• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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 ## At a certain fruit stand, the price of each apple is 40 ##### This topic has 5 expert replies and 0 member replies ### Top Member ## At a certain fruit stand, the price of each apple is 40 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 OA E Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1697 messages Followed by: 28 members Upvotes: 470 BTGmoderatorDC wrote: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 OA E Source: Official Guide Say Mary x numbers of apples and y numbers of oranges. Thus, x +y = 10 and 40x + 60y = 56*10 40x + 60y = 560 Say Mary put back p numbers of oranges, thus, we have 40x + 60y - 60 p = 52(10 - p) 560 - 60 p = 520 - 52p p = 5. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Chennai | GMAT Prep Himayatnagar | GRE Prep Hyderabad | Bangalore GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12534 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 It turns out that the cost per apple is irrelevant. Here's why: The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents So, (total value of all 10 pieces of fruit)/10 = 56 cents This means, total value of all 10 pieces of fruit = 560 cents How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? Let x = the number of oranges to be removed. Each orange costs 60 cents, so the value of the x oranges to be removed = 60x This means 560 - 60x = the value of the REMAINING fruit Also, if we remove x oranges, then 10 - x = the number of pieces of fruit REMAINING. We want the REMAINING fruit to have an average value of 52 cents. We can write: (value of REMAINING fruit)/(number of pieces of fruit REMAINING) = 52 Rewrite as: (560 - 60x)/(10 - x) = 52 Multiply both sides by (10-x) to get: 560 - 60x = 52(10 - x) Expand right side to get: 560 - 60x = 520 - 52x Add 60x to both sides: 560 = 520 + 8x Subtract 520 from both sides: 40 = 8x Solve: x = 5 Answer: 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 25 May 2010 Posted: 15019 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 The original total cost of the 10 pieces of fruit = 10*56 = 560. According to the answers, after 1, 2, 3, 4, or 5 oranges are removed -- so that 9, 8, 7, 6, or 5 pieces of fruit remain -- the average cost per piece decreases to 52. Since the original total cost is a multiple of 10, and the price per orange is a multiple of 10, the new total cost after the oranges are removed must also be a multiple of 10. Only answer choice E will yield a new total cost that is a multiple of 10: 5 remaining pieces of fruit with an average price of 52 cents = 5*52 = 260. The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1105 messages Followed by: 29 members Upvotes: 59 BTGmoderatorDC wrote: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Source: Official Guide $$? = b\,\,\left( {{\rm{back}}} \right)$$ $$10 \to 10 - b\,\,{\rm{fruits}}\,\,\,\left\{ \matrix{ \,{\rm{apples}}\,\, = a\,\,{\rm{units}}\,\,,\,\,40\,\,{\rm{cents}}\,\,{\rm{each}} \hfill \cr \,{\rm{oranges}}\,\,{\rm{ = }}\,\,10 - a\,\,\, \to \,\,\,{\rm{10}} - b - a\,\,{\rm{units}}\,\,,\,\,60\,\,{\rm{cents}}\,\,{\rm{each}} \hfill \cr} \right.$$ $$\sum\nolimits_{10} {\,\, = \,\,\,10 \cdot 56 = 560\,\,\,{\rm{cents}}\,\,\,\,\,\,\left( {{\rm{homogeneity}}\,\,{\rm{nature}}\,\,{\rm{of}}\,\,{\rm{the}}\,\,{\rm{average}}} \right)}$$ $$\sum\nolimits_{10 - b} {\,\, = \,\,\,\left( {10 - b} \right) \cdot 52\,\,\,{\rm{cents}}\,\,\,\,\,\,\left( {{\rm{homogeneity}}\,\,{\rm{nature}}\,\,{\rm{of}}\,\,{\rm{the}}\,\,{\rm{average}}} \right)}$$ $$\sum\nolimits_{10 - b} {\,\, + b \cdot 60\,\,\, = } \,\,\,\,\sum\nolimits_{10} {\,\,\,\,\, \Rightarrow \,\,\,\,\,\,52\left( {10 - b} \right) + 60b = 560\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\, \ldots \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = b = 5}$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1793 messages Followed by: 14 members Upvotes: 43 BTGmoderatorDC wrote: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 We can let the number of apples = x and the number of oranges = y. Using these variables we can create the following two equations: 1) x + y = 10 Using the formula average = sum/quantity, we have: 2) (40x + 60y)/10 = 56 Letâ€™s first simplify equation 2: 40x + 60y = 560 4x + 6y = 56 2x + 3y = 28 Isolating for y in equation 1 gives us: y = 10 - x. Since y = 10 - x, we can substitute 10 - x for y in the equation 2x + 3y = 28. This gives us: 2x + 3(10 - x) = 28 2x + 30 - 3x = 28 -x = -2 x = 2 Since x + y = 10, then y = 8. We thus know that Mary originally selected 2 apples and 8 oranges. We must determine the number of oranges that Mary must put back so that the average price of the pieces of fruit that she keeps is 52Â¢. We can let n = the number of oranges Mary must put back. Letâ€™s use a weighted average equation to determine the value of n. [40(2) + 60(8-n)]/(10 - n) = 52 (80 + 480 - 60n)/(10 - n) = 52 560 - 60n = 520 - 52n 40 = 8n 5 = n Thus, Mary must put back 5 oranges so that the average cost of the fruit she has kept would be 52 cents. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 68 first replies
2 fskilnik@GMATH 54 first replies
3 Brent@GMATPrepNow 48 first replies
4 GMATGuruNY 31 first replies
5 Rich.C@EMPOWERgma... 27 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

110 posts
2 Max@Math Revolution

Math Revolution

94 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

93 posts
4 Jay@ManhattanReview

Manhattan Review

84 posts
5 GMATGuruNY

The Princeton Review Teacher

77 posts
See More Top Beat The GMAT Experts