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# For a positive integer m, [m] is defined to be the remainder when

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
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For a positive integer m, [m] is defined to be the remainder when  [#permalink]

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08 Jul 2018, 23:56
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25% (medium)

Question Stats:

74% (01:45) correct 26% (01:35) wrong based on 80 sessions

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[GMAT math practice question]

For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n+1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II, &III

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7106 Re: For a positive integer m, [m] is defined to be the remainder when [#permalink] ### Show Tags 09 Jul 2018, 01:58 MathRevolution wrote: [GMAT math practice question] For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1? I. [3n+1] II. [3n] III. [3n] + 2 A. I only B. II only C. I & II only D.I & III only E. I, II, &III I. [3n+1] means remainder when 7*(3n+1) is divided by 3.. 21n+7 div by 3. 21n is divisible by 3 and 7 leaves a remainder of 1.....YES II. [3n] 7*3n is divisible by 3 so 0....not 1.....ans NO III. [3n]+2 [3n] is divisible by 3, so remainder will be 2....ans NO Only I A _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Director Status: Learning stage Joined: 01 Oct 2017 Posts: 931 WE: Supply Chain Management (Energy and Utilities) For a positive integer m, [m] is defined to be the remainder when [#permalink] ### Show Tags 09 Jul 2018, 03:11 MathRevolution wrote: [GMAT math practice question] For a positive integer m, [m]is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1? I. [3n+1] II. [3n] III. [3n] + 2 A. I only B. II only C. I & II only D.I & III only E. I, II, &III I. [3n+1] is the remainder when 7(3n+1) is divided by 3. Or, Rem((21n+7)/3)=Rem(21n/3)+Rem(7/3)=0+1=1 So,[3n+1] =1 II.[3n] is the remainder when 7(3n) is divided by 3. Or,Rem(21n/3)=0 So, [3n]=1 III.From II, we have obtained , [3n]=0 So, [3n]+2=0+2=0 So, the expression in I, yields a value of 1. Ans. (A) _________________ Regards, PKN Rise above the storm, you will find the sunshine Director Joined: 14 Dec 2017 Posts: 518 Location: India Re: For a positive integer m, [m] is defined to be the remainder when [#permalink] ### Show Tags 09 Jul 2018, 11:14 1 MathRevolution wrote: [GMAT math practice question] For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1? I. [3n+1] II. [3n] III. [3n] + 2 A. I only B. II only C. I & II only D.I & III only E. I, II, &III I. [3n+1] means remainder when 7(3n+1) = 21n + 7 is divided by 3, we get remainder as 1. Hence [3n+1] = 1 II. [3n] means remainder when 7(3n) = 21n is divided by 3, we get remainder as 0. Hence, [3n] = 2 III. [3n] + 2 means remainder when 7(3n) + 2 = 21n + 2 is divided by 3, we get remainder as 2. Hence, [3n]+2 = 2 Hence Only I gives remainder as 1. Answer A. Thanks, GyM _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For a positive integer m, [m] is defined to be the remainder when [#permalink] ### Show Tags 11 Jul 2018, 00:10 => Statement I $$7(3n+1) = 21n + 7 = 3(7n+2) + 1$$ Thus, $$[3n+1] = 1$$ Statement II $$7(3n) = 21n = 3*7n + 0$$ Thus, $$[3n] = 0$$ Statement III Since $$[3n] = 0$$, we have $$[3n] + 2 = 2.$$ Thus, only $$[3n+1]$$ equals $$1$$. Therefore, the answer is A. Answer: A _________________ 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: For a positive integer m, [m] is defined to be the remainder when  [#permalink]

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14 Jul 2018, 18:22
MathRevolution wrote:
[GMAT math practice question]

For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n+1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II, &III

Let’s analyze each Roman numeral.

I. [3n+1]

[3n+1] is the remainder when 7(3n + 1) = 21n + 7 is divided by 3. Since 21n is divisible by 3, we see that [3n+1] is equal to the remainder when 7 is divided by 3, which is 1. So I is true.

II. [3n]

[3n] is the remainder when 7(3n) = 21n is divided by 3. Since 21n is divisible by 3, we see that the remainder is 0. So II is not true.

III. [3n] + 2

We saw that in Roman numeral II, [3n] has a remainder 0 when it’s divided by 3. So [3n] + 2 has a remainder of 2 when it’s divided by 3. III is not true.

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Re: For a positive integer m, [m] is defined to be the remainder when  [#permalink]

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27 Jul 2018, 09:42
MathRevolution wrote:
[GMAT math practice question]

For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n+1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II, &III

MathRevolution is it typical of GMAT type of question ? how often can i encounter such kind of questuons on gmat ?
VP
Joined: 09 Mar 2016
Posts: 1225
Re: For a positive integer m, [m] is defined to be the remainder when  [#permalink]

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27 Jul 2018, 09:48
GyMrAT wrote:
MathRevolution wrote:
[GMAT math practice question]

For a positive integer m, [m] is defined to be the remainder when 7m is divided by 3. If n is a positive integer, which of the following are equal to 1?

I. [3n+1]
II. [3n]
III. [3n] + 2

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II, &III

I. [3n+1] means remainder when 7(3n+1) = 21n + 7 is divided by 3, we get remainder as 1. Hence [3n+1] = 1

II. [3n] means remainder when 7(3n) = 21n is divided by 3, we get remainder as 0. Hence, [3n] = 2

III. [3n] + 2 means remainder when 7(3n) + 2 = 21n + 2 is divided by 3, we get remainder as 2. Hence, [3n]+2 = 2

Hence Only I gives remainder as 1.

Thanks,
GyM

hey GyMrAT how did you get remainer of 1? would like to see detailed solution of correct answer choice. thanks for taking time to explain
have a great weekend

I. [3n+1] means remainder when 7(3n+1) = 21n + 7 is divided by 3, we get remainder as 1. Hence [3n+1] = 1
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Joined: 14 Dec 2017
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Location: India
For a positive integer m, [m] is defined to be the remainder when  [#permalink]

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27 Jul 2018, 10:21
1
dave13 wrote:

hey GyMrAT how did you get remainer of 1? would like to see detailed solution of correct answer choice. thanks for taking time to explain
have a great weekend

I. [3n+1] means remainder when 7(3n+1) = 21n + 7 is divided by 3, we get remainder as 1. Hence [3n+1] = 1

(21n + 7)/3 = 21n/3 + 7/3 , we get remainder as 0 for 21n/3 & 1 for 7/3, hence final remainder is (0 + 1) = 1

I think it is called Remainder theorem, which states if $$R_1$$ , $$R_2$$ & $$R_3$$ are remainders when $$N_1$$, $$N_2$$ & $$N_3$$ are each divided by D

then,$$\frac{(N_1 + N_2 - N_3)}{D}$$ the remainder will be $$R_1 + R_2 - R_3$$

Quote:
thanks for taking time to explain
have a great weekend

No Problem! Have a good one!

Cheers!
GyM
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For a positive integer m, [m] is defined to be the remainder when &nbs [#permalink] 27 Jul 2018, 10:21
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