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# When a positive integer n is divided by 5, the remainder is 2. What is

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Math Revolution GMAT Instructor
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When a positive integer n is divided by 5, the remainder is 2. What is  [#permalink]

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13 Apr 2018, 01:38
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73% (01:46) correct 27% (02:03) wrong based on 182 sessions

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[GMAT math practice question]

When a positive integer $$n$$ is divided by $$5$$, the remainder is $$2$$. What is the remainder when $$n$$ is divided by $$3$$?

1) $$n$$ is divisible by $$2$$
2) When $$n$$ is divided by $$15$$, the remainder is $$2$$.

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4959 Location: Canada GMAT 1: 770 Q49 V46 When a positive integer n is divided by 5, the remainder is 2. What is [#permalink] ### Show Tags 13 Apr 2018, 06:48 1 Top Contributor 4 MathRevolution wrote: [GMAT math practice question] When a positive integer $$n$$ is divided by $$5$$, the remainder is $$2$$. What is the remainder when $$n$$ is divided by $$3$$? 1) $$n$$ is divisible by $$2$$ 2) When $$n$$ is divided by $$15$$, the remainder is $$2$$. Target question: What is the remainder when n is divided by 3? Given: When positive integer n is divided by 5, the remainder is 2 ----ASIDE---------------------- When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. ----------------------------------- So, from the given information, we can conclude that some possible values of n are: 2, 7, 12, 17, 22, 27, 32, 37, etc Statement 1: n is divisible by 2 When we examine our list of possible n-values (2, 7, 12, 17, 22, 27, 32, 37, ... ), we see that n could equal 2, 12, 22, 32, 42, etc Let's test two of these possible n-values: Case a: n = 2. In this case, 2 divided by 3 equals 0 with remainder 2. So, the answer to the target question is the remainder is 2 Case b: n = 12. In this case, 12 divided by 3 equals 4 with remainder 0. So, the answer to the target question is the remainder is 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: When n is divided by 15, the remainder is 2 In other words, n is 2 greater than some multiple of 15 We can write: n = 15k + 2, where k is some integer. IMPORTANT: notice we can take n = 15k + 2 and rewrite it as n = 3(5k) + 2 Notice that 3(5k) is a multiple of 3, which means 3(5k) + 2 is 2 MORE than some multiple of 3 This means that, when we divide n by 3, the remainder is 2 So, the answer to the target question is the remainder is 2 Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com ##### General Discussion Current Student Joined: 07 Jan 2016 Posts: 1082 Location: India GMAT 1: 710 Q49 V36 Re: When a positive integer n is divided by 5, the remainder is 2. What is [#permalink] ### Show Tags 13 Apr 2018, 02:34 MathRevolution wrote: [GMAT math practice question] When a positive integer $$n$$ is divided by $$5$$, the remainder is $$2$$. What is the remainder when $$n$$ is divided by $$3$$? 1) $$n$$ is divisible by $$2$$ 2) When $$n$$ is divided by $$15$$, the remainder is $$2$$. n = 5K+2 1)if n is divisble by 2 12,22 n has 0,1 diff values as remainder insufficient 2) 15 is a multiple of 3 so the remainder will be same (B) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9164 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: When a positive integer n is divided by 5, the remainder is 2. What is [#permalink] ### Show Tags 15 Apr 2018, 17:43 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. We have 1 variable (n) and 1 equation. So, D is most likely to be the answer, and we should consider each of the conditions on its own first. Plugging-in numbers is the suggested approach to remainder questions. Condition 1) The possible values of n are $$n = 2, 4, 6, 8, …$$ When these are divided by $$3$$, the remainders are $$0, 1$$ and $$2$$. Since the answer is not unique, condition 1) is not sufficient. Condition 2) The possible values of n are $$n = 17, 32, 47, 62, …$$ When these are divided by $$3$$, the remainder is always $$2$$. Since the answer is unique, condition 2) is sufficient. Therefore, B is the answer. Answer: B If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C 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$79 for 1 month Online Course"
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Re: When a positive integer n is divided by 5, the remainder is 2. What is  [#permalink]

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22 Aug 2018, 23:41
n=5*m+2
1. n=2x
for n=5*m+2, n can be 7,12,..
for n=2x, n can be 2,4,6,8,10,12...
hence n can be expresed as n=LCM(2,5)*y+12=10y+12
so the remainder of n/3 will depend on the value of y. insufficient
2. n=15p+2
n can be 17,32,..
n can be expressed as n=LCM(5,15)*q+32=15q+32
the remainder of n/3 will be 2.
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Re: When a positive integer n is divided by 5, the remainder is 2. What is  [#permalink]

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05 Mar 2020, 11:31
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Re: When a positive integer n is divided by 5, the remainder is 2. What is   [#permalink] 05 Mar 2020, 11:31