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# Is x^2 + y^2 + 2 divisible by 6?

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Intern
Joined: 19 Dec 2016
Posts: 47
Location: India
WE: Consulting (Computer Software)
Is x^2 + y^2 + 2 divisible by 6?  [#permalink]

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25 Jul 2017, 16:11
00:00

Difficulty:

65% (hard)

Question Stats:

41% (00:46) correct 59% (00:44) wrong based on 17 sessions

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Is x^2 + y^2 + 2 divisible by 6?

(1) xy is even
(2) x is odd

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Intern
Joined: 27 May 2017
Posts: 12
Re: Is x^2 + y^2 + 2 divisible by 6?  [#permalink]

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Updated on: 26 Jul 2017, 04:08
XY even means either X or Y is even or both X and Y are even.
If X = 2 and Y = 3 then 2^2 +3^2 + 2 = 15 and its not divisible by 6.
if X = 0 and Y = 2 then 0^2 + 2^2 + 2 = 6.

If X = 4 and Y = 4. 4^2 +4^2 + 2 = 34 and its not divisible by 6
inSuff

St 2. If X and Y are both odd
3^2 + 5^2 + 2 = 36 which is divisible by 6
If X is Odd and Y is even sum wont be divisible by 6 NS

Combined Suff.
X is odd Y is even = 3^2 + 2^2 + 2 = 15. not divisible by 6
Ans C

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Originally posted by Ejiroosa on 25 Jul 2017, 17:21.
Last edited by Ejiroosa on 26 Jul 2017, 04:08, edited 2 times in total.
Senior Manager
Joined: 27 Dec 2016
Posts: 331
Re: Is x^2 + y^2 + 2 divisible by 6?  [#permalink]

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25 Jul 2017, 18:44
S1- xy= even. If x=1 and y=2 then (1^2+2^2+2) will not be divisible by 6. However; if x=0 and y=2 then (0^2+2^2+2) will BE divisible by 6. Hence, INSUFFICIENT

S2- x is odd. If x is 1 and y is 2, then (1^2+2^2+2) will not be divisible by 6. However, if x=3 and y=1 then (3^2+1^2+2) will BE divisible by 6. Hence, INSUFFICIENT

Together- xy is even and x is also odd. If x is odd, that means y has to be an even number in order for xy=even statement to remain true! No matter what value we take for x as a odd number and y as an even number, we will always get a "no" as our answer which is sufficient to answer this question.

Hence, C

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Intern
Joined: 19 Dec 2016
Posts: 47
Location: India
WE: Consulting (Computer Software)
Is x^2 + y^2 + 2 divisible by 6?  [#permalink]

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Updated on: 25 Jul 2017, 19:57
For x^2 + y^2 + 2 to be divisible by 6 it should be divisible 2 &3 both

now from-

1) xy is even

we have 3 possibility-

a) x is even, y is odd
if this is the case then- x^2 = even no, y^2= odd no,
x^2 + y^2 + 2= even no + odd no + even no
this will give an odd no and will not be divisible by 2 as result will not be divisible by 6 as well.

b)x is odd, y is even
this will be same as above this time y^2=even no, x^2= odd no

c) x is even , y is even
if this is the case then x^2 = even no, y^2= even no
x^2 + y^2 + 2 = even + even + even = even no as result "can be or can not be divisible by 3"

so (i) is not sufficient.

2)x is odd

here we have 2 possibility

a) x is odd, y is odd
if this is the case then- x^2 =odd no, y^2= odd no,
x^2 + y^2 + 2 = even no. (as odd+odd=even) can be or can not be divisible 3.

b)x is odd, y is even

in this x^2 + y^2 + 2 = odd+even+even which will be equal to ODD and will not be divisible by 2

so (ii) too is not sufficient

combining both

x is odd, y is even

we will get x^2 + y^2 + 2=odd+even+even = an odd number
this will not be divisible by 2 hence will not be divisible by 6 as well.

so together they are sufficient (Answer is C)

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This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Originally posted by GTExl on 25 Jul 2017, 19:38.
Last edited by GTExl on 25 Jul 2017, 19:57, edited 1 time in total.
Is x^2 + y^2 + 2 divisible by 6?   [#permalink] 25 Jul 2017, 19:38
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