Latest CAT Aptitude Question SOLUTION: What is the last two digit of 74^2365?

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(#M40013718) CAT question Keep an EYE

What is the last two digit of 74^2365?

Asked In CAT Amit kumar (11 years ago)

Solved Ashu Read Solution (3)

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Ashu  (11 years ago)

last 2 digits of 74^1=74
last 2 digits of 74^2= 76... from 5476
last 2 digits of 74^3= 24 ...... from 405224
last 2 digits of 74^4= 76... from 5476
last 2 digits of 74^5= 24


so last 2 digits of 74^(2n)= 76... from 5476
last 2 digits of 74^(2n+1)= 24

so last two digit of 74^2365 will be 24.

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Vinay Sipani   (11 years ago)

74^2 = 5476
76^n has last two digits = 76
=> 74^(2 x 1182) = 76^(1182) = 76
74^(2364) x 74 = 76 x 74 = 24
=> last two digits = 24

You can also apply congruency method.
74^2 ≡ 76 (mod 100)
(74^2)^1182 ≡ 76^1182 ≡ 76 (mod 100)
(74^2364)x 74 ≡ 76 x 74 ≡ 24 (mod 100)
=> last two digits = 24

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Venu Patnam  (10 years ago)

74^2365
ans.24
Take 4^5=1024. separate 4 from it
Now, multiply 7 with 6 i.e., 42.
from 42 take 2 and place it before 4, which we already get.
so, final ans 24

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