reminder

[sanjoy18]

what is the reminder when 3^444+4^333 is divided by 5

A)0
B)1
C)2
D)3
E)4

[vinay1983]

Is it D?

[ganeshrkamath]

what is the reminder when 3^444+4^333 is divided by 5

A)0
B)1
C)2
D)3
E)4

All you need to do here is find the units digit of 3^444 and 4^333 to get to the answer.
Now units digits of powers of 3 follow a rule:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = __9
3^7 = __7
3^8 = __1
The pattern is : 3,9,7,1,3,9,7,1,....

A similar pattern for powers of 4 exists: 4,6,4,6,....

units digit of 3^444 = units digit of (3^4)^111 = 1

units digit of 4^333 = 4

1+4 = 5

So remainder when divided by 5 is 0.

Choose A

Cheers

[GMATGuruNY]

what is the reminder when 3^444+4^333 is divided by 5

A)0
B)1
C)2
D)3
E)4

When an integer with a units digit of 3 is raised to successive powers, the units digits of the resulting integers repeat in a cycle of 4:
3, 9, 7, 1...3, 9, 7, 1...
Implication: when the exponent is a multiple of 4, the units digit of the resulting integer will be 1.
This, 3^444 has a units digit of 1.

When an integer with a units digit of 4 is raised to successive powers, the units digits of the resulting integers alternate between 4 and 6:
4, 6...4, 6...
Implication: when the exponent is odd, the units digit of the resulting integer will be 4.
Thus, 4^333 has a units digit of 4.

Thus, 3^444 + 4^333 = integer with a units digit of 1 + integer with a units digit of 4 = integer with a units digit of 5.
An integer with a units digit of 5 is a multiple of 5.
Since 3^444 + 4^333 is a multiple of 5, dividing it by 5 will yield a remainder of 0.

The correct answer is A.

Sent from my iPod

[vinay1983]

My bad! Got the wrong answer, but happy that could follow the correct process for answering the question!