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

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Manager
Joined: 17 Aug 2009
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Kudos [?]: 112 [0], given: 25

If x is a positive number less than 10, is z greater than [#permalink]  29 Dec 2009, 04:39
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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
Senior Manager
Joined: 30 Aug 2009
Posts: 290
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 102 [0], given: 5

Re: GMATprep DS:Arithmetic mean [#permalink]  29 Dec 2009, 04:51
zaarathelab wrote:
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

1. Since z is closer to 10 than it is to x then avg of x and 10 will be less than z. hence suff

2. z = 5x
if x = 1 and z = 5 then avg of x and 10 = 5.5 and greater than z
if x= 3 and z=15 then avg of x and 10 = 6.5 and less than z. Hence insuff

will go with A
Manager
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Posts: 238
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Kudos [?]: 112 [0], given: 25

Re: GMATprep DS:Arithmetic mean [#permalink]  29 Dec 2009, 05:02
Can u pls explain why A?
Senior Manager
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Re: GMATprep DS:Arithmetic mean [#permalink]  29 Dec 2009, 05:20
zaarathelab wrote:
Can u pls explain why A?

we know x is +ve and to keep things simple lets assume x=1
then to satisfy statement 1 the minimum value of z is > 5.5. If z= 5.5 then z-x = 4.5 and 10 -z is also equal to 4.5 which is incorrect
now avg of x and 10 in this case will be 5.5 and z>5.5.

lets consider another value for x i.e 9.8 [ keeping addition/division simple here :D]
then to satisfy stmnt 1, z will be greater than 9.90 as 10- z = 0.1 and z-x = 0.1 if z = 9.9.Avg of x and 10 will be 9.90 and z is greater than 9.90

hence statement 1 is sufficient. Hope this helps.
Re: GMATprep DS:Arithmetic mean   [#permalink] 29 Dec 2009, 05:20
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