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

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08 Nov 2005, 04:40

5

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A

B

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D

E

Difficulty:

95% (hard)

Question Stats:

42% (03:07) correct
58% (02:26) wrong based on 310 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.

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.

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.

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.)

Re: This one is from GMATPREP as well. DS: If x<10 and n is a [#permalink]

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15 Oct 2013, 14:05

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

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10 Feb 2015, 04:56

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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 10

stated in the stem: x<10

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

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

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.

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

Expert's post

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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