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nick1816
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
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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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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nick1816
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
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.

Posted from my mobile device
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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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