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Unit Digits and Last Two Digits

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Post questions based on Unit Digits and Last Two Digits of a number 

This topic was modified 1 month ago by TathaGat
14 questions & discussions are there under this sub-topic
1

Sir, How to find last two digits of (1785)^95 and how do we know whether it will end in 25 or 75

TG Team 04/07/2018 8:02 pm

(a5 )^even always ends with 25 

 

( a5)^Odd => 

 

If a is odd then last two digits 75

 

and if a is even then , it ends with 25. 

TG Team 04/07/2018 8:07 pm

 

1st method 

 

Divide the number by 100 . Remainder will be last two digits of that number 

1785^95 mod 100 

 

Using Chinese Remainder Theorem 1785^95 mod 4 = 1 and 

 

1785^95 mod 25 = 0 

 

So , 25a = 4b + 1 gives the last two digits : 25. 

TG Team 04/07/2018 8:15 pm

Alternate Approach 

 

Last two digits of [1785^95 ] 

 

= Last two digits of 85^95 

 

Last two digits of= 17^95 × 5^95 

 

Last two digits of17 × [(17)²]^47 × 25

 

Last two digits of [ 17 × 25 × 89^47 ] 

 

Last two digits of 17 × 25 × ( -11)^47 

 

Last two digits of 17 × 25 × (-71 ) 

Last two digits of 17 × 25 × 29 = 25 

 

 

0

Hello sir, please explain 

The difference between a two digit number and the number obtained by
interchanging the positions of its digits is 36. What is the difference between the
two digits of that number?
(a) 4 (b) 9
(c) 3 (d) Cannot be determined

Anonymous Topic starter 26/03/2018 1:27 pm

Hello abhi,

Find the solution below

Let two digit number is ab

(10a + b) – (10b +a) =36

9a -9b = 36

a – b = 4

0

Find the last three digits in the binary expansion of the number 43211724?

 

 

 
TG Team 16/10/2018 3:15 pm

For last three digits in binary divide the number by 2^3 i.e 8 . 

So 43211724 = 724 mod 8 

4 mod 8 . 

4 in base 2 => 100. 

0

What is the unit digit of (1/5)^2000

TG Team 20/01/2019 9:45 pm

(1/5)1 = 2/10 =  0.2 => same as the last digit of 21
(1/5)2 = 1/25= 4/100 = 0.04 => same as the last digit of 22
(1/5)3 = 1/125 = 8/1000 = 0.008 => same as the last digit of 23
(1/5)4 = 1/ 625 = 16/10000 0.0016 => same as the last digit of 24

…………………

thus, the last digit of ( 1/5)2000 is same as the last digit of 22000

2(4k) ends with 6 so last digit of ( 1/5)2000 => 6.

0

how many perfect squares of natural numbers between 30000-50000 are there whose last two digits end with 81?

0

The 111th digit of the series 149162536496481........ is?

0

what are the last two digits of 46^23 -  23^46?

Gaurav Jain 30/06/2019 3:07 pm

46^23 = 23^23*2^23
= 23^3*2^3
= 67*08 = 36

similarity last 2 of 23^46 = 23^6 = 67^2 = 89

hence answer is x36-89 = 47 are last 2 digits

0

Two natural numbers a and b are given in base 10. The number a can be written
as 212 in base b and 128 in base b + 2.
13.

The value of a + b in base 10 is

1. 219
2. 125
3. 114
4. 107

Aditya Dang 21/06/2021 3:46 pm

Hi,
It is given that a= (212)b .
Forming an equation using this
a= 2b2+b+2
Similarly, a= (128)b+2. Forming an equation for it also.
a= (b+2)2+ 2(b+2)+8
Equate both equations we get,
b= 2 or 7, b cannot be equal to 2 for obvious reasons. Therefore, b=7.
Now, if b=7, using this value and putting it in the first equation.
a= 98+9=107
a + b= 114.

0

Great thread ,i tried to do these but not able to do..thanks for sharing this answer.

0

how many perfect squares of natural numbers between 30000-50000 are there whose last two digits end with 81?

0

The 111th digit of the series 149162536496481........ is?

0

In a test match in cricket, the scores of Rohit and Virat in the first innings are in the ratio of 13 : 16. In the second innings as compared to the first innings, their scores increase by the same number of runs and their scores are in the ratio of 53 : 62 in the second innings. What is the ratio of Virat’s second innings score and his first innings score?

A. 5: 4
B. 31: 24
C. 30: 23
D. 31 : 25

0

Find the unit digit of the sum of the factorials of the first 20 natural numbers. 

a. 1     b. 2    c.    3     d.  4

Neraj (Tg)Faculty 10/06/2024 6:27 pm
0

Solve this question.

What is the unit digit of the product 

71.72.73.74.……………..72020

TathaGat 09/06/2024 1:34 am

@mayanksri 

71.72.73.74.……………..72020

= 7(1 + 2+ 3+ ………….2020)

=72020(2020+1)/2 = 71010 x 2021

When 1010 x 2021 is divided by 4 gives remainder = 2 x 1 =2

Unit digit = 72 =>9