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03 Jul 2019, 14:25
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:39) correct
30%
(01:43)
wrong
based on 274
sessions
History
Date
Time
Result
Not Attempted Yet
What is the reminder when 11^122 is divided by 100?
A) 11
B) 21
C) 31
D) 41
E) 51
A) 11
B) 21
C) 31
D) 41
E) 51
05 Jul 2019, 04:02
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Mo2men
I do wonder if people writing these questions have ever seen an actual GMAT. This question is so far outside the scope of the test that there isn't any reason to study it.
But if you did want to solve: we just want to know the last two digits (ten and units digits) of 11^122, since those will give us the remainder when we divide 11^122 by 100. If you've ever solved a question that asks something like "what is the units digit of 8^31", you will have seen that as we work out the units digits of 8^1, 8^2, 8^3 and so on, we start to see a repeating pattern. The same thing will happen here or in any other remainders question:
11^1 ends in 11
11^2 ends in 21
11^3 ends in 31
11^4 ends in 41
and so on, and you can probably predict now how the pattern develops. When we reach 11^10, we'll have a number ending in "01", and then the pattern will begin to repeat; 11^11 ends in 11, 11^12 ends in 21, and so on. Since the pattern repeats in blocks of ten terms, 11^120 is just like 11^10 (so will end in "01"), and 11^122 will be exactly like 11^2, and its last two digits are "21", so that's the answer.
It's not remotely close to being a realistic GMAT question though.
General Discussion
03 Jul 2019, 15:33
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(11^122)/100 —> (11^2(61))/100
(121^61)/100 —> ((100+21)^61)/100
(21^61)/100 —> (21•21^60)/100
(21• (20+1)^60)/100 —> (21•20^60)•1^60/100 —> (21•1^60)/100 —> (21)/100
Remainder is 21
Answer B
Posted from my mobile device
(121^61)/100 —> ((100+21)^61)/100
(21^61)/100 —> (21•21^60)/100
(21• (20+1)^60)/100 —> (21•20^60)•1^60/100 —> (21•1^60)/100 —> (21)/100
Remainder is 21
Answer B
Posted from my mobile device
Also tried the pattern method and the one I posted but don’t know how to further explain to you 
