GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Dec 2018, 00:27

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### 10 Keys to nail DS and CR questions

December 17, 2018

December 17, 2018

06:00 PM PST

07:00 PM PST

Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
• ### R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

December 17, 2018

December 17, 2018

10:00 PM PST

11:00 PM PST

From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.

# Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51243
Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

08 Feb 2018, 23:43
1
12
00:00

Difficulty:

95% (hard)

Question Stats:

36% (01:39) correct 64% (01:20) wrong based on 162 sessions

### HideShow timer Statistics

Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

_________________
Director
Joined: 31 Jul 2017
Posts: 505
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

09 Feb 2018, 03:33
4
1
Bunuel wrote:
Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

Statement I:

Let $$x = \sqrt{20}, x^2$$ is Divisible by 4.
Let $$x = 2, x^2$$ is Divisible by 4.........So, Insufficient.

Statement II:

$$x = 2(2)^{1/4}, x^4$$ is Divisible by 16.
Let, $$x= 2, x^4$$ is Divisible by 16......So, Insufficient.

Combining I & II:

Let $$x = \sqrt{20},$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

Let $$x = 2$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

So, Insufficient. Hence, E.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

##### General Discussion
Senior Manager
Joined: 17 Oct 2016
Posts: 318
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

08 Feb 2018, 23:55
IMO D.

from statement 1, we can say x² has to be even integer. Hence x has to be an even integer. sufficient.

from statement 2, we can say x^4 has to be even integer. Hence x has to be an even integer. sufficient.
_________________

Help with kudos if u found the post useful. Thanks

Intern
Joined: 01 Aug 2017
Posts: 9
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

09 Feb 2018, 05:22
I agree with rahul16singh28.

In statement 1 is said x^2 is divisible by 4, x^2= a*4 ---> x=a^(1/2)*2 (not considering sings)

so, a could be 1.5 and x= 3 (not an even integer) , but a could be 9 and x= 6 (even integer). Not sufficient

Statement two is no different than statement 1. Also not sufficient

And both together Not sufficient
Manager
Joined: 23 Sep 2016
Posts: 216
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

09 Feb 2018, 23:39
Bunuel wrote:
Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

I think E is the answer as x could be 4root 3 or 4 we can't saw anything.
Intern
Joined: 15 Sep 2017
Posts: 23
GMAT 1: 750 Q50 V42
GPA: 3.5
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

27 Feb 2018, 05:44
1
The trick in this question is that it wants us to think of x in terms ox multiples of 2, such as 2, 4, 8 ... If you plug in any of these numbers, for sure they are divible by 4 (in statement I) or by 16 (in statement II)

We should ask ourselves if there is a non integer number x that when x^2 is divisible by 4 or when x^4 is divisible by 16.

(2√2)^2 is equal to 8 and 8 is divisible by 4
(2 * 2^1/4) ^ 4 is equal to 32 and 32 is divisible by for.

Together, (2 * 2^1/4) ^ 2 is not divisible by 4, so there is at least one number that is sufficient for statements I and II but is not an integer.

_________________

"Revenge is a dish best served cold"

Intern
Joined: 19 Jul 2017
Posts: 34
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

10 Aug 2018, 15:44
rahul16singh28 wrote:
Bunuel wrote:
Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

Statement I:

Let $$x = \sqrt{20}, x^2$$ is Divisible by 4.
Let $$x = 2, x^2$$ is Divisible by 4.........So, Insufficient.

Statement II:

$$x = 2(2)^{1/4}, x^4$$ is Divisible by 16.
Let, $$x= 2, x^4$$ is Divisible by 16......So, Insufficient.

Combining I & II:

Let $$x = \sqrt{20},$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

Let $$x = 2$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

So, Insufficient. Hence, E.

Would u explain highlighted part ,plz?
_________________

You never FAIL until you stop TRYING

[wrapimg=][/wrapimg]

Manager
Joined: 06 Nov 2016
Posts: 62
Location: Viet Nam
GPA: 3.54
Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

### Show Tags

11 Aug 2018, 06:21
2
vivapopo wrote:
rahul16singh28 wrote:
Bunuel wrote:
Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

Statement I:

Let $$x = \sqrt{20}, x^2$$ is Divisible by 4.
Let $$x = 2, x^2$$ is Divisible by 4.........So, Insufficient.

Statement II:

$$x = 2(2)^{1/4}, x^4$$ is Divisible by 16.
Let, $$x= 2, x^4$$ is Divisible by 16......So, Insufficient.

Combining I & II:

Let $$x = \sqrt{20},$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

Let $$x = 2$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

So, Insufficient. Hence, E.

Would u explain highlighted part ,plz?

I think what he means is that
Statement II:
Let, $$x = 2*2^\frac{1}{4}$$ (not an even integer) --> $$x^4 = 2^4 * 2 = 16*2$$ --> $$x^4$$ is divisible by 16
Let, $$x= 2$$ (an even integer), $$x^4$$ is Divisible by 16
--> Insufficient.
_________________
Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible &nbs [#permalink] 11 Aug 2018, 06:21
Display posts from previous: Sort by