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Sahana_Kavitha's posts
Sahana_Kavitha replied to Number System - Questions & Discussions
Ans is (2) 192, check the set P, you can get all the digits from
1 ~ till the summation of all the numbers in the set, which is 192
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Sahana_Kavitha replied to Number System - Questions & Discussions
If you want to find the last digit for a number of form N^a or N!, just divide by 10 and get the remainder, which will be the last digit.
N^a % 10,
Cyclicity
Step 1, N%10 = a1 < 10, and now all the number less than 10 follow cyclicity of 4 in their last digit, for ex a1=2, 3,
2^n wil...
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Sahana_Kavitha replied to Number System - Questions & Discussions
Ans is b) 993, another method using eulers
S = (3 + 3^2 + 3^3 + + 3^800) (7 + 7^2 + 7^3 + + 7^401).
= (3/2(3^800 - 1) - 7/6(7^401 - 1)) % 1000, E(1000) = 400
= (3/2(1-1) - 7/6(7-1)) % 1000
= (0-7) % 1000
= 993
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Sahana_Kavitha replied to Number System - Questions & Discussions
Slightly twisted from the previous post, enjoy solvin..
Let S = (3 + 3^2 + 3^3 + + 3^800) (7 + 7^2 + 7^3 + + 7^401).
The last three digits of S are
a.143 b. 993 c. 003 d. 907
Sahana_Kavitha replied to Number System - Questions & Discussions
Just check it with smaller numbers, so as to get the logic by yourself,
ex 7 and 10, difference is 3, which leaves 1 as remainder.
11 and 7, difference is 4, which leaves 3 as remainder.
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Sahana_Kavitha replied to Number System - Questions & Discussions
The number is 34369 - 31513 = 2856 can divide both 34369 and 31513 leaving same remainder 97, hence ans is b) 97
3 digit nos are 2856/3 = 952, 2856/4 = 714, 2856/6 = 476, so on...
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Sahana_Kavitha replied to Number System - Questions & Discussions
check the multiples of 3, as a 9(x-y)/(x+y) is an integer, x+y shall be a multiple of 3
12, 15, 18, 21, 24, 27, 36, 42, 45, 48, 51, 54, 63, 72, 81, 84
hence the ans is 16, any observations pls let me know
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Sahana_Kavitha replied to Number System - Questions & Discussions
From previous post,
1. reminder for 10^1729%1729?
2. last 3 digits of 7^64
Sahana_Kavitha replied to Number System - Questions & Discussions
note: 111^2 / 11^2 = 100,
naga pls check divisth post for the question, so that we can discuss further
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Sahana_Kavitha replied to Number System - Questions & Discussions