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RenB
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What is the remainder when 5^122 is divided by 50? 02 Dec 2023, 19:02
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

70% (01:26) correct 30% (01:34) wrong based on 658 sessions

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Result
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What is the remainder when 5^122 is divided by 50?

A. 0
B. 5
C. 15
D. 25
E. 45
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D
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jack5397
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What is the remainder when 5^122 is divided by 50? 08 Dec 2023, 10:50
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gmatophobia
RenB
What is the remainder when 5^122 is divided by 50?
A. 0
B. 5
C. 15
D. 25
E. 45

Rem(\(\frac{5^{122}}{5^2*2}\))

Cancelling out 25 from the numerator we get -

Rem(\(\frac{5^{120}}{2}\))

Rem(\(\frac{1^{120}}{2}\)) = 1

As we canceled out 25 from the numerator, net remainder = 1 * 25 = 25

Option D
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Hi ,

I have a doubt what if we try to find a pattern of remainders in this kind of questions

5^1 - 5/50 (Rem-5)
5^2 - 25/50 (Rem-25)
5^3 - 125/50 (Rem-25)
now all the powers will have remainder as 25
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What is the remainder when 5^122 is divided by 50? 02 Dec 2023, 23:32
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RenB
What is the remainder when 5^122 is divided by 50?
A. 0
B. 5
C. 15
D. 25
E. 45
Show more

Rem(\(\frac{5^{122}}{5^2*2}\))

Cancelling out 25 from the numerator we get -

Rem(\(\frac{5^{120}}{2}\))

Rem(\(\frac{1^{120}}{2}\)) = 1

As we canceled out 25 from the numerator, net remainder = 1 * 25 = 25

Option D
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What is the remainder when 5^122 is divided by 50? 31 Aug 2025, 06:39
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Natansha
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Hi, could you please share any specific part from the above solutions you did not understand / got stuck at, or your working on the problem; that way it would be easier to explain you and address your doubt.
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What is the remainder when 5^122 is divided by 50? 22 Nov 2025, 12:57
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You can do this

for first cycle - T-0 U-5
second cycle - T-2 U-5
third cycle - T-2 U-5

generally for every number ending with 5, the square digits are
(number) *(number+1) and 25

Eg. 25= (2*3)25= 625

so ther remainder is anways going to be 25 in every case
jack5397


Hi ,

I have a doubt what if we try to find a pattern of remainders in this kind of questions

5^1 - 5/50 (Rem-5)
5^2 - 25/50 (Rem-25)
5^3 - 125/50 (Rem-25)
now all the powers will have remainder as 25
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