Latest Elitmus Aptitude Question SOLUTION: If w and x odd numbers,y and z even numbers then 1/8[(w^2+x^2)*(y^2+z^2)] A.always odd B.always even C.may be both D.not an interger

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(#M40063994) ELITMUS Numerical Ability question Keep an EYE

If w and x odd numbers,y and z even numbers then
1/8[(w^2+x^2)*(y^2+z^2)]
A.always odd
B.always even
C.may be both
D.not an interger

Asked In Elitmus Ravi Ranjan Ojha (9 years ago)

Unsolved Read Solution (22)

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Read Solution (22) :

Mohit Rathore  (9 years ago)

Let,
w = 1(odd), x = 3(odd)
y = 2(even), z=4(even)
we get
1/8* { ( 1 + 9 ) ( 4 +16 ) }
1/8 * { 10 * 20 } = 25 [which is odd]

now,
If we take
w = 1(odd), x = 3(odd)
y = 12(even), z = 20(even)
we get,
1/8 * { ( 1 + 9 ) ( 144 + 400 ) }
1/8 * { (10) (544) } = 680 [which is even]

The value can be even and can be odd.
So, the ans is C.

Is this solution Helpfull? Yes (48) | No (1)  

Ashish  (9 years ago)

Let w=3, x=5
y= 2, z=4
Solve for the given equ-
1/8* [(w^2+x^2)*(y^2+z^2)]
You will get odd no. not a fraction. (Always)
So, A is correct option.

Is this solution Helpfull? Yes (3) | No (9)  

ASHISH MUKHERJEE  (9 years ago)

This is correct that product of two term always gives even but after dividing 8 it is not sure that the out put will be even only or odd only so,
after checking all the possibility Option C is correct.

Is this solution Helpfull? Yes (3) | No   

Abhishek  (9 years ago)

odd*odd=odd => w^2 & x^2 are odd
odd+odd= even => w^2 + x^2 is even-----1
even*even=even => y^2 & z^2 are even
even+even=even => y^2 + z^2 is even-----2

now 1+2 i.e even +even = even

Now even/8 = even or odd
u can check by putting values like
8/8=1

Is this solution Helpfull? Yes (3) | No   

Shruti Gupta  (9 years ago)

D) not an integer because it will always be a fraction

Is this solution Helpfull? Yes (2) | No (6)  

Ravi Ranjan Ojha  (9 years ago)

Option should be C.
When I cheked by putting the values, then I got it may be both an even number or an odd number.

Is this solution Helpfull? Yes (2) | No   

harsh  (9 years ago)

A) Always odd

Is this solution Helpfull? Yes (1) | No (2)  

swati gupta  (9 years ago)

a is correct answer.

Is this solution Helpfull? Yes (1) | No (2)  

priya  (9 years ago)

Always odd answer a) is correct

Is this solution Helpfull? Yes (1) | No (2)  

samm  (8 years ago)

may be both...

Is this solution Helpfull? Yes (1) | No   

veenu  (9 years ago)

how shruti

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gaurav jain  (9 years ago)

B will be the right option check by putting the value in the position.

Is this solution Helpfull? Yes | No (2)  

Rohit Samly  (9 years ago)

try with these,
13, 17 and 56, 2
u will get a fraction... so D is right option....

Is this solution Helpfull? Yes | No (7)  

Ravi Ranjan Ojha  (9 years ago)

Shruti can u explain ur answer??

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kapil  (9 years ago)

Always even

Is this solution Helpfull? Yes | No (1)  

rahul  (9 years ago)

guys this kind of question quite easy to solve just consider different values odd and even and u can verify it it will always be odd;

Is this solution Helpfull? Yes | No (2)  

Abhishek kUNDU  (9 years ago)

If this equation is under the 1 ,then always be a fraction number it is. then option D is perfect. am agree with shruti.

Is this solution Helpfull? Yes | No   

divyansh dwivedi  (9 years ago)

option d is correct when 1 is divided by any no it gives ans in decimal or fraction so in this ques 1/8[......] not a integer.

Is this solution Helpfull? Yes | No   

Ehtesham  (9 years ago)

since , even * even=even;
odd * odd=odd;

even + even= even;
odd+ odd=even;

but even/even or even/odd or odd/even or odd/odd may be even may be odd and may be its not an integer.

these concept is applied here;
now you can find result..Answer : (D)

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padam  (9 years ago)

putting different values of w,x, y,z answer is may be even ,odd or for some values it is not a integer it comes out fraction

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ganesh babu  (8 years ago)

(Odd+odd)*(even+even)/8
Even *even /8
Always even

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pranav kumar  (8 years ago)

(Odd+odd)*(even+even)/8
Even *even /8=even/8
so it may be odd or even=option c

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