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If r, s, and t are all positive integers, what is the remainder of 2^p

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If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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Tough and Tricky questions: Remainders.



If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?

(1) s is even
(2) p = 4t
[Reveal] Spoiler: OA

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Kudos [?]: 132852 [0], given: 12378

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Re: If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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New post 23 Oct 2014, 00:55
Bunuel wrote:

Tough and Tricky questions: Remainders.



If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?

(1) s is even
(2) p = 4t


Check Units digits, exponents, remainders problems directory in our Special Questions Directory.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Remainders.



If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?

(1) s is even
(2) p = 4t


Sol: The questions becomes what is the remainder when 2^(rst)/10 ?

St 1 says: s is even that means r*s*t=even

Now 2^(Even number) can end is 4 or 6..So we have to remainders possible. A and D ruled out

St 2 says p=4*t or p is a multiple of 4 so we will have expression of the form 2^4 or 2^8 or 2^12...all end up in 6..

So remainder will be 6..

Ans is B
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Re: If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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Re: If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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New post 23 Jul 2017, 04:06
Hello from the GMAT Club BumpBot!

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Re: If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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New post 25 Sep 2017, 17:41
Bunuel wrote:

Tough and Tricky questions: Remainders.



If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?

(1) s is even
(2) p = 4t


Bunuel how do we know whether or not the question reads 2^(p/10) pr (2^p) /10?

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Re: If r, s, and t are all positive integers, what is the remainder of 2^p [#permalink]

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New post 25 Sep 2017, 21:11
Nunuboy1994 wrote:
Bunuel wrote:

Tough and Tricky questions: Remainders.



If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?

(1) s is even
(2) p = 4t


Bunuel how do we know whether or not the question reads 2^(p/10) pr (2^p) /10?


2^p/10 can mean nothing but (2^p)/10. If it were 2^(p/10), it would have been written that way.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Kudos [?]: 132852 [0], given: 12378

Re: If r, s, and t are all positive integers, what is the remainder of 2^p   [#permalink] 25 Sep 2017, 21:11
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