Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 90)
90.
What is the unit digit in(795 - 358)?
Answer: Option
Explanation:
Unit digit in 795 = Unit digit in [(74)23 x 73]
= Unit digit in [(Unit digit in(2401))23 x (343)]
= Unit digit in (123 x 343)
= Unit digit in (343)
= 3
Unit digit in 358 = Unit digit in [(34)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9
Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.
So, Option B is the answer.
Discussion:
36 comments Page 2 of 4.
Deepak sharma said:
5 years ago
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.
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.
(2)
Dipankar Mahanta said:
7 years ago
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.
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.
Kunvar said:
1 decade ago
I want to correct you. We are not finding the absolute value of the question. 3-9 = 6 is not the answer as it is -6 and you people don't know the concept of negative remainders and modulo. So the answer 4 is absolutely right.
J GOPINATH said:
9 years ago
Here as per the logic, it's if subtracted it will be 6 but with the negative symbol so you have borrow 10 from the previous place i. e, ten's place which makes the 3 to be 13 and hence 13-9=4 which the correct answer choice.
(1)
Reddivari radha gayathri said:
5 years ago
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.
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.
(7)
Shahid said:
1 decade ago
EVERYTHING THAT I EXPLAINED WAS RIGHT ..BUT I UN NOTICINGLY DIVIDED 95/4 whose remainder is 3
and 58/4 remainder is 2
so 7^3=343 and 3^2=9
and the difference is 343-9 where there 334.
So 4 is the answer.
and 58/4 remainder is 2
so 7^3=343 and 3^2=9
and the difference is 343-9 where there 334.
So 4 is the answer.
(1)
Rajat Kumar said:
8 years ago
The unit digit of 7^95 is 3 and that of 3^58 is 9.
Let 7^95= ......3
Let 3^58= ......9
Subtracting,
13-9= 4 [Since we carried 1 for 3 from its left-hand side].
Let 7^95= ......3
Let 3^58= ......9
Subtracting,
13-9= 4 [Since we carried 1 for 3 from its left-hand side].
Cradlerian said:
10 years ago
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.
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.
Vamshi said:
2 decades ago
Unitdigit in 7^95 is 3 and unit digit in 3^58 is 9
So the answer shoudld be 6.
Then how come 4 is the answer, I didnt get.. please explain
So the answer shoudld be 6.
Then how come 4 is the answer, I didnt get.. please explain
NK Liya said:
4 years ago
Problem:(7^95-3^58).
pb in the form of (a^n-x^n)
So, (a^n-x^n) divided by (a-x)
From the pb a=7, x=3 (a-x=7-3=4).
So the answer is 4.
pb in the form of (a^n-x^n)
So, (a^n-x^n) divided by (a-x)
From the pb a=7, x=3 (a-x=7-3=4).
So the answer is 4.
(4)
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