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# Is x an integer?

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Math Expert
Joined: 02 Aug 2009
Posts: 7035

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14 Jun 2018, 03:49
1
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Difficulty:

95% (hard)

Question Stats:

42% (02:20) correct 58% (01:40) wrong based on 125 sessions

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Is x an integer?
(1) $$x^2=2y$$, where y is an integer.
(2) x*y is an even number.

New question

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 13 Feb 2018
Posts: 135
Re: Is x an integer?  [#permalink]

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14 Jun 2018, 08:17
1
statement 1
x^2=2y
x=sqrt(2*integer) is not definitely an integer not suff.

statement 2
even number means that it is an integer, only integers have +-ve nature but anyway it's not suff
1 case: x=1 y=2
2 case x=1.25 y=4

statements 1&2

P.S I'm very cautious about Chetan's questions, traps everywhere
Manager
Joined: 11 Apr 2018
Posts: 120
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Is x an integer?  [#permalink]

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14 Jun 2018, 08:27
1
1
To find: Is x an integer?

Statement 1:

$$X^2 = 2y$$ and y is an integer.
y = 2 then x = +2 or -2. but yes an integer.
y = 4 then x = + or -$$2\sqrt{2}$$. x is not an integer.
Statement 1 is insufficient.

Statement 2:

x*y is an even number.
x = 1/2 and y = 24. It satisfies even number condition but x is not an integer.
x = 2 and y = 4. It satisfies even number condition but x is an integer.
Statement 2 is insufficient.

From Statement 1 and Statement 2:
From $$X^2 = 2y$$ we can say, $$X = \sqrt{2} * \sqrt{y}$$
And as, x*y is an even number. This implies x * y is even integer ( as even number cannot be a fraction ).
and we already know that y is an integer ( From statemnt 1 ).
We can rewrite x * y as $$\sqrt{2} * \sqrt{y} * y$$= even integer.
$$\sqrt{2y} * y$$ = even integer.
$$\sqrt{2y}$$ this should result in integer then only as a whole x * y will result as evn number.
This implies x should be an integer.
The correct choice is C.
Intern
Joined: 17 Jan 2018
Posts: 13

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14 Jun 2018, 19:58
Statement 1

$$x^2 = 2y$$, y is an integer

y = 2 , $$x^2=4$$, integer
y=3, $$x^2=6$$, not integer ............ (Not Sufficient)

Statement 2

x*y is an even integer

Possible pairs (2,2), (3,2), (1/3,18) ........ (Not sufficient)

Combine both:

$$x = \sqrt{2y}$$

y is an integer and x*y is an even integer
$$\sqrt{2y}*y$$ is an even integer

Hence, $$\sqrt{2y}$$ must be an integer, or x is an integer

Manager
Joined: 30 Mar 2017
Posts: 135
GMAT 1: 200 Q1 V1
Re: Is x an integer?  [#permalink]

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18 Jul 2018, 16:37
(1)
(x,y) can be ($$\sqrt{2}$$,1) or (2,2)
Not suff

(2)
(x,y) can be (1,2) or ($$\frac{1}{2}$$,4)
Not suff

(1)+(2)
x*y is even and y is an integer. So x*integer=even. x cant be a fraction because Statement 1 would not hold, i.e. 2y would be an integer and $$x^2$$ would be a fraction. Also, x cant be a root because then y would also have to be a root, but y is an integer. So x has to be an integer.

Intern
Joined: 16 Jan 2018
Posts: 1
Re: Is x an integer?  [#permalink]

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20 Jul 2018, 12:16
Statement 1:
x^2 = 2*y

Hence y can be 2 => x is an integer
y can be 3 => x is not an integer

Statement 1 not suff

Statement 2:
x*y is even NUMBER

x can be 1/2 or 2

(1)+(2)

from 2nd y=Even /x (integer)

using it in (1)

x^2 = 2*Even/x
x^3 = 2*Even=> Even Integer

Correct ans C
Math Expert
Joined: 02 Aug 2009
Posts: 7035
Re: Is x an integer?  [#permalink]

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23 Jul 2018, 19:07
chetan2u wrote:
Is x an integer?
(1) $$x^2=2y$$, where y is an integer.
(2) x*y is an even number.

New question

Be careful in analysing the information given to you in each statement

(1) $$x^2=2y$$, where y is an integer.
If y is 2 X=2 YES X is an integer..
If y is 3, x^2=2*3=6.....X=√6....NO X is not an integer
Insufficient

(2) x*y is an even number
if y is 4, X can be 1/2.....4*1/2=2
y as 4, X can be any integer..4*3=12
Insufficient

Combined
X*y is even and x^2=2y.....X=√(2y)
So y*√(2y) is even but since y is integer √(2y) has to be an integer..
So X is an integer
Sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: Is x an integer? &nbs [#permalink] 23 Jul 2018, 19:07
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