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GRE Math Challenge-units digit of 57^n
[#permalink]
29 May 2014, 08:22

Expert Reply

Question Stats:

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

_________________

Indicate all such digits.

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

(F) 5

(G) 6

(H) 7

(I) 8

(J) 9

Show: :: OA

B,D,H,J

_________________

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Re: GRE Math Challenge-units 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.

As per me,we should get the answer from multiple of 7 .

In which, all of the options are answer.

Re: GRE Math Challenge-units digit of 57^n
[#permalink]
14 Oct 2018, 15:28

2

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)

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)

Re: GRE Math Challenge-units digit of 57^n
[#permalink]
28 Oct 2018, 02:06

Expert Reply

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.

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*x

So \(57^n\) means 57*57*57...n times

Each digit has a cyclicity when multiplied x times

So 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..

_________________

Some useful Theory.

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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