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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A baker makes chocolate cookies and peanut cookies. His tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A baker makes chocolate cookies and peanut cookies. His ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12412 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 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. We're looking for the smallest possible number of chocolate chip cookies. 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 â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 964 messages Followed by: 27 members Upvotes: 59 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 $x \geqslant 1\,\,\,{\text{choco}}\,\,{\text{batches}}{\text{,}}\,\,\,\,\,{\text{7}}\,\,{\text{choco/batch}}$ $y \geqslant 1\,\,\,{\text{pean}}\,\,{\text{batches}}{\text{,}}\,\,\,\,\,{\text{6}}\,\,{\text{pean/batch}}$ $7x + 6y = 95\,\,\,\,\,\left( * \right)$ ${\text{? = }}{\left( {{\text{7x}}} \right)_{\,\min }}$ ${\left( {{\text{7x}}} \right)_{\,\min }}\,\,\, \Leftrightarrow \,\,\,{x_{\min }}$ ${\left( {multiple\,\,of\,\,6} \right)_{\max }} = {\left( {6y} \right)_{\max }}\mathop = \limits^{\left( * \right)} \,\,95 - 7x$ $\begin{gathered} x = 1\,\,\, \Rightarrow \,\,\,95 - 7x = 88\,\,{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,3\, \hfill \\ x = 2\,\,\, \Rightarrow \,\,\,95 - 7x = {\text{odd}}\,\,\left( {{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,2} \right) \hfill \\ x = 3\,\,\, \Rightarrow \,\,\,95 - 7x = 74\,\,{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,3 \hfill \\ x = 4\,\,\, \Rightarrow \,\,\,95 - 7x = {\text{odd}}\,\,\left( {{\text{not}}\,\,{\text{divisible}}\,\,{\text{by}}\,\,2} \right) \hfill \\ x = 5\,\,\, \Rightarrow \,\,\,95 - \boxed{7x = 35} = {\text{60}}\,\,\underline {{\text{divisible}}\,\,{\text{by}}\,\,6!} \hfill \\ \end{gathered}$ The above follows the notations and rationale taught in the GMATH method. Regards, fskilnik. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1776 messages Followed by: 14 members Upvotes: 43 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 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: 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. Letâ€™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 = 11/7â€¦ this does not work When p is 13, we have: c = 17/7... this does not work When p is 12, we have: c = 23/7â€¦ 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: Letâ€™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, letâ€™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 • FREE GMAT Exam Know how you'd score today for$0

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