Latest Elitmus Aptitude Question SOLUTION: Is x^2+y^2 divisible by 5? (1) When x-y is divided by 5, the remainder is 1 (2) When x+y is divided by 5, the remainder is 3

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(#M40082520) ELITMUS Numerical Ability question probability Keep an EYE

Is x^2+y^2 divisible by 5?

(1) When x-y is divided by 5, the remainder is 1
(2) When x+y is divided by 5, the remainder is 3

Asked In Elitmus M Aslam (9 years ago)

Unsolved Read Solution (13)

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Read Solution (13) :

sangrambadi sahoo  (9 years ago)

its a data sufficiency question...
ans should be the both the statements are required to ans the question because
here x-y is divided by 5 and the remainder is 1.
so it can be written as x-y=5m+1
similarlu x+y =5n+3
and from this we can get xy=(x+y)^2-(x-y)^2
it would be -8+10m+30n
putting the value of xy and x+y in x^2+y^2 as (x+y)^2 -2xy we get
25m^2+10m-60n+25 which can be a multiple of 5 so it is devisible by 5.

Is this solution Helpfull? Yes (13) | No (1)  

Gaurav Kumar  (9 years ago)

X=7,Y=1
x^2+y^2=50/5=10
X+Y=8/5=remainder 3,
X-Y=6/5=remainder1,
kitna aasan tha

Is this solution Helpfull? Yes (10) | No (14)  

anurag kumar  (9 years ago)

if x=12 and y=11 then it is posible..

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

alekya gontla  (9 years ago)

x=7 y=6 is also a possible case .....
7^2 +6^2=85 divisible by 5
7-6=1 when divided by 5 leaves remainder 1
7+6=13 when divided by 5 leaves remainder 3

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

Vedant Khandelwal  (9 years ago)

Let x=7 and y=6
Now,when x-y is divided by 5, remainder is 1 and
When x+y is divided by 5 remainder is 3.

x²+y²=7²+6²=85, which is again divisible by 5.

Is this solution Helpfull? Yes (2) | No   

soudipta  (9 years ago)

YES SAROJANI..This is a DATA SUFFICIENCY QUESTION

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

Shubham Raj  (8 years ago)

ans---alone 1 or 2 can give the answer
because if we take
x=7 ,y=1 then x-y (6) divided by 5 get remainder 1
and another case
x=6 ,y=2 then x+y (8) divided by 5 get remainder 3

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

Bushra  (8 years ago)

we can answer this question using any of statement alone also.... what should be d answer???

Is this solution Helpfull? Yes (1) | No   

anubhav  (9 years ago)

if x=3 and Y=4 then it not possible

Is this solution Helpfull? Yes | No (4)  

sarojani  (9 years ago)

Im getting conffuse...,How 1 is divisible by 5 leaves remainder 1 .. Is 7-6=1 , I think this question belongs to data sufficient .

Is this solution Helpfull? Yes | No (4)  

K. Vanisri  (8 years ago)

either statement is sufficient.
take x=2 and y=1

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Nikhil Joshi  (8 years ago)

Answer to this ques will be both the statements are required.
both the statements satisfies when we put x=12 and y=6
x-y= 12-6= 6, 6/5= 1 remainder
x+y= 12+6=18, 18/5= 3 remainder
x2 + y2= 144 + 36= 180 which is divisible by 5.

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saunak  (8 years ago)

i think statement 4 is sufficient for giving the answer. THe reason is if i cosider x=2 and y=1 (but this case will not happen if we consider xor y as 0 so we are not getting an unique answer .

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