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

 It is currently 17 Jan 2019, 16:05

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If x and y are positive integers, is y divisible by 3?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 15 Feb 2011
Posts: 203
If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

Updated on: 05 Apr 2015, 03:56
3
00:00

Difficulty:

65% (hard)

Question Stats:

57% (02:17) correct 43% (01:53) wrong based on 165 sessions

### HideShow timer Statistics

If x and y are positive integers, is y divisible by 3?

(1) y = 2x^3 + 9x^2 - 5x.
(2) x is an odd number.

Originally posted by DeeptiM on 15 Aug 2011, 05:43.
Last edited by Bunuel on 05 Apr 2015, 03:56, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Status: Quant 50+?
Joined: 02 Feb 2011
Posts: 97
Concentration: Strategy, Finance
Schools: Tuck '16, Darden '16
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

15 Aug 2011, 06:06
DeeptiM wrote:
If x and y are positive integers, is y divisible by 3?
(1) Y=2x^3+9x^2-5x.
(2) x is an odd number.

I think (1) is sufficient

If x = 1, y is not divisible by 3, if x is >1 then y is a fraction and not divisible by 3 obviously.

Would be more interesting is x could be a negative integer.
Status: How can I crack Verbal
Joined: 12 May 2011
Posts: 158
Location: India
Concentration: General Management, Finance
GMAT 1: 700 Q51 V32
GPA: 3
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

15 Aug 2011, 08:16
is it A?
A-factorise it=>x(2x-1)(x+5)..insert any value for X,the equation is divisible by 3
B alone is not sufficient as no info about X is available
Manager
Joined: 15 Feb 2011
Posts: 203
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

15 Aug 2011, 19:23
I got to know my mistake..thnx guys..
Senior Manager
Joined: 17 Mar 2014
Posts: 414
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

07 Mar 2015, 10:32
DeeptiM wrote:
If x and y are positive integers, is y divisible by 3?
(1) Y=2x^3+9x^2-5x.
(2) x is an odd number.

Bunuel could you help to solve this question.

Regards,
Ammu
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13331
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

07 Mar 2015, 12:30
Hi All,

GMAT questions are often based on patterns (in math, in logic, in grammar, etc.), so if you don't immediately see a pattern, there might still be one there...you just might have to do a little bit of work to find it.

This DS question is perfect for TESTing VALUES. While there is one "big" calculation to consider (in Fact 1), the individual math "steps" involved are NOT difficult. You just have to be ready to do a little work.

We're told that X and Y are POSITIVE INTEGERS. We're asked if Y is divisible by 3. This is a YES/NO question.

Fact 1: Y=2(X^3)+9(X^2)-5X

IF....
X = 1
Y = 2(1) + 9(1) - 5(1) = 6 and the answer to the question is YES.

IF....
X = 2
Y = 2(8) + 9(4) - 5(2) = 42 and the answer to the question is YES.

IF...
X = 3
Y = 2(27) + 9(9) - 5(3) = 120 and the answer to the question is YES.

It certainly looks like there's a pattern here: Y will ALWAYS be divisible by 3.
Fact 1 is SUFFICIENT

Fact 2: X is an odd number

This tells us nothing about Y.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 11 Dec 2012 Posts: 27 Re: If x and y are positive integers, is y divisible by 3? [#permalink] ### Show Tags 04 Apr 2015, 11:45 If x and y are positive integers, is y divisible by 3? (1) Y=2x^3+9x^2-5x. (2) x is an odd number. Statement (1) is insufficient because if X=1 than Y is divisible by 3 i.e. Y=2X^3+9X^2-5X => Y=2+9-5=6 which is divisible by Y; if X=2 then Y is not divisible by Y i.e. Y=2X^3+9X^2-5X => Y= 2*8+9*4-5*2=16+32-10=38 which is not divisible by 3. Statement (2) is clearly insufficient. (1)+(2) sufficient, because if we put odd numbers as indicated in statement (2) into Y=2x^3+9x^2-5x we will have a number divisible by 3 e.g.: X=1 has been shown above let's try X=3, X=5 and etc: X=3 Y=2*3^3+9*3^2-5*3=2*27+9*9-15=3(18+27+5) which is divisible by 3; X=5 Y=2*5^3+9*5^2-5*5=2*125+9*25-25=250-25+225=225+225=450 which is divisible by 3; Let's try X=17 then: Y=2*17^3+9*17^2-5*17=17(2*289+9*17-5)=17(578+153-5)=17*726 and 726 is divisible by 3. Hence, the answer is C. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13331 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are positive integers, is y divisible by 3? [#permalink] ### Show Tags 04 Apr 2015, 11:52 1 Hi ziyavutdinov, Your approach to TEST VALUES is a good one, but you made a mistake in one of your calculations. As a result, you've chosen the wrong answer. Take a look at the calculation when X = 2..... ziyavutdinov wrote: If x and y are positive integers, is y divisible by 3? (1) Y=2x^3+9x^2-5x. (2) x is an odd number. Statement (1) is insufficient because if X=1 than Y is divisible by 3 i.e. Y=2X^3+9X^2-5X => Y=2+9-5=6 which is divisible by Y; if X=2 then Y is not divisible by Y i.e. Y=2X^3+9X^2-5X => Y= 2*8+9*4-5*2=16+32-10=38 which is not divisible by 3. Hence, the answer is C. Once you've dealt with that issue, what would you do next? And what answer would you choose? GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Intern
Joined: 11 Dec 2012
Posts: 27
If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

05 Apr 2015, 09:12
Dear Rich,

I acknowledge I've made a calculation mistake. Thanks for correcting me. My answer is A.

ziyavutdinov
Intern
Joined: 27 Jan 2016
Posts: 1
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

15 Mar 2016, 17:35

If 2x^3 + 9x^2 - 5x is not divisible by 3, then 2x^3 - 2x + (9x^2 - 3x) is not divisible by 3.

Since there always exists a k1 where 3k1 = (9x^2 - 3x), then there must not exist a k2 where 3k2 = 2x^3 -2x (otherwise 3(k1 + k2) = y, y divisible by 3)

Thus, 2x^3 -2x is not divisible by 3

However, 2x^3 -2x = 2 * x *(x-1)*(x+1) is clearly divisible by 3

Therefore, the contradiction is false and the statement is true.
Current Student
Joined: 12 Aug 2015
Posts: 2626
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

10 Jan 2017, 23:03
This is such an amazing question.
Here is what i did in this Question=>

We need to see if y/3 is an integer or not.
We are given that a and y are positive integers.
Statement 1=>
$$y = 2x^3 + 9x^2 - 5x$$
Taking out x as a factor we get -> $$x[2x^2+9x-5]=> x(2x-1)(x+5)$$
Now putting in the values of x=> y is always a multiple of 3.
Hence sufficient.

Statement 2=>
No clue of y=> Not sufficient.

Hence A.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Manager
Joined: 30 Mar 2017
Posts: 134
GMAT 1: 200 Q1 V1
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

### Show Tags

31 Mar 2018, 12:01
Statement 1
$$y=2x^3+9x^2-5x = x(2x^2+9x-5)=x(2x-1)(x+5)$$

If one of {$$x, 2x-1,x+5$$} is divisible by 3, then y is divisible by 3.

Let's say we have 3 consecutive integers {$$x,x+1,x+2$$}. One of these will be divisible by 3. Let's check each one.

Case 1 ($$x$$ is div by 3)
Clearly, y is div by 3 since x is factor of y.

Case 2 ($$x+1$$ is div by 3)
$$x+1=3a$$ for some integer $$a$$
$$x=3a-1$$
Substituting into $$2x-1$$ we get $$2(3a-1)-1=6a-3=3(2a-1)$$, which is div by 3.

Case 3 ($$x+2$$ is div by 3)
If x+2 is div by 3, then so is x+5, which is a factor of y.

Thus y is div by 3.
Sufficient

Statement 2
Not sufficient

Re: If x and y are positive integers, is y divisible by 3? &nbs [#permalink] 31 Mar 2018, 12:01
Display posts from previous: Sort by

# If x and y are positive integers, is y divisible by 3?

 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®.