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

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...

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

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

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.

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...

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

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

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

naga pls check divisth post for the question, so that we can discuss further

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