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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 ## Arithmetic mean ##### This topic has 1 expert reply and 27 member replies Goto page • 1, • 2 If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ? (1) On the number line, x is closer to -8 than it is to y. (2) x = 4y Source:Grockit _________________ --Anand-- Senior | Next Rank: 100 Posts Joined 10 Apr 2010 Posted: 44 messages IMO D. OA? Legendary Member Joined 30 May 2010 Posted: 1893 messages Followed by: 6 members Upvotes: 215 selango wrote: If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ? (1) On the number line, x is closer to -8 than it is to y. (2) x = 4y Source:Grockit --------------------Avg--------------------- -8 X Y On the number line if X is closer to -8 then X is definitely less than the average of y and -8 SUFF (2) x = 4y is 4y > (y-8)/2 is 8y > y-8 is 7y > -8 is y> -8/7 Hence when y> -8/7, the answer is YES and when y < -8/7 answer is NO INSUFF pick A _________________ "Once you start working on something, don't be afraid of failure and don't abandon it. People who work sincerely are the happiest." Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC) Senior | Next Rank: 100 Posts Joined 18 Oct 2010 Posted: 42 messages IMO A[/spoiler] Master | Next Rank: 500 Posts Joined 19 Jul 2010 Posted: 126 messages Upvotes: 6 kvcpk wrote: selango wrote: If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ? (1) On the number line, x is closer to -8 than it is to y. (2) x = 4y Source:Grockit --------------------Avg--------------------- -8 X Y On the number line if X is closer to -8 then X is definitely less than the average of y and -8 SUFF (2) x = 4y is 4y > (y-8)/2 is 8y > y-8 is 7y > -8 is y> -8/7 Hence when y> -8/7, the answer is YES and when y < -8/7 answer is NO INSUFF pick A y is a negative number greater than -8 implies that y=-1 ... - 7... case1: avg of -1 and -8 = -4.5... x is closer to - 8 means that x should be <-4.6... hence x is less... case 2: avg of -7 and - 8 = -7.5... x is closer to -8 means that x should be <-4.6... in this case x can be > - 7.5 and < - 4.6... A cannot give the answer... wat is the OA... please lemme know if my understanding is incorrect... Master | Next Rank: 500 Posts Joined 24 Nov 2009 Posted: 163 messages Followed by: 4 members Upvotes: 13 Test Date: 7/8 Target GMAT Score: 760 GMAT Score: 660 OA?? IMO it's A. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1434 messages Followed by: 32 members Upvotes: 59 Quote: If y is a negative number greater than -8, is x greater than the average (arithmetic mean) of y and -8 ? (1) On the number line, x is closer to -8 than it is to y. (2) x = 4y Hi there! We know -8 < y < 0, and we must focus on the question: x > (y+(-8))/2 ? (1) SUFFICIENT: Draw a real line with "points" -8 (left), y (right) and their middle-point (say) M. The question is, therefore, x > M ? From sttm (1) we know that x is less than M, because it is (-8 or less) or (between -8 and M, M excluded). (2) INSUFFICIENT: Please note that the question is equivalent to y < 2x+8 or y < 8(y+1) or (y+1)/y < 1/8 ? (Remember that y<0) > Take y negative but (below and) nearer 0, say y = -1. We get (y+1)/y = 0/-1 = 0 answering positively. > Take y negative but (above and) nearer -8, say y = -7. We get (y+1)/y = -6/-7 = 6/7 answering negatively. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Senior | Next Rank: 100 Posts Joined 13 Sep 2010 Posted: 86 messages Followed by: 2 members Upvotes: 29 Test Date: 04/23/2011 Target GMAT Score: 740 GMAT Score: 710 1. Statement #1 - "On the number line, x is closer to -8 than it is to y". y can be between -1 and -7 and the average would always be middle point of the two (e.g. if y=-2 then average = -5, y=-6, average=-7 etc.) given that x is closer to -8 than y then this means that it is more negative than the average of -8 and y. hence it is smaller than the average (which is the middle point). Hence sufficient data to say that answer is NO 2. Statement #2 - x = 4y this means that whatever y is, x is 4 times as negative (e.g. if y=-6, x = -24) this means that it is smaller than y foresure. now average of -8 and y = (-8+y)/2 ==> -4+y/2 ==> between -4 and -8 somewhere depending on y if y == -1 then x = -4 and average = -4.5 but if y = -6 then x = -24 and average = -7 so insufficient Newbie | Next Rank: 10 Posts Joined 10 May 2011 Posted: 4 messages Upvotes: 1 I am not able to get the solution here. Can anybody help me, where I am wrong?? How A is sufficient? Our problem can be rephrased as Is x>(y-8)/2? 1.On the number line, x is closer to -8 than it is to y. So I took x = -7(which is closer to -8) and y = - 2 Now, this will give me - -7 > (-2-8)/5 -> -7 > -2 -> False. then put x= -5(which is closer to -8) and y = -3 -5 > (-3-8)/2 -> -5 > -5.5 -> True How can A be sufficient. Can anybody help me? Senior | Next Rank: 100 Posts Joined 13 Mar 2011 Posted: 99 messages HRIMJAM, TAKE A LOOK AT STATEMENT 1 AGAIN. I HAD THE SAME ANSWER AS YOU BUT AFTER A FEW MINUTES I REALIZED MY REASONING WAS WRONG. 1.On the number line, x is closer to -8 than it is to y. THE NUMBERS YOU SELECTED DO NOT SATISFY THE STATEMENT. "then put x= -5(which is closer to -8) and y = -3 -5 > (-3-8)/2 -> -5 > -5.5 -> True " HERE X (-5) IS 3 AWAY FROM -8 AND X(-5) IS ONLY 2 AWAY FROM Y(-3). THE STATEMENT IS SAYING THAT THE DIFFERENCE BETWEEN X AND -8 IS LESS THAN THE DIFFERENCE X AND Y ...HERE (-5)X - 8 = 3 AND (-5) - 3 = 2 ... CLEARLYTHESE NUMBERS DO NOT SATISFY THE EQUATION AS X IS CLOSER TO Y THAN IT IS TO -8 ... WE NEED TO USE DIFFERENT #'S TO SATISFY THE EQUATION. HOPE THIS HELPS[/quote] Master | Next Rank: 500 Posts Joined 05 May 2011 Posted: 135 messages Followed by: 1 members Upvotes: 4 Test Date: 16 Aug 2011 GMAT Score: 700 +1 for A . lets see if i can draw this one . ------------(-8)---x--(am)--y-------(0)-------- hope this answers the question For B. ( insufficient , just plug positive and negative values for y . you ll know Master | Next Rank: 500 Posts Joined 11 Sep 2010 Posted: 100 messages Upvotes: 2 DELETE Newbie | Next Rank: 10 Posts Joined 22 May 2010 Posted: 9 messages Upvotes: 2 Test Date: 18th May 2012 Target GMAT Score: 740 GMAT Score: 650 Guys... its actually very simple...when you draw the exact number line.... option A will be easily solved...whether yes or no... Option B : just try taking any two numbers..eg -4 and 2 as Y , in both cases ...X will be either less or greater than the mean.... Hope it helps someone..! _________________ Raging Bull If you never try ..you will never know ..what you're worth ! Coldplay Senior | Next Rank: 100 Posts Joined 27 Oct 2010 Posted: 72 messages Followed by: 1 members Upvotes: 2 hrimahajan wrote: I am not able to get the solution here. Can anybody help me, where I am wrong?? How A is sufficient? Our problem can be rephrased as Is x>(y-8)/2? 1.On the number line, x is closer to -8 than it is to y. So I took x = -7(which is closer to -8) and y = - 2 Now, this will give me - -7 > (-2-8)/5 -> -7 > -2 -> False. then put x= -5(which is closer to -8) and y = -3 -5 > (-3-8)/2 -> -5 > -5.5 -> True How can A be sufficient. Can anybody help me? Hi hrimahajan, There are two mistakes which I find. 1. The data which you have taken y = -3 and x = -5 is wrong. The mean of -8 and -3 is -5.5, so the acceptable range of x is -8 < x < -5.5 . So x = -5 value does not fit in here. Another way of understanding the problem is that the mean is equidistant from both the numbers, say A & B. So if a third number(C) is closer to one of these numbers(A,B), so it can either be greater or lesser than the mean. It cannot be both at the same time. 2. Second mistake hrimahajan wrote: -7 > (-2-8)/5 -> -7 > -2 -> False. Here you have divided (-2-8) by five, it should be by 2 to take the mean. Hope this helps, Best Regards, JOHN Newbie | Next Rank: 10 Posts Joined 13 Aug 2011 Posted: 1 messages Digging a question from past. "x is closer to -8 than y" - Doesnt this mean that x can lie on either side of -8 while still being closer to 08 than y. ? • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 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 • Award-winning private GMAT tutoring Register now and save up to$200

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