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If x, y, and z are consecutive even integers such that 0

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If x, y, and z are consecutive even integers such that 0 [#permalink] New post 19 Mar 2008, 13:32
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If x, y, and z are consecutive even integers such that 0 < x < y < z and the sum of x and z equals 32/y, then the product of xyz is

(A) 0
(B) 48
(C) 96
(D) 144
(E) 192

Last edited by shils01 on 19 Mar 2008, 15:27, edited 1 time in total.
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Re: PS [#permalink] New post 19 Mar 2008, 14:29
Why do I get 60???
The only consecutive integers satisfying the constrains to me seem to be 3,4,5.....what am I missing?
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Re: PS [#permalink] New post 19 Mar 2008, 15:27
My mistake>> never saw the question said they were "even" consecutive integers. Corrected the question. Apologies.
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Re: PS [#permalink] New post 19 Mar 2008, 15:36
In that case the integers can only be 2,4,6: 2+6 = 32/4 = 8;
So Answer is 48.
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Re: PS [#permalink] New post 19 Mar 2008, 15:57
pick numbers

X = 2
y = 4 and
z = 6

X+Z = 32/Y

Substitute these values and you get 48 as the answer
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Re: PS [#permalink] New post 19 Mar 2008, 16:02
axl_oz wrote:
pick numbers

X = 2
y = 4 and
z = 6

X+Z = 32/Y

Substitute these values and you get 48 as the answer


Dude! Are you ready for Chinese Democracy??? :-D
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Re: PS [#permalink] New post 19 Mar 2008, 16:54
grrrr have to read the question carefully !!!! forgot the 'even' part
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Re: PS [#permalink] New post 19 Mar 2008, 19:48
Its easy to overlook the "even" part.....I also need to pay more attention on this type of questions.
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Re: PS [#permalink] New post 06 Apr 2008, 16:46
Does anyone know a more precise way to solve this problem (i.e. not picking numbers)?

Thanks,

-gS
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Re: PS [#permalink] New post 07 Apr 2008, 09:33
for any three consecutive even integers x<y<z, x+z = 2y

2y = 32/y
=> y = 4
hence x=2,y=4,x=6
x*y*z = 48
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Re: PS [#permalink] New post 07 Apr 2008, 09:44
giantSwan wrote:
Does anyone know a more precise way to solve this problem (i.e. not picking numbers)?

Thanks,

-gS

Even consecutive numbers can be x, x+2, x+4
x+x+4 = 32/(x+2)
=>(2x+4)(x+2) = 32
=> (x+2)^2 = 16
=> x = 2
Nos would be 2, 4, 6
2*4*6 = 48
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Re: PS [#permalink] New post 08 Apr 2008, 11:51
PICKING NUMBER WILL MAKE U COMFORTABLE IN THIS PROBLEM BUT U HAVE T PICK THE RIGHT SORT OF NUBER :

STEM TELLS US THAT THE TERM IS EVEN ALSO IT IS POSITIVE

SO IT COULD BE :
0<2<4<6.

ALSO 0<4<6<8

THERE IS ANOTHER CONDITION THAT X+Y=32/Y

NOW TEST:
1) 2+(6)=32/4
8=8 SATISFIED
2) 4+(8)=32/6
12 NOT EQUAL 32/6 DOES NOT SATISFIED

SO THE SERIES IS : 2.4, 6 AND 2.4.6=48

ANS IS 48
Re: PS   [#permalink] 08 Apr 2008, 11:51
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