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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 ## In a certain quiz that consists of 10 questions, each questi ##### This topic has 3 expert replies and 1 member reply ## In a certain quiz that consists of 10 questions, each questi In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth? A. 18 B. 24 C. 26 D. 32 E. 44 Is there a strategic approach to this question? Any experts help please? ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15388 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 ardz24 wrote: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth? A. 18 B. 24 C. 26 D. 32 E. 44 Since each question is worth 4 more points than the preceding question, the point values constitute an EVENLY SPACED SET. For any evenly spaced set: Average = Median. Since the 10 point values sum to 360, we get: Average = median = 360/10 = 36. We can PLUG IN THE ANSWERS, which represent the 3rd value. Since there are 10 values, the median = the average of the 5th and 6th values. When the correct answer is plugged in, the average of the 5th and 6th values = 36. B: 24 Here, the 3rd through 6th values are as follows: 24, 28, 32, 36. The values in red will yield an average that is TOO SMALL. Thus, a greater answer choice is needed. Eliminate A and B. D: 32 Here, the 3rd through 6th values are as follows: 32, 36, 40, 44. The values in red will yield an average that is TOO BIG. Thus, a smaller answer choice is needed. Eliminate D and E. The correct answer is C. C: 26 Here, the 3rd through 6th values are as follows: 26, 30, 34, 38. Average of the 5th and 6th values = (34+38)/2 = 72/2 = 36. Success! _________________ 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 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth? A. 18 B. 24 C. 26 D. 32 E. 44 Is there a strategic approach to this question? Any experts help please? Hi ardz24, Let's take a look at your question. Each question after the first is worth 4 points more than the preceding question, so we can write the sequence of points as: x, x+4, x+8, x+12, ... x+36 (10 questions total) This seems to be an arithmetic sequence with: $$n=10,\ d=4$$ The 10 questions on the quiz are worth a total of 360 points, which represents that the sum of 10 terms of the arithmetic sequence is 360, i.e. $$S=360$$ We know that the sum of the arithmetic sequence can be represented using the formula: $$S=\frac{n}{2}\left[2a_1+\left(n-1\right)d\right]$$ $$360=\frac{10}{2}\left[2a_1+\left(10-1\right)4\right]$$ $$360=5\left[2a_1+\left(9\right)4\right]$$ $$360=5\left[2a_1+36\right]$$ $$\frac{360}{5}=\left[2a_1+36\right]$$ $$72=\left[2a_1+36\right]$$ $$2a_1=72-36$$ $$2a_1=36$$ $$a_1=\frac{36}{2}=18$$ a1 represents the first term in the sequence, i.e. points of the first question. Points of second question = 18 + 4 = 22 Points of the third question = 22 + 4 = 26 Therefore Option C is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 ardz24 wrote: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth? A. 18 B. 24 C. 26 D. 32 E. 44 The first question is worth x, the 2nd worth x + 4, the 3rd worth x + 2(4) = x + 8, ..., the 10th is worth x + 9(4) = x + 36. Since we have a set of evenly-spaced numbers, the average is (x + x + 36)/2 = (2x + 36)/2 = x + 18. Since sum = average * quantity we have: 360 = (x + 18) * 10 36 = x + 18 18 = x The first question is worth x = 18 points. So the third question is worth x + 8 = 18 + 8 = 26 points. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews Senior | Next Rank: 100 Posts Joined 18 Dec 2018 Posted: 31 messages Let the first question is worth â€˜aâ€™ points. Then, Second question is worth a + 4 points, third of worth (a + 4 + 4) = a + 8 points. So, the sum of the series becomes a + a + 4 + a + 8 + a + 12 â€¦â€¦â€¦ upto 10 terms = 10a + 4 + 8 + 12 + â€¦â€¦. upto 9 terms Sum = 10a + Sum of A.P with first term 4 and common difference 4. Sum = 10a + 180 = 360 a = 18 Third question is worth a + 8 points = 18 + 8 = 26 points. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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