Source: Manhattan Prep
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?
A. 7
B. 14
C. 21
D. 28
E. 35
The OA is E.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
A baker makes chocolate cookies and peanut cookies. His
This topic has expert replies
-
BTGmoderatorLU
- Moderator
- Posts: 2207
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
We're looking for the smallest possible number of chocolate chip cookies.BTGmoderatorLU wrote:Source: Manhattan Prep
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?
A. 7
B. 14
C. 21
D. 28
E. 35
The OA is E.
So, let's start by testing answer choice A
A) If we make 7 chocolate chip cookies, then the remaining 88 cookies are peanut cookies.
We're told that peanut cookies are baked in batches of 6
However, 88 is NOT divisible by 6, which means there cannot be 88 peanut cookies.
ELIMINATE A
B) If we make 14 chocolate chip cookies, then the remaining 81 cookies are peanut cookies.
However, 81 is NOT divisible by 6, which means there cannot be 81 peanut cookies.
ELIMINATE B
C) If we make 21 chocolate chip cookies, then the remaining 74 cookies are peanut cookies.
However, 74 is NOT divisible by 6, which means there cannot be 74 peanut cookies.
ELIMINATE C
D) If we make 28 chocolate chip cookies, then the remaining 67 cookies are peanut cookies.
However, 67 is NOT divisible by 6, which means there cannot be 67 peanut cookies.
ELIMINATE D
By the process of elimination, the correct answer is E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
\[x \geqslant 1\,\,\,{\text{choco}}\,\,{\text{batches}}{\text{,}}\,\,\,\,\,{\text{7}}\,\,{\text{choco/batch}}\]BTGmoderatorLU wrote:Source: Manhattan Prep
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?
A. 7
B. 14
C. 21
D. 28
E. 35
\[y \geqslant 1\,\,\,{\text{pean}}\,\,{\text{batches}}{\text{,}}\,\,\,\,\,{\text{6}}\,\,{\text{pean/batch}}\]
\[7x + 6y = 95\,\,\,\,\,\left( * \right)\]
\[{\text{? = }}{\left( {{\text{7x}}} \right)_{\,\min }}\]
\[{\left( {{\text{7x}}} \right)_{\,\min }}\,\,\, \Leftrightarrow \,\,\,{x_{\min }}\]
\[{\left( {multiple\,\,of\,\,6} \right)_{\max }} = {\left( {6y} \right)_{\max }}\mathop = \limits^{\left( * \right)} \,\,95 - 7x\]
\[\begin{gathered}
x = 1\,\,\, \Rightarrow \,\,\,95 - 7x = 88\,\,{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,3\, \hfill \\
x = 2\,\,\, \Rightarrow \,\,\,95 - 7x = {\text{odd}}\,\,\left( {{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,2} \right) \hfill \\
x = 3\,\,\, \Rightarrow \,\,\,95 - 7x = 74\,\,{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,3 \hfill \\
x = 4\,\,\, \Rightarrow \,\,\,95 - 7x = {\text{odd}}\,\,\left( {{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,2} \right) \hfill \\
x = 5\,\,\, \Rightarrow \,\,\,95 - \boxed{7x = 35} = {\text{60}}\,\,\underline {{\text{divisible}}\,\,{\text{by}}\,\,6!} \hfill \\
\end{gathered} \]
The above follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let c = the number of batches of chocolate chip cookies made and p = the number of batches of peanut cookies made and create the equation:BTGmoderatorLU wrote:Source: Manhattan Prep
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?
A. 7
B. 14
C. 21
D. 28
E. 35
7c + 6p = 95
7c = 95 - 6p
c = (95 - 6p)/7
In order for c to be an integer, we need (95 - 6p) to be a multiple of 7.
Let's start with the largest value of p and work our way down.
When p is 15, we have:
c = 5/7... this does not work
When p is 14, we have:
c = 11/7... this does not work
When p is 13, we have:
c = 17/7... this does not work
When p is 12, we have:
c = 23/7... this does not work
When p is 11, we have:
c = 29/7... this does not work
When p is 10, we have:
c = 35/7 = 5... this works!
So, the minimum number of batches of chocolate chip cookies is 5, and, thus, the minimum number of chocolate chip cookies is 5 x 7 = 35.
Alternate Solution:
Let's test each answer choice, starting with the smallest value:
Answer Choice A: c = 7
If c = 7, then the number of peanut butter cookies is 95 - 7 = 88; however, since 88 is not divisible by 6, c = 7 is not possible.
Answer Choice B: c = 14
If c = 14, then the number of peanut butter cookies is 95 - 14 = 81; however, since 81 is not divisible by 6, c = 14 is not possible.
Answer Choice C: c = 21
If c = 21, then the number of peanut butter cookies is 95 - 21 = 74; however, since 74 is not divisible by 6, c = 21 is not possible.
Answer Choice D: c = 28
If c = 28, then the number of peanut butter cookies is 95 - 28 = 67; however, since 67 is not divisible by 6, c = 28 is not possible.
Since we eliminated every other answer choice, we know by this point that the correct answer is E; however, let's verify this as an exercise:
Answer Choice E: c = 35
If c = 35, then the number of peanut butter cookies is 95 - 35 = 60, which is a possible value since 60 is divisible by 6.
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
