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
Find the units digit
This topic has expert replies
-
- Legendary Member
- Posts: 541
- Joined: Thu May 31, 2007 6:44 pm
- Location: UK
- Thanked: 21 times
- Followed by:3 members
- GMAT Score:680
Last edited by rohangupta83 on Tue Nov 25, 2008 8:59 am, edited 1 time in total.
-
- Legendary Member
- Posts: 683
- Joined: Tue Jul 22, 2008 1:58 pm
- Location: Dubai
- Thanked: 73 times
- Followed by:2 members
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.
(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.
-
- Legendary Member
- Posts: 541
- Joined: Thu May 31, 2007 6:44 pm
- Location: UK
- Thanked: 21 times
- Followed by:3 members
- GMAT Score:680
Sorry mals24 - mistake in posting the question. I've updated the question. Please try again..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.
-
- Legendary Member
- Posts: 683
- Joined: Tue Jul 22, 2008 1:58 pm
- Location: Dubai
- Thanked: 73 times
- Followed by:2 members
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
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
-
- Legendary Member
- Posts: 2467
- Joined: Thu Aug 28, 2008 6:14 pm
- Thanked: 331 times
- Followed by:11 members
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)
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)
-
- Legendary Member
- Posts: 541
- Joined: Thu May 31, 2007 6:44 pm
- Location: UK
- Thanked: 21 times
- Followed by:3 members
- GMAT Score:680
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!
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!
-
- Legendary Member
- Posts: 2467
- Joined: Thu Aug 28, 2008 6:14 pm
- Thanked: 331 times
- Followed by:11 members
I am hoping u mean in the example above u would look at the cylicity of units digit of 2.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
If so, you are correct.
-
- Legendary Member
- Posts: 541
- Joined: Thu May 31, 2007 6:44 pm
- Location: UK
- Thanked: 21 times
- Followed by:3 members
- GMAT Score:680
Yes my friend - this is exactly what I meancramya wrote:I am hoping u mean in the example above u would look at the cylicity of units digit of 2.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
If so, you are correct.