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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) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 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 integers, is x/3 an integer?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Senior Manager Status: 1,750 Q's attempted and counting Affiliations: University of Florida Joined: 09 Jul 2013 Posts: 496 Location: United States (FL) Schools: UFL (A) GMAT 1: 600 Q45 V29 GMAT 2: 590 Q35 V35 GMAT 3: 570 Q42 V28 GMAT 4: 610 Q44 V30 GPA: 3.45 WE: Accounting (Accounting) If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags Updated on: 02 Oct 2013, 23:28 1 4 00:00 Difficulty: 35% (medium) Question Stats: 71% (01:20) correct 29% (01:26) wrong based on 388 sessions ### HideShow timer Statistics If x and y are integers, is x/3 an integer? (1) x + 14 = 2y (2) (2y+1)/3 is an integer. Originally posted by avohden on 02 Oct 2013, 15:54. Last edited by Bunuel on 02 Oct 2013, 23:28, edited 1 time in total. Edited the question. ##### Most Helpful Community Reply Senior Manager Status: 1,750 Q's attempted and counting Affiliations: University of Florida Joined: 09 Jul 2013 Posts: 496 Location: United States (FL) Schools: UFL (A) GMAT 1: 600 Q45 V29 GMAT 2: 590 Q35 V35 GMAT 3: 570 Q42 V28 GMAT 4: 610 Q44 V30 GPA: 3.45 WE: Accounting (Accounting) Re: If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags 02 Oct 2013, 16:02 5 Official Explanation CORRECT ANSWER IS C. The question is really asking whether or not x is divisible by 3. The stem doesn't offer much more information, so move on to the statements. Statement (1): insufficient. Solving for x, we have that x = 2y – 14. We thus know that x is divisible by 2 (since y is an integer), but we don't know whether x is also divisible by 3. Statement (1) is insufficient. Eliminate (A) and (D). Statement (2): insufficient. This equation does not contain x, so it can't tell us whether x is divisible by 3. Eliminate (B). Statements (1) and (2): sufficient. Both statements contain 2y, so use substitution to solve. Substituting x + 14 for 2y in the second expression, we have that is an integer. This simplifies to , and since is an integer, must be an integer. The answer to the question must be "yes," and choice (C) is correct. ##### General Discussion Intern Joined: 30 Apr 2013 Posts: 15 Location: India Re: If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags 02 Oct 2013, 20:24 Thanks avohden! Good explanation. _________________ GMAT RC Vocab - No nonsense(Only for GMAT) http://gmatclub.com/forum/gmat-rc-vocab-no-nonsense-only-for-gmat-162129.html#p1283165 Quant Document to revise a week before exam - Mixedbag http://gmatclub.com/forum/document-to-revise-a-week-before-exam-mixedbag-162145.html Best questions to revise few days before exam- Mixed bag(25) http://gmatclub.com/forum/best-questions-to-revise-few-days-before-exam-mixed-bag-162124.html#p1283141 Manager Joined: 18 Oct 2013 Posts: 72 Location: India Concentration: Technology, Finance GMAT 1: 580 Q48 V21 GMAT 2: 530 Q49 V13 GMAT 3: 590 Q49 V21 WE: Information Technology (Computer Software) Re: If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags 26 Nov 2013, 12:59 Given: X & Y are Integers Find: Is X/3=Integer ? 1) Not sufficient.Eliminate A&D 2) Not Sufficient. Eliminate B. 1+2) x=2y-14 ----------- 1 x=2y+1-15 ---------- Add +1 & -1 in RHS Therefore, 15 is divisible by 3 and 2y+1 is divisible by 3. Hence ,C Director Joined: 25 Apr 2012 Posts: 689 Location: India GPA: 3.21 WE: Business Development (Other) Re: If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags 26 Nov 2013, 21:33 avohden wrote: If x and y are integers, is x/3 an integer? (1) x + 14 = 2y (2) (2y+1)/3 is an integer. From St 1, we have x= 2y-14 and x/3 = (2y-14)/3 Now if y= 7 then we have x/3 as 0/3 =0, which is an integer But if y=8 then we have x/3= 2/3 not an Integer so A and D ruled out From St 2, we know nothing about X and hence B also ruled out Combining the 2 equations we get x= 2y-14 or x = (2y+1) -15 x/3 = (2y+1)/3 - 15/3---------> Now (2y+1)/3 is an integer and also 15/3 is an integer and therefore x/3 is an integer Hence E ruled. Ans C _________________ “If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.” Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags 06 Jul 2017, 16:23 avohden wrote: If x and y are integers, is x/3 an integer? (1) x + 14 = 2y (2) (2y+1)/3 is an integer. We are given that x and y are integers and need to determine whether x/3 is an integer. Statement One Alone: x + 14 = 2y The information in statement one is not sufficient to answer the question. For example, if x = 4 (and y = 9), x is not divisible by 3; however if x = 6 (and y = 10), then x is divisible by 3. Statement one alone is not sufficient to answer the question. Statement Two Alone: (2y+1)/3 is an integer. We see that y can be values such as 1, 4, 7, etc. Thus, we see that y = 3k - 2, where k is an integer. However, since we do not know anything about x, statement two alone is not sufficient to answer the question. Statements One and Two Together: We can substitute 3k - 2 for y in statement one and we have: x + 14 = 2(3k - 2) x + 14 = 6k - 4 x = 6k - 18 x = 6(k - 3) Since x is a multiple of 6, x/3 will always be an integer. Answer: C _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6504 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, is x/3 an integer? [#permalink] ### Show Tags 07 Jul 2017, 22:09 avohden wrote: If x and y are integers, is x/3 an integer? (1) x + 14 = 2y (2) (2y+1)/3 is an integer. Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. There are 2 variables and 0 equation. By Variable Approach method, the answer is C most likely. The question asks if $$x$$ is a multiple of $$3$$. Condition 1) : $$x + 14 = 2y$$ is equivalent to $$x = 2y - 14$$. If $$y = 0$$, then $$x = -14$$ is not a multiple of $$3$$. If $$y = 7$$, then $$x = 0$$ is a multiple of $$3$$. Thus the solutions are not unique. Hence this condition is not sufficient. Condition 2) : We don't have any information about $$x$$. Thus this is not sufficient. Condition 1) & 2) The second condition that $$\frac{2y + 1}{3}$$ is an integer is equivalent to the statement that $$2y + 1$$ is a multiple of $$3$$. If $$2y + 1$$ is a multiple of $$3$$, then $$2y$$ has a remainder $$2$$ when it is divided by $$3$$, that is $$2y = 3k + 2$$ for some an integer $$k$$. Then $$x = 2y - 14 = 3k + 2 - 14 = 3k - 12 = 3(k-4)$$. Thus $$x$$ is a multiple of $$3$$. Therefore, C is the answer as expected. Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If x and y are integers, is x/3 an integer?  [#permalink]

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04 Jan 2018, 01:30
this question is a common pattern in gmat. The question asks about the value of x / 3, not the value of x; hence, C is the answer even though the st 2 gives no value about x.
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Re: If x and y are integers, is x/3 an integer?  [#permalink]

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19 Oct 2018, 17:02
The question is really asking whether or not x is divisible by 3. The stem doesn't offer much more information, so move on to the statements.

Statement (1): insufficient. Solving for x, we have that x = 2y - 14. We thus know that x is divisible by 2 (since y is an integer), but we don't know whether x is also divisible by 3. Statement (1) is insufficient. Eliminate (A) and (D).

Statement (2): insufficient. This equation does not contain x, so it can't tell us whether x is divisible by 3. Eliminate (B).

Statements (1) and (2): sufficient. Both statements contain 2y, so use substitution to solve. Substituting x + 14 for 2y in the second expression, we have that is an integer. This simplifies to (x + 15)/3 , and since (x/3) + 5 is an integer, (x/3 ) must be an integer. The answer to the question must be "yes," and choice (C) is correct.

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Re: If x and y are integers, is x/3 an integer? &nbs [#permalink] 19 Oct 2018, 17:02
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