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What is the remainder when 7^700 is divided by 100?

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AbdulMalikVT
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What is the remainder when 7^700 is divided by 100? [#permalink] New post   23 Aug 2019, 11:43
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What is the remainder when 7^700 is divided by 100?

A 1
B 61
C 41
D 21
E 3
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What is the remainder when 7^700 is divided by 100? [#permalink] New post   23 Aug 2019, 12:13
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The remainder when \(7^{700}\) is divided by 100 is the last 2 digits of \(7^{700}\).

\(7^2\)=49= 49 Mod 100
\(7^4\)= 2401= (01) mod 100

\(7^{4k}\)= 01 MOD 100
as 700 is a multiple of 4, last 2-digit of \(7^{700}\) is 01.

A


AbdulMalikVT wrote:
What is the remainder when 7^700 is divided by 100?

A 1
B 61
C 41
D 21
E 3
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Re: What is the remainder when 7^700 is divided by 100? [#permalink] New post   27 Sep 2020, 06:41
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\(\frac{(7^{250} * 7^{250}) }{ (10 * 10)}\)

=> \(\frac{7 }{ 10}\): remainder will be -3

Therefore, \(\frac{7}{10}\) * \(\frac{7}{ 10}\) = \(\frac{-3 }{10}\) * \(\frac{-3 }{10}\) = \(\frac{-9 }{10}\) * \(\frac{-9 }{10}\) = -9 + 10 = 1 is the remainder.

Answer A
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Re: What is the remainder when 7^700 is divided by 100? [#permalink] New post   07 Oct 2020, 11:29
nick1816 wrote:
The remainder when \(7^{700}\) is divided by 100 is the last 2 digits of \(7^{700}\).

\(7^2\)=49= 49 Mod 100
\(7^4\)= 2401= (01) mod 100

\(7^{4k}\)= 01 MOD 100
as 700 is a multiple of 4, last 2-digit of \(7^{700}\) is 01.

A


AbdulMalikVT wrote:
What is the remainder when 7^700 is divided by 100?

A 1
B 61
C 41
D 21
E 3


Is there a thread to explain the mod piece? How do you know that you're using the last two digits instead of the units digit?
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Re: What is the remainder when 7^700 is divided by 100? [#permalink] New post   11 Oct 2020, 06:21
Expert Reply
AbdulMalikVT wrote:
What is the remainder when 7^700 is divided by 100?

A 1
B 61
C 41
D 21
E 3

Solution:

To solve this problem, we need to know the following two facts:

The remainder when a number is divided by 100 is the last two digits of the number.
If the remainder of a when divided by b is r, then a^n and r^n have the same remainder when each is divided by b.

Notice that 7^4 = 2401, which has a remainder of 1 when 7^4 is divided by 100. Since 7^700 = (7^4)^175 = 2401^175, the remainder when 2401^175 is divided by 100 is the same as the remainder when 1^175 is divided by 100. Since 1^175 = 1 has a remainder of 1 when divided by 100, then 2401^175, or 7^700, also has a remainder of 1 when divided by 100.

Answer: A
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Re: What is the remainder when 7^700 is divided by 100? [#permalink] New post   11 Oct 2020, 07:06
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Asariol wrote:
nick1816 wrote:
The remainder when \(7^{700}\) is divided by 100 is the last 2 digits of \(7^{700}\).

\(7^2\)=49= 49 Mod 100
\(7^4\)= 2401= (01) mod 100

\(7^{4k}\)= 01 MOD 100
as 700 is a multiple of 4, last 2-digit of \(7^{700}\) is 01.

A


AbdulMalikVT wrote:
What is the remainder when 7^700 is divided by 100?

A 1
B 61
C 41
D 21
E 3


Is there a thread to explain the mod piece? How do you know that you're using the last two digits instead of the units digit?


Because the remainder after division with 100 is asked, last two digits are being considered.
Had it been 10 , then last digit would have been considered.
Yes there is a blog by Veritas karishma on same. Check reading material/ all resources in gmatclub quantitative forum, compiled by Bunuel. It should help you for sure.

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Re: What is the remainder when 7^700 is divided by 100? [#permalink] New post   11 Oct 2020, 11:15
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\(7^{700} = (7^3)^{233} * 7\)

=> \(7^3\) divided by 100 gives remainder as '43' and 7 divided by 100 gives remainder as '7'

=> 43 * 7 = 301 divided by 100 gives remainder as '1'

Answer A
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Re: What is the remainder when 7^700 is divided by 100? [#permalink] New post   27 Nov 2022, 03:08
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Re: What is the remainder when 7^700 is divided by 100? [#permalink]
27 Nov 2022, 03:08
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