Number System
Aptitude

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Q.

What is the unit's digit of the number $6^{256} – 4^{256}$

 A.

0

 B.

1

 C.

4

 D.

7

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Solution:
Option(A) is correct

Since the exponents are even, we can apply the property that,

If '$x$' is even $a^x – b^x$ is always divisible by $(a+b)$.
$6^256 - 4^256$ will always be divisible by $(6 + 4) = 10$.

Now any number multiplied by 10 gives the last digit as 'zero'.

Alternative:

The last digit of both the number are same as '6'
Thus after subtracting the unit's digit be '0'.


(2) Comment(s)


Omi
 ()

real answer is 2 bcoz 6-4 = 2 but in sol is given 6+4 = 10 ....



Shobia
 ()

$6^256$ unit digit is 6 (i.e. $\dfrac{256}{4}$ remainder $0, 6^4$ unit digit is 6)

$4^{256}$ unit digit is 6(i.e $\dfrac{256}{4}$ remainder $0, 4^4$ unit digit is 6)

$6-6=0$

answer $=0$