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GRE Math Challengeunits digit of 57^n [#permalink]
29 May 2014, 08:22
Question Stats:
84% (00:24) correct
15% (00:26) wrong based on 13 sessions
Which of the following could be the units digit of \(57^n\) where n is a positive integer? Indicate all such digits. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 (F) 5 (G) 6 (H) 7 (I) 8 (J) 9
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Re: GRE Math Challenge [#permalink]
07 Aug 2014, 02:41
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(B) 1 (D) 3 (H) 7 (J) 9



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Re: GRE Math Challengeunits digit of 57^n [#permalink]
04 Sep 2018, 19:14
Can someone please answer the question. As per me,we should get the answer from multiple of 7 . In which, all of the options are answer.



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Re: GRE Math Challengeunits digit of 57^n [#permalink]
14 Oct 2018, 15:28
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Easiest to just take the units number 7 from 57 and then test exponents of this. 7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5 =16807.
Once you get to 7^5, you notice the pattern for the units, 7...9...3...1...7. So regardless of the value of the exponent, the result for the units will be one of those 4 values.
The answers are 7, 9, 3, 1.
(You can test this by raising 57^2 and getting the answer 2349, which has the same tens and units number as 7^2. The same is for 57^3 = 185193)



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Re: GRE Math Challengeunits digit of 57^n [#permalink]
28 Oct 2018, 02:06
NixonDutt wrote: Can someone please answer the question. As per me,we should get the answer from multiple of 7 . In which, all of the options are answer. Hi power \(x^2\) means x multiplied two times x*xSo \(57^n\) means 57*57*57...n times Each digit has a cyclicity when multiplied x timesSo 7 has cyclicity which repeats after every 4th term 7^1=7..7^2=7*7=9....7^3=7*7*7=9*7=3...7^4=7*7*7*7=3*7=1 So cyclicity is 7,9,3,1,7.... Also it is multiple of odd, so all even are out.. 5 as units digit requires 5 as a multiple but here we have 7..
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




Re: GRE Math Challengeunits digit of 57^n
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28 Oct 2018, 02:06





