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
Please explain the answer
Source: Manhattan Gmat
OA is A
Digits, power
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- kmittal82
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Assuming here the question means multiplication, we know that
.....9 * xy = n (9 will be the units digit when 243 is multiplied with 463)
(1)
Not enough, since x = 6 y = 1 will result in a unit digit of 4 (...9 x 6), and x = 4 y = 3 will result in a units digit of 8 (...9 x 12)
(2)
Not enough
x = 4 reduces the question further to ....6*y = n
Depending on y, n could take any units digit.
Combining (1) and (2), we know that x = 4, y = 3
Question reduces to ...9 x 12, so n will have a units digit of 8.
(C) should be the answer. OA please?
.....9 * xy = n (9 will be the units digit when 243 is multiplied with 463)
(1)
Not enough, since x = 6 y = 1 will result in a unit digit of 4 (...9 x 6), and x = 4 y = 3 will result in a units digit of 8 (...9 x 12)
(2)
Not enough
x = 4 reduces the question further to ....6*y = n
Depending on y, n could take any units digit.
Combining (1) and (2), we know that x = 4, y = 3
Question reduces to ...9 x 12, so n will have a units digit of 8.
(C) should be the answer. OA please?
- Gurpinder
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Not sure about OA or whether I am wrong but IMO (C).
243*463 = units digit = 9.
so 9*xy=n
(1) x+y=7
there are so many combination's of x+y that can give you 7. and if we take each of those values and multiply it with 9, we get different answers.
Insufficient.
(2) x=4
so 9*y*4
then we have 6*y
Now y could be anything. therefore, this one is also insufficient.
Together:
4+y=7
x=4
y=3
9*4*3
8 is the units digit.
243*463 = units digit = 9.
so 9*xy=n
(1) x+y=7
there are so many combination's of x+y that can give you 7. and if we take each of those values and multiply it with 9, we get different answers.
Insufficient.
(2) x=4
so 9*y*4
then we have 6*y
Now y could be anything. therefore, this one is also insufficient.
Together:
4+y=7
x=4
y=3
9*4*3
8 is the units digit.
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- Gurpinder
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No wonder!uwhusky wrote:The question is copied incorrectly.
https://www.beatthegmat.com/exponent-pro ... 24675.html
Thanks!
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- beatthegmatinsept
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That explains.. BTW, I got C too for the 'modified' question posted above.Gurpinder wrote:No wonder!uwhusky wrote:The question is copied incorrectly.
https://www.beatthegmat.com/exponent-pro ... 24675.html
Thanks!
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- uwhusky
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You can simply pretend they have the same base, since we are only concerned with the unit digit.
So even though it's 243^x * 463^y, you can simplify it down to 3^x * 3^y. We know that when two exponents have the same base multiplying, we simply add them together: 3^(x+y).
Answer is A.
Hope I am clear on this one.
So even though it's 243^x * 463^y, you can simplify it down to 3^x * 3^y. We know that when two exponents have the same base multiplying, we simply add them together: 3^(x+y).
Answer is A.
Hope I am clear on this one.
- Gurpinder
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Yes you are,uwhusky wrote:You can simply pretend they have the same base, since we are only concerned with the unit digit.
So even though it's 243^x * 463^y, you can simplify it down to 3^x * 3^y. We know that when two exponents have the same base multiplying, we simply add them together: 3^(x+y).
Answer is A.
Hope I am clear on this one.
I was about the write the same thing.
Since we are ONLY dealing with units digits we simply need to be worried about the units digit.
so the question becomes 3^x * 3^y as you pointed out. And modifying this > 3^7
So stmt 1 is sufficient.
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
- Alfred A. Montapert, Philosopher.