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potive integers

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potive integers

by acorra » Sat Oct 25, 2008 7:21 am
If x, y and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessary an integer?

A) (x+y)/z

B) (y+z)/x

C) (x+y)/z

D) xy/z

E) yz/x

Could you please let me know how to crack this problem? I read the solution but I think that there is something easier.

Thanks
Andrew
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by dmateer25 » Sat Oct 25, 2008 9:08 am
I just chose numbers that satisfied the given information:

X = 4 (factor of y and multiple of z)
Y = 8
Z = 2

In the answer choices you have A and C the same, but the answer should be B.

(8 + 2) / 4
10/4 is not an integer
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by earth@work » Sat Oct 25, 2008 2:54 pm
Given, x is a factor of y i.e y=x*m.......(1)
x is a multiple of z i.e x=z*n...........(a)
we can also write (1) as y=z*s........(b)
Lets now use (a) & (b) on given options...
(x+y)/z = (z*n +z*s)/z ...... it is an integer ,
similarly for C) (x+y)/z D) xy/z E) yz/x ...so all these options r integers except B) (y+z)/x .... NOT integer
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by 2009wish » Sun Oct 26, 2008 1:36 am
Is plugging in the best method for this question ? or is there any logical mathematical approach to this problem?

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by rohangupta83 » Sun Oct 26, 2008 2:07 am
2009wish wrote:Is plugging in the best method for this question ? or is there any logical mathematical approach to this problem?

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plugging in would be the simplest method to solve this particular question

i picked
x = 8
y = 32
z = 2

(y+z)/x = (32+2)/8 = 34/8 (not an integer) therefore, choice B
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by stop@800 » Sun Oct 26, 2008 2:00 pm
IMO uing numbers should be the last option.
No offence, only my personal views :)


acorra,
A and C are same.
I think you missed something.
may be sign is different


x is a factor of y
means
y contains x [ie y=x or y is integer multiple of x]
hence
y/x is integer


x is a multiple of z
so
x/z is an integer


y/x is an integer and
x/z is an integer
multiply both
so we have
y/z also an integer

now all option other than B will turn out to be some / multiplication on integers.

remember Qn says x, y, z are integers...

You can try yourself :)

Hope it helps!!
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