Aptitude - Numbers - Discussion

I think the answer should be 7.

7^95= 95/4 = remainder 3 = 7^3 = 3 from cyclicity.

3^58= 58/4 = remainder 2 = 3^2 =9 from cyclicity.

NOW, the answer CANNOT be a -ve no, so in order to subtract 9 from 3, we borrow to make it 13 such that= 13-9 = 4 which is a unit digit itself.

Step1. Find the period of 7=7^0=1.
7^1=7.
7^2=9.
7^3=3.
So the period of 7 is 4.

Divide the power of 7 is 95 by 4 and find the remainder.

So the remainder is 3.so the 3rd unit digit of the period is 3.
step2: Similarly find the period of 3 and find the remainder. this remainder is 2nd, so the 2nd unit digit of the 3 periods is =9.

Step3: The Final ans=(3-9)=4 hints:3 is small as compare 9. So borrow 1 from left digit.

To all values of n = (x*m-a*m) is divisible by (x- a) thus 7-3 = 4 is the Ans.

How come we take,
7^95 = 7^92+7^3?

What happens if we take, 7^95 = 7^93 + 7^2, How to solve this? Please tell me.

Because 6 is an actual difference but negative come to take 10 value.

i.e means 10-6 = 4 is the right answer.

By using cyclicity:

95/4= rem 3.
58/4= rem 2.

So, replace the power with the remainder
= 7^3-3^2.
= 343-9.
= 334.
They asked unit digit so we have to consider the unit digit the unit digit is 4.

So, the Answer is 4.

I got it. Thank you all.

To find unit digit first we should know the periodic value;

Ex:-for 2

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64 and so on.

Clearly observe that unit digit follows a cyclic form i.e after 4 terms it again repeating. So the period of 2 is 4.

Similarly for 3, 7, 8 also the same period 4.

For 0, 1, 5, 6 period is always the same as itself irrespective of their powers.

So to find a unit digit find the period of that number then divided the power value by the period.

7^95 = 95/4 = remainder 3.
3^58 = 58/4 = remainder 2.

So, 7^3 = 343 & 3^2 = 9.

Since we have (7^95-3^58),
Therefore, 343-9 = 334.
Unit digit is = 4.

7^4=2401 here the unit place is 1 similarly,
3^4=81 here also the unit place is 1.

So we do;

(7^4)^23 * 7^3=(2401)^23 * 343.
=1^23 x 343 = 1 x 343 = 343.

(3^4)^14 x 3^2=(81)^14 x 9
=1 x 9= 9.

(343-9) = 334 here unit place is 4. So 4 is the correct answer.