Number System
Aptitude

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Q.

Find the unit's digit in $264^{102} + 264^{103}$

 A.

0

 B.

2

 C.

4

 D.

6

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Solution:
Option(A) is correct

Required unit's digit = unit's digit in $4^{102} + 4^{103}.$

Now, $4^2$ gives unit digit 6.

⇒ $4^{102}$ gives unit digit 6.

⇒ $4^{103}$ gives unit digit of the product $6 × 4$ i.e., 4.

Hence, unit's digit in $264^{102} + 264^{103}$

= unit's digit in $(6 + 4) = 0$

Edit: For an alternative solution, check comment by Shobia.

Edit 2: For yet another alternative solution, check comment by Arkaprava Sinha.

Edit 3: For yet-yet another alternative solution, check comment by Chilakala Inna Reddy.


(6) Comment(s)


Manoj Tripathi
 ()

$4^(EVEN)$= UNIT DIGIT 6

$4^(ODD)$= UNIT DIGIT 4

($6+4=10$)

SO UNIT DIGIT IS 0



Chilakala Inna Reddy
 ()

4)102(25 4)103(25

100 100

----- ----

2 3 the last digit in 2 times+ 3times

4*4 + 4*4*4

16+64

only last digits 6+4=10

the last digit is 0



Arkaprava Sinha
 ()

take $264^{102}$ outside...

so it will be then $(1+264)=265$...

as we take $264^{102}$ is even..

so the last digit will be 0.....


Sravan Reddy
 ()

This one is faster :)


Shobia
 ()

Let take.. $264^102+264^103$

i)$\dfrac{102}{4}$ will give remainder 2

take last digit of 264 which means 4

now $4^2=16$ take last digit as a unit digit 6.

ii) $\dfrac{103}{4}$ will give remainder 3

take last digit of 264 likewise the (i)

now $4^3=64$ take last digit 4.

then $6+4=10$ here unit digit is 0.. so ans is 0.

this is one of the trick.



Apoorv
 ()

how $4^{102}$ gives unit digit as 6 ? Huh