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# For which of the above lists is the average of the numbers less than t

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6661
GMAT 1: 760 Q51 V42
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For which of the above lists is the average of the numbers less than t  [#permalink]

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14 Nov 2017, 00:16
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Difficulty:

65% (hard)

Question Stats:

66% (02:46) correct 34% (02:05) wrong based on 67 sessions

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[GMAT math practice question]

I. $$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$$
II. $$\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}$$
III. $$\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}$$
For which of the above lists is the average of the numbers less than the median of numbers?

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 For which of the above lists is the average of the numbers less than t [#permalink] ### Show Tags 14 Nov 2017, 02:48 1 MathRevolution wrote: [GMAT math practice question] I. $$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$$ II. $$\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}$$ III. $$\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}$$ For which of the above lists is the average of the numbers less than the median of numbers? A. I only B. II only C. III only D. II and III E. I, II and III LCM of 2, 3, 4, 5, 6 = 60 So multiply numerator and denominator of each fraction by 60 I. becomes => 30, 40, 45, 48, 50 Average of above numbers = 42.6 and Median=45. clearly this satisfies the required condition II. becomes => 30, 20, 15, 12, 10 Average of above numbers = 17.4 and Median = 15. Does not satisfy our condition. We can Stop here and eliminate all option. so our answer is A for the sake of testing - III becomes => 10, 20, 30, 40, 50 Average of above numbers = median of above set = 30. Hence does not satisfy given condition. Option A Math Expert Joined: 02 Aug 2009 Posts: 7112 For which of the above lists is the average of the numbers less than t [#permalink] ### Show Tags 14 Nov 2017, 06:34 MathRevolution wrote: [GMAT math practice question] I. $$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$$ II. $$\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}$$ III. $$\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}$$ For which of the above lists is the average of the numbers less than the median of numbers? A. I only B. II only C. III only D. II and III E. I, II and III Hi... If you don't want to get into lengthy calculations as it would surely eat into your time, some observations... here is a method... III. $$\frac{1}{6},\frac{2}{6},\frac{3}{6},\frac{4}{6},\frac{5}{6}$$ this is clearly an AP with difference $$\frac{1}{6}$$, so MEDIAN = MEAN so III is out ONLY A and B are without III which means either I is correct or II, but only one here you have been able to get down to TWO choices out of 5, so 50% chance to answer correctly But lets see II II. $$\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}$$ median is 1/4 and highest value is 1/2, which is1/4 away from the median 1/4, so lowest should be 0 to reach median mean = median at 0,1/4,1/2 but it is 1/6,1/4,1/2 BUT the lowest value is >0, so HIGHER values are MORE farther from the MEDIAN, so MEAN will be above median so mean>median.... so NO ans is I or the choice A but lets see why I is correct.. I. $$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}$$ these can be written as I. $$1-\frac{1}{2},1-\frac{1}{3},1-\frac{1}{4},1-\frac{1}{5},1-\frac{1}{6}$$ MEAN will be 1-(average of 1/2,1/3,1/4,1/5,1/6) this is OPPOSITE of B, here we are subtracting higher values from 1 in 1/2 and 2/3 as compared to 1/5 and 1/6 so m MEAN<median _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6661 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For which of the above lists is the average of the numbers less than t [#permalink] ### Show Tags 16 Nov 2017, 00:41 1 1 => I. The differences between the consecutive terms are $$\frac{1}{6} (= \frac{2}{3} – \frac{1}{2} )$$, $$\frac{1}{12} (= \frac{3}{4} – \frac{2}{3} )$$, $$\frac{1}{20} (= \frac{4}{5} – \frac{3}{4} )$$, and $$\frac{1}{30} (= \frac{5}{6} – \frac{4}{5})$$. As these are decreasing, the average is smaller than the median. II. The differences between consecutive terms are - $$\frac{1}{6}(= \frac{1}{3} – \frac{1}{2})$$,$$-\frac{1}{12}(= \frac{1}{4} – \frac{1}{3} )$$, - $$\frac{1}{20}(= \frac{1}{5} – \frac{1}{4})$$, and $$-\frac{1}{30}(= \frac{1}{6} – \frac{1}{5})$$. As these are increasing, the average is larger than the median. III. As the data are symmetric, the average and the median are equal. Therefore, the answer is A Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: For which of the above lists is the average of the numbers less than t &nbs [#permalink] 16 Nov 2017, 00:41
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