GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jul 2020, 01:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is x an even integer?

Author Message
TAGS:

### Hide Tags

GMAT Club team member
Status: GMAT Club Team Member
Affiliations: GMAT Club
Joined: 02 Nov 2016
Posts: 6192
GPA: 3.62
Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 03:52
00:00

Difficulty:

55% (hard)

Question Stats:

36% (01:09) correct 64% (01:04) wrong based on 36 sessions

### HideShow timer Statistics

Is $$x$$ an even integer?

(1) $$\sqrt{x}$$ is a multiple of 2.

(2) $$x^2$$ is a multiple of 4.

_________________
Intern
Joined: 14 Apr 2020
Posts: 23
Location: India
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:25
Is $$x$$ an even integer?

(1) $$\sqrt{x}$$ is a multiple of 2.

(2) $$x^2$$ is a multiple of 4.

Analyze statement (1) alone
(1) $$\sqrt{x}$$ is a multiple of 2.
$$\sqrt{x}$$=2k, k is an integer
[($$\sqrt{x}$$$$)]^2$$= $$(2k)^2$$
x=4$$k^2$$, $$k^2$$ is an integer
=> x is an even integer
Sufficient

Analyze statement (2) alone
(2)$$x^2$$ is a multiple of 4.
$$x^2$$=4=> x=2 is an even integer
$$x^2$$=8=> x=$$\sqrt{8}$$ is not an even integer
Not Sufficient

_________________
Manisha Shrivastava
GMAT-GRE Quant Expert
PrepMinds-Founderhttp://www.theprepminds.com
IESE School Moderator
Joined: 11 Feb 2019
Posts: 264
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:29
IMO D.

Statement 1: √x is a multiple of 2 i.e. √x can be written as 2^a * P^b. where P can be any other prime number. Surely x ( {√x} ^ 2) will be having 2 as one of its prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient

Statement 2: x^2 is a multiple of 4 i.e. x^2 has prime factors of the form: 2^2 * P^2b where P can be any other prime number. Surely x will be having 2 as a prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient
Ex: 4, 16, 36
_________________

Cheers,
NJ
IESE School Moderator
Joined: 11 Feb 2019
Posts: 264
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:31
Mannisha wrote:
Is $$x$$ an even integer?

(1) $$\sqrt{x}$$ is a multiple of 2.

(2) $$x^2$$ is a multiple of 4.

Analyze statement (1) alone
(1) $$\sqrt{x}$$ is a multiple of 2.
$$\sqrt{x}$$=2k, k is an integer
[($$\sqrt{x}$$$$)]^2$$= $$(2k)^2$$
x=4$$k^2$$, $$k^2$$ is an integer
=> x is an even integer
Sufficient

Analyze statement (2) alone
(2)$$x^2$$ is a multiple of 4.
$$x^2$$=4=> x=2 is an even integer
$$x^2$$=8=> x=$$\sqrt{8}$$ is not an even integer
Not Sufficient

Hello Mannisha,

8 cannot be written as x^2.

x^2 as a multiple of 4 will be : 4,16, 36, 64....
_________________

Cheers,
NJ
Math Expert
Joined: 02 Aug 2009
Posts: 8738
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:42
2
1
NitishJain wrote:
IMO D.

Statement 1: √x is a multiple of 2 i.e. √x can be written as 2^a * P^b. where P can be any other prime number. Surely x ( {√x} ^ 2) will be having 2 as one of its prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient

Statement 2: x^2 is a multiple of 4 i.e. x^2 has prime factors of the form: 2^2 * P^2b where P can be any other prime number. Surely x will be having 2 as a prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient
Ex: 4, 16, 36

You do not know if x is integer..
x^2=4y
say y=2, so $$x^2=4*2...x=2\sqrt{2}$$,...Not an even integer.
when y=4...x=4..Yes
So Statement II is insuff
_________________
IESE School Moderator
Joined: 11 Feb 2019
Posts: 264
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:47
chetan2u wrote:
NitishJain wrote:
IMO D.

Statement 1: √x is a multiple of 2 i.e. √x can be written as 2^a * P^b. where P can be any other prime number. Surely x ( {√x} ^ 2) will be having 2 as one of its prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient

Statement 2: x^2 is a multiple of 4 i.e. x^2 has prime factors of the form: 2^2 * P^2b where P can be any other prime number. Surely x will be having 2 as a prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient
Ex: 4, 16, 36

You do not know if x is integer..
x^2=4y
say y=2, so $$x^2=4*2...x=2\sqrt{2}$$,...Not an even integer.
when y=4...x=4..Yes
So Statement II is insuff

ohh ok thanks for pointing my mistake.

_________________

Cheers,
NJ
Intern
Joined: 14 Apr 2020
Posts: 23
Location: India
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:50
NitishJain wrote:
chetan2u wrote:
NitishJain wrote:
IMO D.

Statement 1: √x is a multiple of 2 i.e. √x can be written as 2^a * P^b. where P can be any other prime number. Surely x ( {√x} ^ 2) will be having 2 as one of its prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient

Statement 2: x^2 is a multiple of 4 i.e. x^2 has prime factors of the form: 2^2 * P^2b where P can be any other prime number. Surely x will be having 2 as a prime factor and we know EVEN * Odd = Even . Hence x is even. Sufficient
Ex: 4, 16, 36

You do not know if x is integer..
x^2=4y
say y=2, so $$x^2=4*2...x=2\sqrt{2}$$,...Not an even integer.
when y=4...x=4..Yes
So Statement II is insuff

ohh ok thanks for pointing my mistake.

No worries it happens:)
_________________
Manisha Shrivastava
GMAT-GRE Quant Expert
PrepMinds-Founderhttp://www.theprepminds.com
Math Expert
Joined: 02 Aug 2009
Posts: 8738
Re: Is x an even integer?  [#permalink]

### Show Tags

30 May 2020, 04:50
2
Is $$x$$ an even integer?

(1) $$\sqrt{x}$$ is a multiple of 2.
$$\sqrt{x}=2y$$, where y is an integer.
So $$x=4y^2$$, and so x is even.
Suff

(2) $$x^2$$ is a multiple of 4.
$$x^2=4y$$ where y is an integer.
so x will be even integer only when y is a perfect square.....$$y=4.....x^2=4*4=16...x=4$$
If y= any other number, x is not an integer....$$y=3.....x^2=4*3=12...x=2\sqrt{3}$$
Insuff

A
_________________
Re: Is x an even integer?   [#permalink] 30 May 2020, 04:50