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# Find the remainder when 71234 is divided by 10

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2278
Find the remainder when 71234 is divided by 10  [#permalink]

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Updated on: 21 Nov 2018, 03:44
00:00

Difficulty:

25% (medium)

Question Stats:

66% (00:51) correct 34% (00:55) wrong based on 62 sessions

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Interesting Applications of Remainders – Practice question 1

Find the remainder when $$7^{1234}$$ is divided by 10?

A. 1
B. 3
C. 4
D. 7
E. 9

To solve question 2: Question 2

To read the article: Interesting Applications of Remainders

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Originally posted by EgmatQuantExpert on 21 Nov 2018, 02:55.
Last edited by EgmatQuantExpert on 21 Nov 2018, 03:44, edited 3 times in total.
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Re: Find the remainder when 71234 is divided by 10  [#permalink]

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21 Nov 2018, 03:24
2
Numbers 2, 3, 7 and 8 have a cyclicity of 4.
Numbers 4 and 9 have a cyclicity of 2.
Numbers 0, 1, 5 and 6 have a cyclicity of 1.

The remainder when 1234 is divided by 4 is 2.
hence $$7^{1234} = 7^2$$

So the remainder when 49 is divided by 10 is 9.

E is the answer.
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Re: Find the remainder when 71234 is divided by 10  [#permalink]

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25 Nov 2018, 16:35
1

Solution

To find:
• The remainder, when $$7^{1234}$$ is divided by 10

Approach and Working:
We know that if we divide a number by 10, then the remainder is same as the units digit of the given number.
• Hence, we need to determine the units digit of $$7^{1234}$$.

As per our conceptual understanding, the units digit cycle of 7 is as follows:
• $$7^1 = 7^5 = 7^{4k+1} = 7$$
• $$7^2 = 7^6 = 7^{4k+2} = 9$$
• $$7^3 = 7^7 = 7^{4k+3} = 3$$
• $$7^4 = 7^8 = 7^{4k+4} = 1$$

As we can write $$7^{1234}$$ as $$7^{4k+2}$$, the unit digit of the number is 9.

Hence, the correct answer is option E.

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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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

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Re: Find the remainder when 71234 is divided by 10 &nbs [#permalink] 25 Nov 2018, 16:35
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# Find the remainder when 71234 is divided by 10

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