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joyce
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Gmatprep - number line 08 Feb 2007, 14:21
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OA: A



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Gmatprep - number line 08 Feb 2007, 15:33
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can't Z be equal to the avg. and still closer to X than to 10?

For example, let's set x = 1. Now, the avg. of 1 + 10 is 5.5. 5.5 is closer to 10 than to X. what's to say 5.5 isn't Z?
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Gmatprep - number line 08 Feb 2007, 15:37
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joyce
OA: A
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From Question: 0 < x < 10. z > (x + 10)/2 ?

(1) 0 < x < z < 10

If x = 1, z = 9, (x+10)/2 = 5.5, 9 > 5.5 True
If x = 1, z = 2, (x+10)/2 = 5.5, 2 > 5.5 False

INSUFF.

I do not know how the OA said that (1) is suff. :cry:

(2) z = 5x

Since 0 < x < 10
0 < 5x < 50
0 < z < 50
and we know that (x+10)/2 < 10
z could be more or less than (x+10)/2 INSUFF

(1) + (2)
If x = 0.5, Z = 2.5. (0.5+10)/2 = 5.25. 2.5 > 5.25 False
If x = 1.5, Z = 7.5, (1.5+10)/2 = 5.75, 7.5 > 5.75 True

INSUFF.

I would pick E as the answer.
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Gmatprep - number line Updated on: 08 Feb 2007, 19:37
Originally posted by amorpheus on 08 Feb 2007, 16:47.
Last edited by amorpheus on 08 Feb 2007, 19:37, edited 2 times in total.
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Condition 1 says on the number line z is closer to 10 than it is to x
Meaning the distance between z and 10 has to be less than distance between z and x
Let's say z = 9 and x = 1 in this case the distance of z and 10 is 1 and z and x is 8 hence z is closer to 10 than it is to x
Now let;s find avg = x+10/2 = 1+10/2 = 5.5 z is greater than the avg.
Let's take values of z and x such that distance between z and 10 is equal to distance between z and x (though this not speficied, but just to see what it does)
z=5.5 and x=1
avg = x+10/2 = 1+10/2 = 5.5 z = avg in this case
So when the distance is equal at that time the z = avg. So or all the values where the distance between z and 10 has to be less than distance between z and x. I think z will be greater than the avg.
Hence condition 1 is sufficient.

z = 5x
Say x=1, z = 5
avg = 1+10/2 = 5.5 z < avg----1
Say x = 2, z=10
avg = 2+10/2 = 6 hence z > avg----2
From 1 and 2 Condition 2 is not sufficient.
Answer is A
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Gmatprep - number line 08 Feb 2007, 17:16
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devilmirror
joyce
OA: A

From Question: 0 < x <10> (x + 10)/2 ?

(1) 0 < x < z <10> 5.5 True
If x = 1, z = 2, (x+10)/2 = 5.5, 2 > 5.5 False

INSUFF.

I do not know how the OA said that (1) is suff. :cry:

(2) z = 5x

Since 0 < x < 10
0 < 5x < 50
0 < z < 50
and we know that (x+10)/2 <10> 5.25 False
If x = 1.5, Z = 7.5, (1.5+10)/2 = 5.75, 7.5 > 5.75 True

INSUFF.

I would pick E as the answer.
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You cannot take the value of z = 2 as the distance between z and 10 is 8 where as the distance between z and x is 1, but according to condition 1 says that the distance between z and 10 has to be less than the distance between z and x (8>1, not an option we can choose)
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Gmatprep - number line 08 Feb 2007, 17:59
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amorpheus
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joyce
OA: A

From Question: 0 < x <10> (x + 10)/2 ?

(1) 0 < x < z <10> 5.5 True
If x = 1, z = 2, (x+10)/2 = 5.5, 2 > 5.5 False

INSUFF.

I do not know how the OA said that (1) is suff. :cry:

(2) z = 5x

Since 0 < x < 10
0 < 5x < 50
0 < z < 50
and we know that (x+10)/2 <10> 5.25 False
If x = 1.5, Z = 7.5, (1.5+10)/2 = 5.75, 7.5 > 5.75 True

INSUFF.

I would pick E as the answer.

You cannot take the value of z = 2 as the distance between z and 10 is 8 where as the distance between z and x is 1, but according to condition 1 says that the distance between z and 10 has to be less than the distance between z and x (8>1, not an option we can choose)
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How brilliant! :o
I too made the same mistake by not reading closely the first option (A) =>
Plugged in 9 for z and 8 for x to end up with E.

Thanks y'all! :idea:
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Gmatprep - number line 08 Feb 2007, 18:01
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amorpheus

You cannot take the value of z = 2 as the distance between z and 10 is 8 where as the distance between z and x is 1, but according to condition 1 says that the distance between z and 10 has to be less than the distance between z and x (8>1, not an option we can choose)
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Thank you my friend :wink:. I have to read more carefully next time.

Ok, now I will show how to deal with (1)

From (1) we can conclude that
|Z - 10|
...........................x........................10


case 1: 10 - z (10 + x)/2

SUFF.

Thank you for pointing this out.



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