December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 946
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
Updated on: 04 Oct 2012, 03:23
Question Stats:
61% (00:50) correct 39% (00:54) wrong based on 3054 sessions
HideShow timer Statistics
If n = (33)^43 + (43)^33 what is the units digit of n? A. 0 B. 2 C. 4 D. 6 E. 8
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Archit143 on 03 Oct 2012, 23:13.
Last edited by Bunuel on 04 Oct 2012, 03:23, edited 1 time in total.
Moved to PS forum.




Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If n = (33)^43
[#permalink]
Show Tags
09 Mar 2014, 12:04
Bunuel wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
A. 0 B. 2 C. 4 D. 6 E. 8
First of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^33 is the same as that of 3^33. So, we need to find the units digit of 3^43 + 3^33.
Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}: 3^1=3 (the units digit is 3) 3^2=9 (the units digit is 9) 3^3=27 (the units digit is 7) 3^4=81 (the units digit is 1) 3^5=243 (the units digit is 3 again!) ...
Thus: The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3). The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^43 + (43)^33 is 7 + 3 = 0.
Answer: A. For more on this check theory and problems listed below: Problem Solving: 650+ whatisthetensdigitof127023.htmlifyoudivide7131by5whichremainderdoyouget83350.htmlifnisapositiveintegerwhatistheremainderwhen105067.htmlwhatistheunitsdigitof101015.htmlifnisapositiveintegerwhatistheremainderwhen96262.htmlwhatistheremainderwhen3243isdividedby141050.htmlfindtheonesdigitof141071.htmlm1272970.html700+ when5125isdividedby13theremainderobtainedis130220.htmlm2573474.htmlwhichofthefollowingnumbersisprime168179.htmlwhatistheremainderwhen4386isdividedby134778.htmlwhen5125isdividedby13theremainderobtainedis130220.htmlwhatistheremainderwhen4371743628232isdividedby154889.htmlifn33434333whatistheunitsdigitofn140037.html750+ whatistheunitsdigitof126681.htmlwhatistheremainderof126493.htmlwhatistheremainderwhen323232isdividedby100316.htmlalgebram26145109.htmlwhatistheremainderwhen333222isdividedby156379.htmlwhatistheremainderwhen182210isdividedby99724.htmlData Sufficiency: 600+ ifkisapositiveintegerwhatisthereminderwhen2k126478.html650+ ifxisapositiveintegeristheremainder0when3x109075.htmlif243x463ynwherexandyarepositiveintegers102054.htmlifrsandtareallpositiveintegerswhatisthe136746.html700+ toughandtrickyexponentsandrootsquestions125967.html#p1029239ifxandyarepositiveintegerswhatistheremainderwhen109636.htmlHope this helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 25 Jun 2012
Posts: 62
Location: India
WE: General Management (Energy and Utilities)

Re: If n = (33)^43
[#permalink]
Show Tags
03 Oct 2012, 23:33
Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
0 2 4 6 8
pls suggest approach for such probs In such type of exponents problem, first find the cyclicity of unit digit of 3. which is (3,9,7,1) Now convert exponent value in to multiple of 4. here 43=4(10)+3 so take 3^3 as unit value of first term which is 27 ===> unit digit is 7 (3,9, 7,1) Now 33=4(8)+1,so take 3^1 as unit value of second term which is 3^1====> unit digit is 3 (3,9,7, 1) Now unit digit of n = unit digit of first term + unit digit of 2nd term = 7+3=1 0 = unit digit is 0




Manager
Joined: 08 Apr 2012
Posts: 118

Re: If n = (33)^43
[#permalink]
Show Tags
03 Oct 2012, 23:41
Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
0 2 4 6 8
pls suggest approach for such probs Hi Archit, Just follow the unit digits: n = (33)^43 + (43)^33 Here the last digits would determine the power. So, n = (33)^43 + (43)^33 ~ 3^43 + 3 ^33 Now last digits of 3^1, 2, 3, 4, 5 = 3, 9, 7, 1, 3. The cycle repeats after every 4 rounds. So n = 3^43 + 3 ^33 = 3^(40+3) + 3^(32+1) = {(3^(4*10)}{3^3} + {(3^(4*8)}{3^1} Now last digits of these terms would be {1}{7} + {1}{3} = 10 Hence the last digit is 0. Hope this helps. Regards, Shouvik
_________________
Shouvik http://www.Edvento.com admin@edvento.com



Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
04 Oct 2012, 03:27



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1825
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
26 Feb 2014, 19:16
Both terms has 3 at the units place, so the units place cycle around 3,9,7,1 33^43 will have 7 & 43^33 will have 3 7 + 3 = 10, 0 would be in the units place of the resultant Answer = 0 = A
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 25 Jul 2013
Posts: 1

Re: If n = (33)^43
[#permalink]
Show Tags
09 Mar 2014, 10:43
bhavinshah5685 wrote: Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
0 2 4 6 8
pls suggest approach for such probs In such type of exponents problem, first find the cyclicity of unit digit of 3. which is (3,9,7,1) Now convert exponent value in to multiple of 4. here 43=4(10)+3 so take 3^3 as unit value of first term which is 27 ===> unit digit is 7 (3,9, 7,1) Now 33=4(8)+1,so take 3^1 as unit value of second term which is 3^1====> unit digit is 3 (3,9,7, 1) Now unit digit of n = unit digit of first term + unit digit of 2nd term = 7+3=1 0 = unit digit is 0I can't understand why it has to be a multiple of 4. I mean, 43 can also be expressed as (2)(21)+1 but this would be wrong. Generally in such exercises it has to be a multiple of 4, or I don't get something?



Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If n = (33)^43
[#permalink]
Show Tags
09 Mar 2014, 11:56
Chrysopigi89 wrote: bhavinshah5685 wrote: Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
0 2 4 6 8
pls suggest approach for such probs In such type of exponents problem, first find the cyclicity of unit digit of 3. which is (3,9,7,1) Now convert exponent value in to multiple of 4. here 43=4(10)+3 so take 3^3 as unit value of first term which is 27 ===> unit digit is 7 (3,9, 7,1) Now 33=4(8)+1,so take 3^1 as unit value of second term which is 3^1====> unit digit is 3 (3,9,7, 1) Now unit digit of n = unit digit of first term + unit digit of 2nd term = 7+3=1 0 = unit digit is 0I can't understand why it has to be a multiple of 4. I mean, 43 can also be expressed as (2)(21)+1 but this would be wrong. Generally in such exercises it has to be a multiple of 4, or I don't get something? If n = (33)^43 + (43)^33 what is the units digit of n?A. 0 B. 2 C. 4 D. 6 E. 8 First of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^33 is the same as that of 3^33. So, we need to find the units digit of 3^43 + 3^33. Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}: 3^1=3 (the units digit is 3) 3^2=9 (the units digit is 9) 3^3=27 (the units digit is 7) 3^4=81 (the units digit is 1) 3^5=243 (the units digit is 3 again!) ... Thus: The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3). The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1). Therefore the units digit of (33)^43 + (43)^33 is 7 + 3 = 0. Answer: A.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 482
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
09 Sep 2014, 01:46
Bunuel, I found mistake in the solution given by you The Cycle here is 9, 7, 1, 3 Not 3, 9, 7 , 1 (as you stated) Multiply 33 x 33 Once, what do we get 1089, Unit digit is 9. So the cycle should start at 9 By that logic we should add 1 + 9 = 10 Answer is still A. But lets tweak it (33)^43 + (43)^34 Bunuel you will do this with your chosen cycle 7+9 = 16, Your answer will be 6 With my chosen Cycle 1+7 = 8. That could be a trap if they play on the starting point of the cycle.
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
09 Sep 2014, 06:13
honchos wrote: Bunuel,
I found mistake in the solution given by you
The Cycle here is
9, 7, 1, 3 Not 3, 9, 7 , 1 (as you stated)
Multiply 33 x 33 Once, what do we get 1089, Unit digit is 9. So the cycle should start at 9
By that logic we should add
1 + 9 = 10 Answer is still A.
But lets tweak it
(33)^43 + (43)^34
Bunuel you will do this with your chosen cycle 7+9 = 16, Your answer will be 6
With my chosen Cycle 1+7 = 8.
That could be a trap if they play on the starting point of the cycle. Please reread the solution and follow the links given above. You should start with power of 1: 3^1=3 (the units digit is 3) 3^2=9 (the units digit is 9) 3^3=27 (the units digit is 7) 3^4=81 (the units digit is 1) 3^5=243 (the units digit is 3 again!) ...
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 09 Feb 2014
Posts: 8

If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
05 Oct 2014, 04:40
Based on the Number Theory > Last digit of a power (in the GMATclub forum, I cannot link to the post) Step 1: Find the last digit of 33^43find the cyclicity of 33 33^1= _3 33^2= _9 33^3= _7 33^4= _1 33^5= _3 > 33 has the cyclicity of 4 Divide the power by the cyclicity: 43/4 > remainder is 3 (refer to the 3rd position in the cyclicity) > the last digit of 33^43 is the same as that of 33^3 > 7 is the last digitStep 2: Similarly, find the last digit of 43^3343 also has the cyclicity of 4 (ends with 3) Divide 33 by 4 > remainder is 1 > refer to the 1st position in the cyclicity > last digit is 3 Step 3: 7+3 = 10 > the last digit is 0 Answer A



Manager
Joined: 07 Apr 2015
Posts: 165

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
10 May 2015, 00:50
Bunuel wrote: Thus: The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3). The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).
Therefore the units digit of (33)^43 + (43)^33 is 7 + 3 = 0.
Answer: A. I do not understand this part with remainder and cyclicity, why do i need to divide 43 by 4 to get a remainder of one which is then the units digit??



Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
11 May 2015, 02:03



Manager
Joined: 10 Jun 2015
Posts: 118

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
14 Aug 2015, 21:38
Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
A. 0 B. 2 C. 4 D. 6 E. 8 the unit digit of 3^1=3 3^5=3 3^9=3 3^33=3 therefore, 3^33+3^33=6 the correct answer is D



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
23 Jun 2016, 08:33
Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
A. 0 B. 2 C. 4 D. 6 E. 8 This is a units digit pattern question. The first thing to recognize is that in units digit pattern questions we only care about the units digit place value. Thus, we can rewrite the problem as: (3)^43 + (3)^33 We now need to determine the units digit of (3)^43 + (3)^33. Let's determine the pattern of units digits that we get when a base of 3 is raised to consecutive exponents. 3^1 = 3 3^2 = 9 3^3 = 27 (units digit of 7) 3^4 = 81 (units digit of 1) 3^5 = 243 (units digit of 3) Notice at 3^5, the pattern has started over: 3^6 = units digit of 9 3^7 = units digit of 7 3^8 = units digit of 1 So we can safely say that the base of 3 gives us a units digit pattern of 3, 9, 7, 1, 3, 9, 7, 1, …) that repeats every four exponents. Also notice that every time 3 is raised to an exponent that is a multiple of 4, we are left with a units digit of 1. This is very powerful information, which we can use to solve the problem. Let’s start with the units digit of (3)^43. An easy way to determine the units digit of (3)^43, is to find the closest multiple of 4 to 43, and that is 44. Thus we know: 3^44 = units digit of 1 So we can move back one exponent in our pattern and we get: 3^43 = units digit of 7 Let’s now determine the units digit of (3)^33. We already know that the pattern of units digits for powers of 3 will be 3, 9, 7, 1, 3, 9, 7, 1, … An easy way to determine the units digit of (3)^33 is to find the closest multiple of 4 to 33, and that is 32. Thus we know: 3^32 = units digit of 1 So we can move up one exponent in our pattern and we get: 3^33 = units digit of 3 The last step is to add the two units digits together so we have: 7 + 3 = 10, which has a units digit of zero) Answer is A.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 02 Sep 2016
Posts: 681

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
01 Apr 2017, 05:07
Units digit of a product will ALWAYS depend on the units digits of the numbers being multiplied.Just focus on the units digit. Units digit of n=(3)^43+(3)^33 The cyclicity of 3 is 4. 3^1=3 3^2=9 3^3=27 (Units digit 7) 3^4=81 (Units digit 1) After this the digits will start repeating (3,9,7,1,3,9,7,1, and so on) A the cyclicity is 4 (here), write the powers as multiple of 4 and look for the remainder (if any). 43=4*10+ 3Therefore the units digit of (3)^43= 7 33=4*8+1 Therefore the units digit of (3)^33= 3 The units digit of n= 7+3=10 (Just consider the last digit i.e. the unit's digit) The answer is 0.
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.



Intern
Joined: 11 Aug 2017
Posts: 26
Location: United States
GPA: 3.4

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
29 Dec 2017, 14:02
How is this only a 600 to 700 level question? Manhattan GMAT has it listed as "Devilish" under the difficulty.



Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
29 Dec 2017, 23:03



VP
Joined: 09 Mar 2016
Posts: 1234

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
30 Dec 2017, 07:18
bhavinshah5685 wrote: Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
0 2 4 6 8
pls suggest approach for such probs In such type of exponents problem, first find the cyclicity of unit digit of 3. which is (3,9,7,1) Now convert exponent value in to multiple of 4. here 43=4(10)+3 so take 3^3 as unit value of first term which is 27 ===> unit digit is 7 (3,9, 7,1) Now 33=4(8)+1,so take 3^1 as unit value of second term which is 3^1====> unit digit is 3 (3,9,7, 1) Now unit digit of n = unit digit of first term + unit digit of 2nd term = 7+3=1 0 = unit digit is 0Hello bhavinshah5685 if exponent 33=4(8)+1 and unit digit is 3^1 than why did you highligh 1 in red instead of 3 ? thanks!



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2313

Re: If n = (33)^43 + (43)^33 what is the units digit of n?
[#permalink]
Show Tags
31 Dec 2017, 10:06
dave13 wrote: bhavinshah5685 wrote: Archit143 wrote: If n = (33)^43 + (43)^33 what is the units digit of n?
0 2 4 6 8
pls suggest approach for such probs In such type of exponents problem, first find the cyclicity of unit digit of 3. which is (3,9,7,1) Now convert exponent value in to multiple of 4. here 43=4(10)+3 so take 3^3 as unit value of first term which is 27 ===> unit digit is 7 (3,9, 7,1) Now 33=4(8)+1,so take 3^1 as unit value of second term which is 3^1====> unit digit is 3 (3,9,7, 1) Now unit digit of n = unit digit of first term + unit digit of 2nd term = 7+3=1 0 = unit digit is 0Hello bhavinshah5685 if exponent 33=4(8)+1 and unit digit is 3^1 than why did you highligh 1 in red instead of 3 ? thanks! He must have done it by mistake and highlighted 1 after getting the remainder as 1. By the way, his approach and answer are absolutely correct. Regards, Saquib eGMATQuant Expert
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com




Re: If n = (33)^43 + (43)^33 what is the units digit of n? &nbs
[#permalink]
31 Dec 2017, 10:06



Go to page
1 2
Next
[ 21 posts ]



