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If x is a positive number less than 10, is z greater than th [#permalink]
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This one is from GMATPREP as well. DS: If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10) (1) on the number line, z is closer to 10 than x. (2) z=5x I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B. Thanks! MODERATOR: EDITED THE QUESTION.
ORIGINAL QUESTION: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 OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/ifxisapo ... 67734.html
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Originally posted by rianah100 on 08 Nov 2005, 04:40.
Last edited by Bunuel on 17 Dec 2017, 23:48, edited 4 times in total.
EDITED THE QUESTION.



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 05:48
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I think it is C.
let's look at I) z is closer to 10 than x. and x is less than 10.
lest pick number if x= 1 and z=9 then (x+10)/2 = 5.5 which is less than z
how ever if x=1 and z=2 then (x+10)/2 = 5.5 which is more than z
simillarly using II) if x = 1 and z=5 then (x+10)/2 = 5.5 which is more than z
and if x = 3 and z=15 then (x+10)/2 = 6.5 which is less than z
but if we combine the both
z is greater than (x+10)/2
So the answer is C.
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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 06:05
Nakib,
Looks like you are leaving out the fact that z is closer to 10 than to x.



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 06:12
rianah100 wrote: This one is from GMATPREP as well. DS:
If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)
(1) on the number line, z is closer to 10 than x. (2) z=5x
I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.
Thanks!
uhm, the bold part is easily misunderstood ....some can understand that z is closer to 10 than to x ...others may think: z is closer to 10 than x is . IMO, it is the latter one . They are totally different and thus lead to completely different outcomes.



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 06:17
rianah100 wrote: Nakib, Looks like you are leaving out the fact that z is closer to 10 than to x.
If z is closer to 10 than to x, then answer will be obviously D.
but If z is closer to 10 than x, the answer will be C.
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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 07:27
I'm getting totally another answer: E
Number picking:
1 and 2 alone are clearly not sufficient.
But BOTH TOGETHER are also not sufficient:
x=1, z=5 (z closer to 10 and z = 5x) > 5 < 5.5
BUT x=3, z=15 (conditions are also fullfilled) > 15 > 6.5
It's not told that z < 10!!!
> E
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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 07:43
lazy_k wrote: I'm getting totally another answer: E
Number picking:
1 and 2 alone are clearly not sufficient.
But BOTH TOGETHER are also not sufficient:
x=1, z=5 (z closer to 10 and z = 5x) > 5 < 5.5
BUT x=3, z=15 (conditions are also fullfilled) > 15 > 6.5
It's not told that z < 10!!!
> E
in which way do you understand statement 1?!! ...uhm, I'm not sure with the statement as my above post pointed out why ..



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 07:55
I understand it in the way, that z is closer to 10 as x IS... (10z < 10x)
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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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08 Nov 2005, 11:37
rianah100 wrote: This one is from GMATPREP as well. DS:
If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)
(1) on the number line, z is closer to 10 than x. (2) z=5x
I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.
Thanks!
I don't know why there is an 'n' in the stem. Anyway.. I got B.
(1) assume x = 8, z = 8.1.
(x+10)/2 = 9
Hence z < (x+10)/2
If x = 1 and z is 8.
z > (x+10)/2
since (x +10)/2 = 5.5.
so insuff.
(2) If z = 5x
stem can be is 5x > (x+10)/2
which is 5x > x/2 + 5 which is always true.
Hence B answers the Q.



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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29 Apr 2010, 16:08
If x = 1, z = 5, answer to the question is NO. If x= 4, z = 20, answer to the question is YES. Why is the answer B?
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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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30 Apr 2010, 10:01
vscid wrote: If x = 1, z = 5, answer to the question is NO. If x= 4, z = 20, answer to the question is YES.
Why is the answer B? Edited the question. the original question is below: 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. \(z<10\) > \(10z=10z\) > \(10z<zx\) becomes: \(10z<zx\) > \(2z>10+x\). Answer to the question YES. B. \(z\geq{10}\) > \(10z=z10\) > \(10z<zx\) becomes: \(z10<zx\) > \(z>10\) > now, as \(z>10\), then \(2z>20\) 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.
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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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22 Oct 2010, 21:53
A it is..



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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11 Feb 2015, 05:07
rianah100 wrote: This one is from GMATPREP as well. DS:
If x<10 and n is a positive integer, is z>(x+10)/2? (average of x and 10)
(1) on the number line, z is closer to 10 than x. (2) z=5x
I am getting (D) as answer because (1) seems to be good enough info to conclude that z>(x+10)/2. Ofcourse, it is clear that (2) is ok too. But the answer is B.
Thanks!
MODERATOR: EDITED THE QUESTION.
ORIGINAL QUESTION:
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 Here's my take the question simply asks that is z>than the midpoint of x and 10stated in the stem: x<10 STATEMENT 1) On the number line, z is closer to 10 than it is to x. Mmidpint case1 XMz10 case 2 XM10z In any of the case z is greater than the midpoint as it is closer to 10 than x and if it is on the midpoint then it is at equal distance from x and 10. so SUFFICIENT. STATEMENT 2) z=5x if X=1 then Z=5 but average of x and 10=5.5 so Z<(X+10)/2 :NO if X=4 then Z=20 but average of x and 10=7 so Z>(X+10)/2 :YES so NOT SUFFICIENT. ANSWER A



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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24 Feb 2015, 12:27
Please help me with statement (1). If x=8, and z=9, which z is closer to 10 on the number line, then 2(9)= 8 + 20.... So answer is "no". Every other scenarios make 2(z) > x+10 as "yes".... So I got this statement as Insufficient. What did I do wrong? Thanks. Posted from GMAT ToolKit



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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24 Feb 2015, 12:32



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Re: If x is a positive number less than 10, is z greater than th [#permalink]
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