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What is the remainder when 7^100 is divided by 50?
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24 May 2018, 17:29
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69% (01:06) correct 31% (01:28) wrong based on 136 sessions
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[GMAT math practice question] What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\)
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Re: What is the remainder when 7^100 is divided by 50?
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24 May 2018, 18:03
MathRevolution wrote: [GMAT math practice question]
What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\) This question essentially asking what are the last 2 digits of the expression \(7^{100}\)... as what ever is in the hunderds digit, if the last two are 00, the number is always divided by 50. Now cyclicity of 7 is 4, And the numbers are 7,9,3,1........ Hence the last digit is 1 as 25*4=100 now \(7^{4}\) = 7*7*7*7= 2401 And the expression is \(2401^{25}\)= in that case the last two will be always 01 ( can be tested quickly with \(101^{2}\) & \(101^{3}\)) Hence the reminder is 01.....................Hence , I would go for option B.
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Re: What is the remainder when 7^100 is divided by 50?
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24 May 2018, 18:04
Option B
\(7^1\) = 7 \(7^2\) = 49 \(7^3\) = 343 \(7^4\) = 2401 \(7^5\) = 16807 \(7^6\) = 117649 \(7^7\) = 823543 \(7^8\) = 5764801
...
So, 7^100 is something that ends with 01.
The remander is 1.



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Re: What is the remainder when 7^100 is divided by 50?
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24 May 2018, 19:35
These type of questions become really simple if you understand the concept of negative remainders. Always try and reduce the dividend to 1 or 1. = Rem [7^100 / 50] = Rem [49^50/50] = Rem [ (1)^50 / 50] = Rem [1 / 50] = 1 hence B
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Re: What is the remainder when 7^100 is divided by 50?
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27 May 2018, 17:21
=> The remainder when \(7^{100}\) is divided by \(50\) depends only on the units and tens digits. The units digits of \(7^n\) cycle through the four values \(7, 9, 3\), and \(1\). The tens digits of \(7^n\) cycle through the four values \(0, 4, 4\), and \(0\). We have the following sequence of units and tens digits for \(7^n\): \(7^1 = 07 ~ 07\) \(7^2 = 49 ~ 49\) \(7^3 = 343 ~ 43\) \(7^4 = 2401 ~ 01\) \(7^5 = 16807~ 07\) … So, \(7^{100} = (7^4)^{25}\) has the same units and tens digits as \(7^4\), that is, \(01\). Thus, the remainder when \(7^{100}\) is divided by \(50\) is \(1\). Therefore, B is the answer. Answer : B
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Re: What is the remainder when 7^100 is divided by 50?
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29 May 2018, 08:24
MathRevolution wrote: [GMAT math practice question]
What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\) We see that 7^2 = 49, which is 50  1. Although 49/50 = 0 R 49, rather than using the remainder of 49, let’s call the remainder “1”. Since 7^100 = (7^2)^50 = 49^50, which is equivalent to (1)^50 when it’s divided by 50, and since (1)^50 = 1, so when (1)^50 is divided by 50, the remainder is 1. Answer: B
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What is the remainder when 7^100 is divided by 50?
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27 Aug 2018, 05:43
\(7^{100}/50=49^{50}/50=(501)^{50}/50\)  only \((1)^{50} = 1^{50}=1\)  won't be devisable by 50. The remainder is 1.
Answer B.



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Re: What is the remainder when 7^100 is divided by 50?
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23 Sep 2018, 04:00
ScottTargetTestPrep wrote: MathRevolution wrote: [GMAT math practice question]
What is the remainder when \(7^{100}\) is divided by \(50\)? \(A. 0\) \(B. 1\) \(C. 7\) \(D. 21\) \(E. 49\) We see that 7^2 = 49, which is 50  1. Although 49/50 = 0 R 49, rather than using the remainder of 49, let’s call the remainder “1”. Since 7^100 = (7^2)^50 = 49^50, which is equivalent to (1)^50 when it’s divided by 50, and since (1)^50 = 1, so when (1)^50 is divided by 50, the remainder is 1. Answer: B Hi, thanks for this solution, but I have a doubt. this question doesn't say that there is exponent for 50. then, How can we take (1)^50 ? Waiting for reply. Regards, Kishlay




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