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

Question

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

chineseburned · Answer

Why do I get 60???
The only consecutive integers satisfying the constrains to me seem to be 3,4,5.....what am I missing?

shils01 · Answer

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

chineseburned · Answer

In that case the integers can only be 2,4,6: 2+6 = 32/4 = 8;
So Answer is 48.

axl_oz · Answer

pick numbers

X = 2
y = 4 and 
z = 6

X+Z = 32/Y

Substitute these values and you get 48 as the answer

chineseburned · Answer

Dude! Are you ready for Chinese Democracy??? :-D

pmenon · Answer

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

gwamaka · Answer

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

giantSwan · Answer

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

Thanks,

-gS

pandeyrav · Answer

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

Juaz · Answer

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

shobuj · Answer

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

Prep Toolkit