You are watching: What is the units digit of 3^43
ForumForum HomeGMAT prepare & ADMISSIONS GMAT food Reviews MBA Admissions Consulting evaluate MBA RANKINGSSTORE & DEALSFree StuffFORUM Forum GMAT prepare & ADMISSIONS GMAT course Reviews MBA Admissions Consulting evaluate MBA RANKINGS save & deals complimentary Stuff cost-free Resources
If n = (33)^43 + (43)^33 what is the units digit the n?A. 0B. 2C. 4D. 6E. 8The OA is A.How have the right to I know the systems digit without making the whole calculation? I need some help. Please.
GMATGuruNYGMAT Instructor Posts: 15533Joined: 25 might 2010Location: new York, NY Thanked: 13060 time Followed by:1900 members GMAT Score:790
3¹ --> units digit the 3. 3² --> systems digit of 9. (Since the product the the coming before units digit and also 3 = 3*3 = 9.) 3³ --> systems digit the 7. (Since the product of the coming before units digit and also 3 = 9*3 = 27.) 3� --> units digit the 1. (Since the product the the coming before units digit and 3 = 7*3 = 21.) from here, the devices digits will certainly repeat in the very same pattern: 3, 9, 7, 1. The units digit repeat in a cycle OF 4. Implication: as soon as an integer with a systems digit of 3 is elevated to a strength that is a lot of of 4, the devices digit will certainly be 1. Thus:33�� and also 43³² each have actually a units digit of 1. From here, the bike of systems digits will certainly repeat: 3, 9, 7, 1...Thus:33�¹ and also 43³³ each have a units digit the 3.33�² has actually a units digit of 9.33�³ has actually a devices digit of 7.Result:Since n = 33�³ + 43³³, n ---> (units number of 3) + (units number of 7) = devices digit that 0.The exactly answer is A.
Mitch HuntPrivate Tutor for the GMAT and also GRE
Since we space asked to recognize only the units digit that n, we can rewrite the expression as:n = 3^43 + 3^33Let"s now recognize the units digit that 3^43 and also 3^33Let"s begin by analyzing the sample of the systems digits of 3^n for confident integer values of n. The is, let"s look in ~ the sample of the devices digits of powers of 3. When writing the end the pattern, notification that we are ONLY concerned with the devices digit that 3 elevated to every power. 3^1 = 3 3^2 = 9 3^3 = 7 3^4 = 1 3^5 = 3The pattern of the devices digit of strength of 3 repeats every 4 exponents. The pattern is 3-9-7-1. In this pattern, all optimistic exponents that are multiples that 4 will create a 1 as its units digit. Thus: 3^44 has a systems digit that 1.Therefore, 3^43 has actually a units digit the 7.and3^32 has actually a units digit of 1.Therefore, 3^33 has a units digit of 3.Thus, n has actually a systems digit that 0, since the systems digit that 7 + 3 = 10 is 0.Answer: A
Jeffrey müller Head that GMAT Instruction
ceilidh.ericksonGMAT Instructor Posts: 2094Joined: 04 Dec 2012 Thanked: 1443 times Followed by:246 members
See more: Timel In The 1950S What Discovery Revolutionized Biotechnology ?
As Mitch described, finding the pattern in units digits is the crucial to addressing this problem. For an ext practice top top this concept, see:https://www.stclairdrake.net/what-is-the ... Tml#554073https://www.stclairdrake.net/what-is-the ... Tml#544267https://www.stclairdrake.net/what-is-the ... Tml#800962https://www.stclairdrake.net/if-n-and-a- ... Tml#784629