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Find the units digit

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by rohangupta83 » Tue Nov 25, 2008 7:54 am
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
Last edited by rohangupta83 on Tue Nov 25, 2008 8:59 am, edited 1 time in total.
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Source: — Data Sufficiency |
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by mals24 » Tue Nov 25, 2008 8:57 am
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.
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by rohangupta83 » Tue Nov 25, 2008 8:59 am
mals24 wrote: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..
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by cramya » Tue Nov 25, 2008 9:09 am
I am getting A).
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by mals24 » Tue Nov 25, 2008 9:14 am
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
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by cramya » Tue Nov 25, 2008 9:18 am
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)
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by rohangupta83 » Tue Nov 25, 2008 10:27 am
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!
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by mals24 » Tue Nov 25, 2008 10:43 am
Every problem has a solution. We just have to look in the right direction
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by cramya » Tue Nov 25, 2008 12:23 pm
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.
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by rohangupta83 » Wed Nov 26, 2008 2:28 am
cramya wrote:
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 :)
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