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If x is a positive number less than 10, is z greater than th

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

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New post Updated on: 17 Dec 2017, 22:48
4
8
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

46% (02:20) correct 54% (02:41) wrong based on 448 sessions

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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/if-x-is-a-po ... 67734.html

Originally posted by rianah100 on 08 Nov 2005, 03:40.
Last edited by Bunuel on 17 Dec 2017, 22:48, 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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New post 08 Nov 2005, 04:48
1
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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New post 08 Nov 2005, 05:05
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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New post 08 Nov 2005, 05:12
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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New post 08 Nov 2005, 05:17
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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New post 08 Nov 2005, 06:27
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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New post 08 Nov 2005, 06:43
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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New post 08 Nov 2005, 06:55
I understand it in the way, that z is closer to 10 as x IS... (10-z < 10-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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New post 08 Nov 2005, 10:37
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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New post 29 Apr 2010, 15:08
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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New post 30 Apr 2010, 09:01
1
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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 --> \(|10-z|<|z-x|\) --> as z is closer to 10 than it is to x, then z>x, so \(|z-x|=z-x\) --> two cases for 10-z:

A. \(z<10\) --> \(|10-z|=10-z\) --> \(|10-z|<|z-x|\) becomes: \(10-z<z-x\) --> \(2z>10+x\). Answer to the question YES.

B. \(z\geq{10}\) --> \(|10-z|=z-10\) --> \(|10-z|<|z-x|\) becomes: \(z-10<z-x\) --> \(z>10\) --> 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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New post 11 Feb 2015, 04:07
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 10

stated in the stem: x<10

STATEMENT 1) On the number line, z is closer to 10 than it is to x.

M-midpint
case1
---------------------X----------M--z------10--------------------

case 2
---------------------X----------M---------10---z-----------------

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

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

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New post 24 Feb 2015, 11:27
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.

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

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New post 24 Feb 2015, 11:32
freesoybean wrote:
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.

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If x = 8 and z = 9, then z = 9 is NOT closer to 10 than it (z) is it x = 8. 9 is exactly in the middle of 8 and 10.
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Re: If x is a positive number less than 10, is z greater than th  [#permalink]

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New post 17 Dec 2017, 22:49
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OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-is-a-po ... 67734.html
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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

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Re: If x is a positive number less than 10, is z greater than th &nbs [#permalink] 17 Dec 2017, 22:49
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