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If x is a positive number less than 10, is z greater than [#permalink]
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08 Nov 2009, 21:32
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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? (1) On the number line, z is closer to 10 than it is to x (2) z = 5x
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Last edited by Bunuel on 23 Mar 2012, 01:57, edited 1 time in total.
Edited the question and added the OA



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Re: x is a positive number less than 10 [#permalink]
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08 Nov 2009, 21:37
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amitgovin wrote: if x is a positive number less than 10 is z greater than the average of x and 10?
1) on the number line, z is closer to 10 than it is to x
2) z=5x
********************************* please explain. thanks. IMO A 1) The distance between Z and 10 is lesser than distance between Z and X. So Z is greater than the center of the line segment X to 10. That means Z is greater than the average of X and 10. Sufficient. 2) Z = 5X If X=1, then Z = 5. Avg of X and 10 = 5.5. So Z<Avg. If X=2, then Z = 10. Avg of X and 10 = 6. So Z>Avg. Statement is Insufficient.



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Re: x is a positive number less than 10 [#permalink]
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09 Nov 2009, 08:01
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Yup A.
stmt1: 10z < zx , here x and z are +ve ( as Z is closer to 10 than to x, and x is +ve ) 10z < zx => z > Av of 10 and x.
stmt2: x=1, z=5, 5 < 5.5 x=2, z=10, 10 > 6



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Re: DS Problem [#permalink]
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amp0201 wrote: Hi,
Can anyone please suggest me the solution. I arrived at B, but unfortunately it was wrong. Thanks. If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?Given: \(0<x<10\). Q: is z greater than the average of x and 10? Or: is \(z>\frac{10+x}{2}\)? > \(2z>10+x\)? (1) On the number line, z is closer to 10 than it is to x > \(10z<zx\) > as z is closer to 10 than it is to x, then z>x, so \(zx=zx\) > two cases for 10z: A. \(z\leq{10}\) > \(10z=10z\) > \(10z<zx\) becomes: \(10z<zx\) > \(2z>10+x\). Answer to the question YES. B. \(z>{10}\) > in this case \(2z>20\) and as \(x<10\), then \(x+10<20\), hence \(2z>10+x\). Answer to the question YES. OR another approach: Given: x average 10  (average of x and 10 halfway between x and 10). Now, as z is closer to 10 than it (z) is to x, 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.html?hilit=number%20line%20closer
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Re: DS Problem [#permalink]
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19 Apr 2011, 14:07
hello Bunuel,
how did u get Z>10 ? above in red. from your inequality i got 10>x
thx



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Re: x is a positive number less than 10 [#permalink]
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19 Apr 2011, 16:29
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If x is a positive number less than 10 is z greater than the average of x and 10? 1) on the number line, z is closer to 10 than it is to x 2) z=5x Drawing a number line can help you see the answer quickly. Attachment:
Ques2.jpg [ 4.71 KiB  Viewed 20279 times ]
So x is somewhere between 0 and 10 and average of x and 10 is between x and 10. z can be in any of the 5 regions as shown. 1) on the number line, z is closer to 10 than it is to x In which regions is z closer to 10 than to x? Only the two rightmost regions. There, z is greater than the average of x and 10. Sufficient. 2) z = 5x Put x = 1 z = 5 but average of 1 and 10 is 5.5 so z is less than the average. Actually, this is where I stop and mark (A) as the answer without checking to see if there is a value of x for which z is greater than the average. Think, why?
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Re: x is a positive number less than 10 [#permalink]
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19 Apr 2011, 21:50
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@Karishma We stop in (2) because we've found something contrary to the answer in (1), while in earlier choice we had a definite answer. So the answer can't be B,C,D oe E. The goal in DS is to get No as answer first for the choices, or to find the inconsistencies. (1) 0xAv10z 0xAvz10 From the diagram above, it's evident that the answer is Yes (2) is insufficient if x is very close to 0, then z may not be closer to 10 e.g, x = 0.1, then z = 0.5 if x = 2, then z = 10 (greater than average) Answer  A
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Re: x is a positive number less than 10 [#permalink]
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20 Apr 2011, 04:28
subhashghosh wrote: @Karishma We stop in (2) because we've found something contrary to the answer in (1), while in earlier choice we had a definite answer. So the answer can't be B,C,D oe E.
The goal in DS is to get No as answer first for the choices, or to find the inconsistencies.
(1) 0xAv10z
0xAvz10
From the diagram above, it's evident that the answer is Yes
(2) is insufficient
if x is very close to 0, then z may not be closer to 10
e.g, x = 0.1, then z = 0.5
if x = 2, then z = 10 (greater than average)
Answer  A Yes, it is not possible to get inconsistent answers from the two statements i.e. we cannot have 'Yes. z is greater. Sufficient Alone.' from statement 1 and 'No. z is smaller. Sufficient Alone.' from statement 2. From statement 2, we will either get 'Yes. z is greater. Sufficient Alone.' or 'z can be smaller or greater so not sufficient alone' From statement 1, we got that z is greater than the average. From statement 2, we tried a value and we got that z is less than the average. Then there must be a value for which z is greater than the average too in statement 2. We don't even need to try it. Definitely statement 2 alone is not sufficient and answer is (A).
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If x is a positive number less than 10, is z greater than th [#permalink]
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24 Apr 2012, 09:18
If x is a positive number less than 10, is z greater than the average(Arithmetic mean) of x and 10? 1. On the number line, z is closer to 10 than it is to x. 2. z = 5x.
Please explain your answer choice. Thanks



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Re: If x is a positive number less than 10, is z greater than [#permalink]
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25 Apr 2012, 17:22
just wondering about statement 1, am i misunderstanding the question?
"on the number line, z is closer to 10 than it is to x"
z = 11 x = 8 so z is closer to 10 than x is
is 11 > (8+10)/2 11 > (18/2) becomes 11 > 9 so the answer is YES
z = 9 x = 8 so z is closer to 10 than x is
is 9 > (8+10)/2 9 > (18/2) becomes 9 > 9 so the answer is NO
or is the question stating z is closer to 10 than z is to x? i interpreted it as z is closer to 10 than 10 is to x.



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Re: If x is a positive number less than 10, is z greater than [#permalink]
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17 Dec 2014, 16:50
Hmm...I don't understand why the answer is A.
for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient?



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Re: If x is a positive number less than 10, is z greater than [#permalink]
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17 Dec 2014, 21:01
GMATAnnihilator wrote: Hmm...I don't understand why the answer is A.
for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient? The case you are considering with z=9,x=8 then z is equidistant from x and 10 both....So this is not valid. Case 2 where z=2 ie. average of x+10 > (x+10)/2=2 or x+10=4 or x =6...But we are told x is positive number less than 10...so x=6 is not possible... Hope it is clear
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Re: If x is a positive number less than 10, is z greater than [#permalink]
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WoundedTiger wrote: GMATAnnihilator wrote: Hmm...I don't understand why the answer is A.
for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient? The case you are considering with z=9,x=8 then z is equidistant from x and 10 both....So this is not valid. Case 2 where z=2 ie. average of x+10 > (x+10)/2=2 or x+10=4 or x =6...But we are told x is positive number less than 10...so x=6 is not possible... Hope it is clear Thanks Wounded Tiger...now where do I find that facepalm emoticon. I clearly misread the question... one of more deficiencies with timed exams... This will have to do: http://vignette3.wikia.nocookie.net/car ... 1217081420



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Re: If x is a positive number less than 10, is z greater than [#permalink]
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04 Jan 2015, 10:26
Quote: Hmm...I don't understand why the answer is A.
for Statement A it states that "On the number line, z is closer to 10 than it is to x". Let's say Z is 9 and X is 8...then the average of X and 10 is 9. This equals Z... OR, let's say Z is 2 and X is 1...then Z < avg (x & 10). How can statement A be sufficient? For semplicity sake: rephrase the question into is 2z > 10 + x? 1) We know a few interesting things about x: it has to be smaller than 10; it can be a rational number; it is positive. According to this statement > if z=9 then x<8, say x=7,9 so that if 7,9 works any smaller value of x will work too. 2z=18 > 10+x. Thus z is always going to be greater than the average of 10 and x. hope it helps
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Re: If x is a positive number less than 10, is z greater than [#permalink]
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18 May 2015, 06:36
Hi Karishma,
This is regarding the number line approach that you have explained.Please share some problems where i could apply this technique.
Regards,
Kirti



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Re: If x is a positive number less than 10, is z greater than [#permalink]
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18 May 2015, 06:49
Hi Karishma,
How can we be sure that the average is not more than z.The pictorial representation suits your explanation but somewhere i am not able to convince myself with it.
Would be glad if we could discuss
Regards




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