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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # If x and y are positive integers, is y divisible by 3?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 15 Feb 2011 Posts: 205 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. Retired Thread Master Status: How can I crack Verbal Joined: 12 May 2011 Posts: 163 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: 205 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: 380 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: 12841 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 Final Answer: 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
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Re: If x and y are positive integers, is y divisible by 3?  [#permalink]

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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.

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

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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.

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

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05 Apr 2015, 09:12
Dear Rich,

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

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

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

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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.

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

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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
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