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What is the remainder when 7^30 is divided by 100?

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What is the remainder when 7^30 is divided by 100? [#permalink]

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[GMAT math practice question]

What is the remainder when \(7^{30}\) is divided by \(100\)?

A. \(19\)
B. \(29\)
C. \(39\)
D. \(49\)
E. \(59\)
[Reveal] Spoiler: OA

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Re: What is the remainder when 7^30 is divided by 100? [#permalink]

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New post 06 Dec 2017, 06:57
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7 has cyclicity of 4

7^4 =2401, when divided by 100 will leave remainder as 1

((7^4)^7*7^2)/100
=> 1*49/100
Remainder =49

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Re: What is the remainder when 7^30 is divided by 100? [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the remainder when \(7^{30}\) is divided by \(100\)?

A. \(19\)
B. \(29\)
C. \(39\)
D. \(49\)
E. \(59\)

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Re: What is the remainder when 7^30 is divided by 100? [#permalink]

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New post 06 Dec 2017, 12:03
MathRevolution wrote:
[GMAT math practice question]

What is the remainder when \(7^{30}\) is divided by \(100\)?

A. \(19\)
B. \(29\)
C. \(39\)
D. \(49\)
E. \(59\)



Straight D.

Remainders when divided by 100 are
7^1 = 7
7^2 = 49
7^3 = 43
7^4 = 1
7^5 = 7

So, cyclicity of 4. 30%4=2
Remainder when divided by 100 is 49.
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Posts: 5288
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GPA: 3.82
Re: What is the remainder when 7^30 is divided by 100? [#permalink]

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New post 08 Dec 2017, 01:07
=>

The tens digit of \(7^k\) cycles through \(0-->4-->4--->0--->0-->…..\)
The units digit of \(7^k\)cycles through \(7-->9-->3--->1--->7-->…..\)

Since \(30=4(7)+2, 7^{30}=7^{4(7)+2}\) ends in \(49\).

Therefore, the answer is D.

Answer: D
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Re: What is the remainder when 7^30 is divided by 100?   [#permalink] 08 Dec 2017, 01:07
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What is the remainder when 7^30 is divided by 100?

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