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If x is a positive integer less than 10, is z greater than [#permalink]
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24 Feb 2012, 16:50
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If x is a positive integer less than 10, is z greater than the average (arithmetic mean) of x and 10 ? (1) The positive difference between z and x is greater than the positive difference between z and 10. (2) z = 5x
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Re: If x is a positive integer less than 10, is z greater than [#permalink]
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24 Feb 2012, 22:15
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If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?Given: \(0<x<10\). Question: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? > \(2z>10+x\)? (1) The positive difference between z and x is greater than the positive difference between z and 10 > \(zx>z10\), which means that the distance between z and x is greater than the distance between z and 10: xaverage10 (average of x and 10 halfway between x and 10). Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES. Sufficient. (2) z = 5x > is \(2z>10+x\)? > is \(10x>10+x\)? > is \(x>\frac{10}{9}\). We don't now that. Not sufficient. (we've gotten that if \(x>\frac{10}{9}\), then the answer to the question is YES, but if \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.) Answer: A. Similar questions to practice: https://gmatclub.com/forum/ifxisapo ... 67734.html ( OG) https://gmatclub.com/forum/ifyisane ... 95138.htmlhttps://gmatclub.com/forum/ifxisapo ... 31322.htmlhttps://gmatclub.com/forum/ifaisapo ... 05650.htmlhttps://gmatclub.com/forum/ifxandza ... 55651.htmlHope it helps.
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Re: If x is a positive integer less than 10, is z greater than [#permalink]
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25 Feb 2012, 03:07
Thanks Bunuel  I am struggling to understand this: Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average.
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Re: If x is a positive integer less than 10, is z greater than [#permalink]
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25 Feb 2012, 03:17
enigma123 wrote: Thanks Bunuel  I am struggling to understand this:
Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. xaverage10 Just try to place z in the green or blue area and you'll see that the distance between z and x will be greater than the distance between z and 10; Now, place z in the red area (or to the left of x) and you'll see that the distance between z and x will be less than the distance between z and 10. So we have that in order the distance between z and x to be greater than the distance between z and 10 it must be either in blue or red areas so in any case z is more than the average. Hope it's clear.
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Re: If x is a positive integer less than 10, is z greater than [#permalink]
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27 Feb 2012, 22:12
Hi, while solving statement A, I took the following critical points to solve the eqn zx>z10 z<x : discard x<z<10 : True .. Also the answer z>10: solving this I got x<10. which is information given in the question stem. I dint know how this can answer the ques. hence, considered A as insufficient .. Pl help Bunuel wrote: If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?Given: \(0<x<10\). Question: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? > \(2z>10+x\)? (1) The positive difference between z and x is greater than the positive difference between z and 10 > \(zx>z10\), which means that the distance between z and x is greater than the distance between z and 10: xaverage10 (average of x and 10 halfway between x and 10). Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES. Sufficient. (2) z = 5x > is \(2z>10+x\)? > is \(10x>10+x\)? > is \(x>\frac{10}{9}\). We don't now that. Not sufficient. (we've gotten that if \(x>\frac{10}{9}\), then the answer to the question is YES, but if \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.) Answer: A. Similar question: 600levelquestion95138.htmlHope it helps.



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Re: If x is a positive integer less than 10, is z greater than [#permalink]
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27 Feb 2012, 23:07
devinawilliam83 wrote: Hi, while solving statement A, I took the following critical points to solve the eqn zx>z10 z<x : discard x<z<10 : True .. Also the answer z>10: solving this I got x<10. which is information given in the question stem. I dint know how this can answer the ques. hence, considered A as insufficient .. Pl help Bunuel wrote: enigma123 wrote: If x is a positive integer less than 10, is z less than the average (arithmetic mean) of x and 10 ?
(1) The positive difference between z and x is greater than the positive difference between z and 10. (2) z = 5x
Any idea guys how come the answer is A? If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?Given: \(0<x<10\). Question: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? > \(2z>10+x\)? (1) The positive difference between z and x is greater than the positive difference between z and 10 > \(zx>z10\), which means that the distance between z and x is greater than the distance between z and 10: xaverage10 (average of x and 10 halfway between x and 10). Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES. Sufficient. (2) z = 5x > is \(2z>10+x\)? > is \(10x>10+x\)? > is \(x>\frac{10}{9}\). We don't now that. Not sufficient. (we've gotten that if \(x>\frac{10}{9}\), then the answer to the question is YES, but if \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.) Answer: A. Similar question: 600levelquestion95138.htmlHope it helps. You don't need to work with absolute values here. Again, in order the distance between z and x to be greater than the distance between z and 10 (in order first statement tot hold true) z MUST be to the right of the average, so more than it.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: If x is a positive integer less than 10, is z greater than [#permalink]
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21 Jun 2015, 01:49
Bunuel wrote: If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?Given: \(0<x<10\). Question: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? > \(2z>10+x\)? (1) The positive difference between z and x is greater than the positive difference between z and 10 > \(zx>z10\), which means that the distance between z and x is greater than the distance between z and 10: xaverage10 (average of x and 10 halfway between x and 10). Now, as the distance between z and x is greater than the distance between z and 10, then z is either in the blue area, so more than average OR in the green area, so also more than average. Answer to the question YES. Sufficient. (2) z = 5x > is \(2z>10+x\)? > is \(10x>10+x\)? > is \(x>\frac{10}{9}\). We don't now that. Not sufficient. (we've gotten that if \(x>\frac{10}{9}\), then the answer to the question is YES, but if \(0<x\leq{\frac{10}{9}}\), then the answer to the question is NO.) Answer: A. Similar question: 600levelquestion95138.htmlHope it helps. If the question said Z is less than the average of X & 10, would be get a yes answer only from the second statement as X<10/9 which would be 1 and avg would be 5.5. Z would be 5 and less than average?



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