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If x, y, and z are consecutive even integers such that 0 [#permalink ]
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

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shils01 on 19 Mar 2008, 15:27, edited 1 time in total.

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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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My mistake>> never saw the question said they were "even" consecutive integers. Corrected the question. Apologies.

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In that case the integers can only be 2,4,6: 2+6 = 32/4 = 8;

So Answer is 48.

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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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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???

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grrrr have to read the question carefully !!!! forgot the 'even' part

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Its easy to overlook the "even" part.....I also need to pay more attention on this type of questions.

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Does anyone know a more precise way to solve this problem (i.e. not picking numbers)? Thanks, -gS

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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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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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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

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