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# If 2, x, y, and z are different positive integers whose

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Manager
Joined: 03 Oct 2008
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If 2, x, y, and z are different positive integers whose [#permalink]  09 Oct 2008, 04:35
If 2, x, y, and z are different positive integers whose average (arithmetic mean) is 10, what is the greatest possible value of z ?

A. 10
B. 24
C. 34
D. 36
E. 40
Manager
Joined: 22 Sep 2008
Posts: 124
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Kudos [?]: 38 [1] , given: 0

Re: math--positive integers [#permalink]  09 Oct 2008, 04:58
1
KUDOS
avg = 10 means sum will be 40.

one of them is 2 , so x+y+z = 38

now all are diff. POSITIVE integers , so z has max value when x and y has lowest value: means x= 1, y = 3 , x=y = 4

38-4= 34

Z = 34
IMO C
VP
Joined: 17 Jun 2008
Posts: 1404
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Re: math--positive integers [#permalink]  09 Oct 2008, 06:24
albany09 wrote:
If 2, x, y, and z are different positive integers whose average (arithmetic mean) is 10, what is the greatest possible value of z ?

A. 10
B. 24
C. 34
D. 36
E. 40

If 35 had been an opion i woulkd have surely ended u[p marking that !!!

tricky picks are always gmat qant questions !!! IMO C here
_________________

cheers
Its Now Or Never

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Joined: 05 Jul 2006
Posts: 1519
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Kudos [?]: 115 [0], given: 39

Re: math--positive integers [#permalink]  09 Oct 2008, 09:17
albany09 wrote:
If 2, x, y, and z are different positive integers whose average (arithmetic mean) is 10, what is the greatest possible value of z ?

A. 10
B. 24
C. 34
D. 36
E. 40

average = sum/no

sum = avearge * no = 10*4 = 40

x+y+z = 38, z is max when x+y is min

x,y min possibe is 1,3

thus z = 38-4 = 34

Senior Manager
Joined: 04 Jan 2006
Posts: 280
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Re: math--positive integers [#permalink]  09 Oct 2008, 12:23
albany09 wrote:
If 2, x, y, and z are different positive integers whose average (arithmetic mean) is 10, what is the greatest possible value of z ?

A. 10
B. 24
C. 34
D. 36
E. 40

(2 + x + y + z) / 4 = 10
2 + x + y + z = 4 x 10 = 40
x + y + z = 40 - 2 = 38 ---------- (1)

To Max(z), we have to Min(x) and Min(y)
Min(x) = 1
Mix(y) = 3 ---------- because x is not equal to y and y cannot be 2

Therefore,
1 + 3 + z = 38 ---------- From (1)
z = 38 - 1 - 3 = 34

Re: math--positive integers   [#permalink] 09 Oct 2008, 12:23
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