Find the units digit

[rohangupta83]

If (243)^x (463)^y = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

[mals24]

IMO C

(243)x(483)y

1. x+y = 7

Possible combination = (5,2), (6,1), (3,4)

For each of these combinations the units digits will differ.

2. x = 3
No information about y.

combining both you have both x and y
So suff.

[rohangupta83]

IMO C

(243)x(483)y

1. x+y = 7

Possible combination = (5,2), (6,1), (3,4)

For each of these combinations the units digits will differ.

2. x = 3
No information about y.

combining both you have both x and y
So suff.

Sorry mals24 - mistake in posting the question. I've updated the question. Please try again..

[cramya]

I am getting A).

[mals24]

grrrr

ok now my answer is A

See its a simple logic. In 243 and 463, the units digit is the same 3.

So the possible values for the units digit = 3, 9, 7, 1

So we can write 243^x*463^y in a simplified way of 3^x*3^y.

[PS in both the cases your units digit will be the same

For instance if you have 13^2*23^3, the units digit of this number will be same as units digit for 3^2*3^3 = 3^5].

3^x*3^y = 3^(x+y)

St 1 gives you x+y = 7---INSUFF
St 2 gives you x = 4 no information about y so INSUFF

[cramya]

Stmt I

X+Y=7

No matter how you distribute the power values for x and y the units digit will be the 7th units digit in 3's unit digit cycle

3 9 7 1 3 9 7 i.e 7

SUFF

Stmt II

x=4
y can be 1,2,3,4... So units digit of the product varies

INSUFF

A)

[rohangupta83]

So, this logic is valid irrespective of the fact the units digit of the two numbers in question are not 3. As long as the units digits are same for all the numbers in question we should be able to use the above approach.

For example 12^x 52^y

or

84^x 10894^y

man! I had no idea we could solve like this..

thanks mals24 and cramya!

[mals24]

Every problem has a solution. We just have to look in the right direction

[cramya]

So, this logic is valid irrespective of the fact the units digit of the two numbers in question are not 3. As long as the units digits are same for all the numbers in question we should be able to use the above approach.

I am hoping u mean in the example above u would look at the cylicity of units digit of 2.

For example 12^x 52^y

If so, you are correct.

[rohangupta83]

So, this logic is valid irrespective of the fact the units digit of the two numbers in question are not 3. As long as the units digits are same for all the numbers in question we should be able to use the above approach.

I am hoping u mean in the example above u would look at the cylicity of units digit of 2.

For example 12^x 52^y

If so, you are correct.

Yes my friend - this is exactly what I mean