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
OA after some discussion.
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- ankur.agrawal
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Interesting question!ankur.agrawal wrote: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
OA after some discussion.
As always, one key to success is to understand exactly what the question is asking. Here, we only care about the units (i.e. ones) digit of n; accordingly, we only care about the units digit of (243^x)*(463^y).
Since both terms end in "3", we're multiplying (x+y) numbers that end in 3. In effect, we could simplify the question to:
or, even simpler:What's the units digit of (3^x)*(3^y)?
Consequently, to determine the units digit of the product, we need to know the value of (x+y).What's the units digit of 3^(x+y)?
(1) exactly what we're looking for! Sufficient.
(2) no info about y, so insufficient.
(1) is sufficient, (2) isn't: choose (A)!
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- force5
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Hi IMO- A
Actually its all about 3.
since both the figures are ending in 3 we actually are calculating 3^x+y =n
statement 1 gives value of x+y hence sufficient
statement 2 gives only x
Actually its all about 3.
since both the figures are ending in 3 we actually are calculating 3^x+y =n
statement 1 gives value of x+y hence sufficient
statement 2 gives only x
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Wait a minute guys, as i see twist in the tail!!!!According to me, it is not just about 3 but knowing exactly which value would a unit digit take. I set out my approach below,
The question asks what is the unit digit of n when 243^x * 463^y = n
A] x+y = 7
possible scenarios for unit digit
x y 3^x 3^y Unit digit of the product
1 6 3 9 7
2 5 9 1 9
3 4 7 1 7
repeat as x&y interchange
Now there is no one value for the unit digit so A is ruled out
Choice left BCE
B] x=4 not clear as y not stated
B is out
combine A&B and you get one answer
So answer is C
The question asks what is the unit digit of n when 243^x * 463^y = n
A] x+y = 7
possible scenarios for unit digit
x y 3^x 3^y Unit digit of the product
1 6 3 9 7
2 5 9 1 9
3 4 7 1 7
repeat as x&y interchange
Now there is no one value for the unit digit so A is ruled out
Choice left BCE
B] x=4 not clear as y not stated
B is out
combine A&B and you get one answer
So answer is C
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I'm really not sure where you came up with that pattern, but it definitely doesn't match what will happen on this question.eccentric wrote:Wait a minute guys, as i see twist in the tail!!!!According to me, it is not just about 3 but knowing exactly which value would a unit digit take. I set out my approach below,
The question asks what is the unit digit of n when 243^x * 463^y = n
A] x+y = 7
possible scenarios for unit digit
x y 3^x 3^y Unit digit of the product
1 6 3 9 7
2 5 9 1 9
3 4 7 1 7
repeat as x&y interchange
Now there is no one value for the unit digit so A is ruled out
Choice left BCE
If you take ANY 7 numbers ending in 3 and multiply them together, the units digit of the full product will be the same as the units digit of 3^7.
Now, powers of 3 definitely have a cycle to their units digits:
3, 9, 27, 81, 243, ..9, ...7, ...1, and so on...
So, for powers of 3, the units digit will be one of the 4 numbers {3, 9, 7, 1}.
Since we're multiplying 7 "3"s, our units digit will be 7, regardless of the specific values of x and y.
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Thanks Stuart, your explanation lead me to revisit my pattern{(0,7),(1,6),(2,5),(3,4),(4,3),...} and was realized my silly mistake. yes A is sufficient as unit value for each pattern is 7..