2=11 [E]
1.there are 35 cookies sold(no more no less)
2.in packets of 3 and 4
3.maximum no. of packets
when will maximum no. of packets will occur >> when the least combination of packets is sold more(no. of choc cookies packets is sold more)
choc cookies are sold in packet of 3, now the highest possible no.(< 35) that is divisible by 3 is 33(3*11=33)
for peanut cookies >> 3533=2
as the peanut cookies are sold in packet of 4(2 is not divisible by 4)
next highest possible no. is 30,that leaves us with 5 for peanut cookies(again not possible,leaves remainder)
next highest possible no. is 27,that leaves us with 8 for peanut cookies(which is 4*2=8,no remainder)
hence 3*[9]=27 and 4*[2]=8
27+8=35
the ans is 9+2=11 [E]

 Junior  Next Rank: 30 Posts
 Posts: 24
 Joined: 09 Jul 2011
 Location: Tajikistan, Dushanbe
 Thanked: 2 times
It seems such an easy answer, but at the same time it could be the trick of this problem.
Here we go:
To get max number of chocolate chip cookies, we need to get the smallest number of peanut butter cookies, as follow: 0, 1, 2 etc.
So here 0 could not be, as the question stem states that a certain number of peanut butter cookies were sold, hence it must be either 1 or 2.
If, 1 then the number of chocolate chip cookies would be: 3x+4=35 or 3x=31, hence can not be 1. That leaves us with 2, here we get 3x+2*4=35 or 3x=358=27, hence x=9  max number of packets of chocolate chip cookies that could have been sold (D).
Plese, correct me if I went awry. I want to learn and share, this is the only purpose why I am here:)
Here we go:
To get max number of chocolate chip cookies, we need to get the smallest number of peanut butter cookies, as follow: 0, 1, 2 etc.
So here 0 could not be, as the question stem states that a certain number of peanut butter cookies were sold, hence it must be either 1 or 2.
If, 1 then the number of chocolate chip cookies would be: 3x+4=35 or 3x=31, hence can not be 1. That leaves us with 2, here we get 3x+2*4=35 or 3x=358=27, hence x=9  max number of packets of chocolate chip cookies that could have been sold (D).
Plese, correct me if I went awry. I want to learn and share, this is the only purpose why I am here:)
Life begins at the End of your Comfort Zone...

 Master  Next Rank: 500 Posts
 Posts: 135
 Joined: 03 Oct 2011
 Followed by:4 members
 neelgandham
 Community Manager
 Posts: 1060
 Joined: 13 May 2011
 Location: Utrecht, The Netherlands
 Thanked: 318 times
 Followed by:52 members
At a certain bakery, the chocolate chip cookies are sold only in packets of three while the peanut butter cookies are sold only in packets of four. If a total of 35 chocolate chip and peanut butter cookies were sold last Tuesday, what is the maximum number of packets of chocolate chip cookies that could have been sold that day.
Let the number of chocolate chip cookie packets be C and
Let the number of peanut butter cookies packets be P
3C + 4P = 35, where P,C are positive integers
3C = 35  4P
Different combinations of (C,P) that satisfy the equation are (9,2), (5,5), (1,8).
So 9 is the maximum number of packets of chocolate chip cookies that could have been sold that day
Let the number of chocolate chip cookie packets be C and
Let the number of peanut butter cookies packets be P
3C + 4P = 35, where P,C are positive integers
3C = 35  4P
Different combinations of (C,P) that satisfy the equation are (9,2), (5,5), (1,8).
So 9 is the maximum number of packets of chocolate chip cookies that could have been sold that day
Anil Gandham
Welcome to BEATtheGMAT  Photography  Getting Started  BTG Community rules  MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT  Photography  Getting Started  BTG Community rules  MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
 GMATGuruNY
 GMAT Instructor
 Posts: 15533
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1901 members
 GMAT Score:790
We can plug in the answers, which represent the maximum possible number of chocolatechip cookie packets.nidhis.1408 wrote:At a certain bakery, the chocolate chip cookies are sold only in packets of three while the peanut butter cookies are sold only in packets of four. If a total of 35 chocolate chip and peanut butter cookies were sold last Tuesday, what is the maximum number of packets of chocolate chip cookies that could have been sold that day.
a. 5
b. 8
c. 9
d. 10
e. 11
Since we need the MAXIMUM possible value, we should start with the GREATEST answer choice.
When the correct answer choice is plugged in, the remaining number of cookies must be a multiple of 4, since each peanutbutter cookie packet contains 4 cookies.
Answer choice E: 11
Number of chocolatechip cookies in 11 threecookie packets = 11*3 = 33.
Remaining number of cookies = 3533 = 2.
2 is not a multiple of 4.
Eliminate E.
Answer choice D: 10
Number of chocolatechip cookies in 10 threecookie packets = 10*3 = 30.
Remaining number of cookies = 3530 = 5.
5 is not a multiple of 4.
Eliminate D.
Answer choice C: 9
Number of chocolatechip cookies in 9 threecookie packets = 9*3 = 27.
Remaining number of cookies = 3527 = 8.
Success!
The 8 remaining cookies could be contained in 2 packets of peanutbutter cookies, each packet with 4 cookies.
The correct answer is C.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3