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

 It is currently 16 Aug 2018, 16:47

### 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

# x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47946
x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 05:24
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:02) correct 17% (01:28) wrong based on 66 sessions

### HideShow timer Statistics

x is a positive integer. Is x even?

(1) 9x^2 is divisible by 4
(2) 3x + 2 is divisible by 8

_________________
Manager
Joined: 13 Feb 2018
Posts: 126
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 06:34
1 stm. tells us that $$9x^2$$ is even. We know that neither square root, nor multiplication by odd number change the +- nature of x, so x is even --> suff.
2 stm. tells that $$3x+2$$ is even. We know that neither adding even number, nor multiplication by odd number change the +- nature of x, so x is even --> suff.

In My Opinion
Ans: D
Senior Manager
Joined: 14 Dec 2017
Posts: 451
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 10:15
Bunuel wrote:
x is a positive integer. Is x even?

(1) 9x^2 is divisible by 4
(2) 3x + 2 is divisible by 8

Given x > 0

Statement 1: 9x^2 = 4k, hence 9x^2 = even. x = even, since Odd * Even = Even. Statement 1 is Sufficient.

Statement 2: 3x + 2 = 8k, hence 3x + 2 = even. x = even, since Even + Even = Even. Statement 2 is Sufficient.

Thanks,
GyM
Senior Manager
Status: Learning stage
Joined: 01 Oct 2017
Posts: 486
WE: Supply Chain Management (Energy and Utilities)
x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 10:21
GyMrAT wrote:
Bunuel wrote:
x is a positive integer. Is x even?

(1) 9x^2 is divisible by 4
(2) 3x + 2 is divisible by 8

Given x > 0

Statement 1: 9x^2 = 4k, hence 9x^2 = even. x = even, since Odd * Even = Even. Statement 1 is Sufficient.

Statement 2: 3x + 2 = 8k, hence 3x + 2 = even. x = even, since Even + Even = Even. Statement 2 is Sufficient.

Thanks,
GyM

Hi gym,
In st2, at x= 4,8 etc. 3x+2 is not divisible by 8.
But st2 is valid for some of the even integers(2,10 etc) not all.
In this case Is x even? Yes or No.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 14 Dec 2017
Posts: 451
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 10:52
PKN wrote:
GyMrAT wrote:
Bunuel wrote:
x is a positive integer. Is x even?

(1) 9x^2 is divisible by 4
(2) 3x + 2 is divisible by 8

Given x > 0

Statement 1: 9x^2 = 4k, hence 9x^2 = even. x = even, since Odd * Even = Even. Statement 1 is Sufficient.

Statement 2: 3x + 2 = 8k, hence 3x + 2 = even. x = even, since Even + Even = Even. Statement 2 is Sufficient.

Thanks,
GyM

Hi gym,
In st2, at x= 4,8 etc. 3x+2 is not divisible by 8.
But st2 is valid for some of the even integers(2,10 etc) not all.
In this case Is x even? Yes or No.

In DS questions, we need to consider the given statements are True. Consider them as constraints for us to solve the question.

The task at hand is to determine is X = even?

In statement 2 it is given 3x + 2 is divisible by 8, our job is to determine which value of x can satisfy this condition.

As rightly identified by you, the condition is satisfied by x = 2, 10, etc. our task at hand is to determine whether these values which satisfy (3x + 2) = 8k are even or not.

Using statement 2, we can answer the question as YES, x = even.

However, If we were to find values of x as odd as well as even & satisfying statement 2, then statement 2 would not be sufficient. Since we will get answer for X = even? as YES & NO.

Thanks,
GyM
Senior Manager
Status: Learning stage
Joined: 01 Oct 2017
Posts: 486
WE: Supply Chain Management (Energy and Utilities)
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 10:57
In DS questions, we need to consider the given statements are True. Consider them as constraints for us to solve the question.

The task at hand is to determine is X = even?

In statement 2 it is given 3x + 2 is divisible by 8, our job is to determine which value of x can satisfy this condition.

As rightly identified by you, the condition is satisfied by x = 2, 10, etc. our task at hand is to determine whether these values which satisfy (3x + 2) = 8k are even or not.

Using statement 2, we can answer the question as YES, x = even.

However, If we were to find values of x as odd as well as even & satisfying statement 2, then statement 2 would not be sufficient. Since we will get answer for X = even? as YES & NO.

Thanks,
GyM[/quote]

Thanks gym,
My point was:- Although 3x+2 is even as mentioned in your explanation, it is not divisible by 8.
Now you have made it clear.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 14 Dec 2017
Posts: 451
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 11:13
PKN wrote:

Thanks gym,
My point was:- Although 3x+2 is even as mentioned in your explanation, it is not divisible by 8.
Now you have made it clear.

No problem. My fault I wasn't clear enough, thankfully GMAT is an objective test.

Cheers!
GyM
Senior Manager
Joined: 31 Oct 2013
Posts: 477
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

05 Jul 2018, 13:58
Bunuel wrote:
x is a positive integer. Is x even?

(1) 9x^2 is divisible by 4
(2) 3x + 2 is divisible by 8

Statement 1 :

9$$x^2$$ is divisible by 4.

9 is not divisible by 4. So, $$x^2$$has to be divisible by 4. It means$$x^2$$ is a multiple of 4 . even times even yields even all time. So, Sufficient.

Statement 2 :

3x + 2 is divisible by 8. As 3x + 2 is divisible by 8 , 3x + 2 must be the multiple of 8 . It means 3x + 2 is even. Thus x is even. Sufficient.

So both of the statements are sufficient. The best answer is D.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1894
Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x  [#permalink]

### Show Tags

06 Jul 2018, 01:36

Solution

Given:
• x is a positive integer

To find:
• Is x even?

Analysing Statement 1
“$$9x^2$$ is divisible by 4”
• Implies, $$9x^2 = 4k$$ .................. (1), where k is a positive integer
• The right-hand side of equation (1) is even, which implies that the left-hand side should be even
• Thus, x is even (since 9 is odd)

Therefore, Statement (1) ALONE is sufficient to answer this question

Analysing Statement 2
“3x + 2 is divisible by 8”
• Implies, 3x + 2 = 8k, where k is a positive integer
o 3x + 2 = 8k
o 3x = 8k -2
o 3x = 2*(4k -1) ............................. (2)
• The right-hand side of equation (2) is even, which implies that the left-hand side should be even
• For 3x to be even, x should be even

Thus, Statement (2) ALONE is sufficient to answer this question

Therefore, EACH Statement ALONE is sufficient to answer this question

Hence, the correct answer is option D.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: x is a positive integer. Is x even? (1) 9x^2 is divisible by 4 (2) 3x &nbs [#permalink] 06 Jul 2018, 01:36
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.