Latest Elitmus Aptitude Question SOLUTION: if w and x are odd numbers and y and z is even then 1/8[(w^2+x^2)*(y^2+z^2) is option 1. always even 2. always odd 3. even or odd 4. can be fractional

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(#M40030489) ELITMUS question Keep an EYE

if w and x are odd numbers and y and z is even then 1/8[(w^2+x^2)*(y^2+z^2) is
option
1. always even
2. always odd
3. even or odd
4. can be fractional

Asked In Elitmus lovkesh goyal (10 years ago)

Unsolved Read Solution (28)

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RAKESH  (10 years ago)

1/8[(w^2+x^2)*(y^2+z^2)]
=1/8[(odd^2+odd^2)*(even^2+even^2)]
=1/8[(2*odd)*4(may even or odd)]
=odd*(even or odd)
=odd or even

Is this solution Helpfull? Yes (15) | No (2)  

srivalli kadali  (10 years ago)

odd^2=odd(W^2= X^2=odd)
eve^2=eve(y^2=z^2=eve)
odd+odd=eve (w^2+x^2=odd+odd=eve)
eve+eve=eve (y^2+z^2=eve+eve=eve)
eve*eve=eve {[(w^2+x^2)*(y^2+z^2)]=eve*eve=eve}
so finally
eve/8
let 'n' is any num
eve=2*n
2*n/8=n/4
ans: can be fractional (except 4 multiples) , option 4

Is this solution Helpfull? Yes (9) | No (13)  

RAKESH  (10 years ago)

1/8[(w^2+x^2)*(y^2+z^2)]
=1/8[(odd^2+odd^2)*(even^2+even^2)]
now, odd^2+odd^2=even=2*odd(ex 3^2+5^2=34=2*17)
even^2+even^2=(2m)^2+(2n)^2=4(m^2+n^2),value of m^2 & n^2 may even or odd
ex 2^2+6^2=40=4*10=4*even
8^2+10^2=164=4*41=4*odd

=1/8[(2*odd)*4(may even or odd)]
=odd*(even or odd)
=odd or even

Is this solution Helpfull? Yes (9) | No (2)  

SOURAV KUNWAR  (10 years ago)

both even and odd

Is this solution Helpfull? Yes (8) | No (6)  

SOURAV KUNWAR  (10 years ago)

for w=5, x=3, y=2, z=4
the expression = 1/8[(25+9)*(4+16)]= 34*20 / 8 = 85 (odd)
so ans:- both even and odd..

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ABHINAV SHRIVASTAVA  (10 years ago)

ans.4-Can be fractional

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srivalli kadali  (10 years ago)

let a,b,c,d are any numbers
odd^2=odd(W^2= X^2=odd)
eve^2=eve(y^2=z^2=eve, y^2=2*a, z^2=2*b)
odd+odd=eve (w^2+x^2=odd+odd=eve = 2*c)
eve+eve=eve (y^2+z^2=eve+eve= (2*a)^2+ (2*b)^2 = 4*(a^2+b^2)= 4*d)
eve*eve=eve {[(w^2+x^2)*(y^2+z^2)]=eve*eve= 2*c * 4*d= 8*c*d}
so finally
8*c*d/8= c*d
if in c and d any one is eve number, we get eve number
else we get odd
so ans : even or odd

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saikumar  (10 years ago)

Hi friends all going blindly
you are correct
odd+odd =even
even+even =even

even*even =even

but there is no rule that an even number when divided by a number must be an even number

For example : 120/8 =15
even number/8 =odd

in the same way
suppose consider

w=3
x=9

y=4
z=6

then 1/8[(w^2+x^2)*(y^2+z^2)]
1/8[(9+81)*(16+36)]
1/8[90*52]
13*45

Final product is odd number it mi8 be even in case of
w=5
x=11

y=6
z=10

so answer is even or odd
Thank you

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Richa  (10 years ago)

always even

Is this solution Helpfull? Yes (2) | No (13)  

TRIPURANENI MONIKA  (10 years ago)

3option
lets supose consider w be 3 x be 5 y=2 z=4
1/8[(9+25)*(4+16)]=1/8[34*20]=1/8[680]=85 similarly if we consider w,x be 1,1 y,z be 2,2 we wil get 2

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Pappu Kumar Chaudhary  (10 years ago)

4.can be fractional
x1,w3,y2,z4 provides 200/8 ie fraction means not always even,not always odd,and not even or odd

Is this solution Helpfull? Yes (2) | No (4)  

Ritesh Sangwan  (10 years ago)

option 1 always even

w,x are odd so w^2+x^2 = odd+odd = even
y,z are even so y^2+z^1 = even + even = even
divided by 8 even/even = even
Also the result cannot be fractonal as 8=2*2*2, there are more then three 2's in the numerator to cancel out 8

Is this solution Helpfull? Yes (1) | No (7)  

abc  (10 years ago)

its 2)
always odd

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OMKAR G B  (10 years ago)

guys its option 4 rite..........how come 1/[680]=85.....its fraction....

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sumit kumar chourasia  (10 years ago)

even or odd

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ravi gangwar  (10 years ago)

AFTR CALCULTING odd^2+odd^2=even as odd+odd=even
even^2+even^2=even
their multiplication wll be even
...

we alwys get even value when we multiply a even no to even or odd so in this case revers will also true.
so answer will be even or odd.

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ankit chauhan  (10 years ago)

@ pappu bhai 200/8=25 it is not a fraction

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Netesh  (10 years ago)

? wrong lag raha h

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rohit chaurasiya  (10 years ago)

odd+odd=odd;
even+even=even;
odd*even=even;
&even/even=even;
then the ans is always even(A)

Is this solution Helpfull? Yes | No (7)  

Harshvardhan Nilmani  (10 years ago)

even/even can be odd. As in 24/8 equals 3. So it can be a fraction as well coz 44/8 is always a fraction even both are even.

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Sagar Gandhi  (10 years ago)

always even

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ankit chauhan  (10 years ago)

@harshvardhan how can 44 comes give example..bhai it is not possible ..

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Gaurav  (10 years ago)

Can be even or odd
square of odd is odd and square of even is even
odd+odd = even
even+even =even
even*even= even
even/8 = can be even or odd
it can't be fractional you can check bg taking any values.

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Bala Daggubati  (10 years ago)

3 is the answer.

if w=1 and x=3
y=2 and z=4
value we get is 25(odd)

if w=7 and x=9
y=8 and z=6
value we get is 2000(even)

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vinod  (10 years ago)

both even and odd.....

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Subhasis Mandal  (10 years ago)

always odd.
take w=1, x=3, y=2, z=4
so,
[(1^2+3^2)*(2^2+4^4)]/8= 25
Hence always odd..
try with any no..

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Ankit Gupta  (10 years ago)

ans : a= even(n)/8 _ now (if n = 8 then a= 1 which is odd) & (if n=16 then a= 2 which is even) so ans should be """even or odd"""

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ajay negi  (10 years ago)

always odd..
because put any number u'll get odd number as a reslut.
eg. w/x=1,3,5,7,9....
nd y/z= 2,4,6,8,10...
reslut = 5 / 0.5 /0.05... in last (i.e 5 is odd)

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