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Manager  Joined: 16 Feb 2011
Posts: 190
If x and y are positive integers, is y divisible by 3?  [#permalink]

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5 00:00

Difficulty:   75% (hard)

Question Stats: 52% (02:12) correct 48% (02:05) wrong based on 154 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, 06:43.
Last edited by Bunuel on 05 Apr 2015, 04:56, edited 2 times in total.
Renamed the topic and edited the question.
Manager  Status: Quant 50+?
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Concentration: Strategy, Finance
Schools: Tuck '16, Darden '16
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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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: 152
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]

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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: 16 Feb 2011
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Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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I got to know my mistake..thnx guys..
Senior Manager  P
Joined: 17 Mar 2014
Posts: 441
Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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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
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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern  B Joined: 11 Dec 2012 Posts: 25 Re: If x and y are positive integers, is y divisible by 3? [#permalink] ### Show Tags 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 V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14590 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 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 *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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Intern  B
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If x and y are positive integers, is y divisible by 3?  [#permalink]

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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]

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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.
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GRE 1: Q169 V154 If x and y are positive integers, is y divisible by 3?  [#permalink]

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1
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.

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GMAT 1: 200 Q1 V1 Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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1
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

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Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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_________________ Re: If x and y are positive integers, is y divisible by 3?   [#permalink] 09 Apr 2019, 07:42
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