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If (243)x(463)y = n, where x and y are positive integers,

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If (243)x(463)y = n, where x and y are positive integers,  [#permalink]

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New post 27 May 2008, 19:45
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/if-243-x-463- ... 02054.html

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Re: DS - Units Digit  [#permalink]

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New post 27 May 2008, 20:51
1
ldpedroso 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


I am guessing the answer is C.
With Statement 1: possible combos are x=0, y=7; x=1, y=6; x=2, y=5; x=3, y=4; x=4, y=3; x=5, y=2; x=6, y=1; x=0, y=7.
therefore, insufficent

Statement 2 is insufficient as well.

Together x = 4, y =3, then the unit digit of n = 8.
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Re: DS - Units Digit  [#permalink]

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New post 27 May 2008, 21:11
ldpedroso 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


1)

the units digit of 9*x*y is the units digit of n
x+y=7-> 7-y=x
9*y*(7-y)
63*y-9*y^2->
the units digit of 3*y minus the units digit of 9*y^2 is the units digit of n
insufficient

2)
9*4*y=36*y->6*y
insufficient

1&2)
4+y=7
->
y=3
3*3 minus the units digit of 9*3^2
9-1=8
the units digit of n is 8


alt solution:
3*3*4*3=a units digit of 8
sufficient

C
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Re: DS - Units Digit  [#permalink]

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New post 27 May 2008, 21:13
I am not a fan of Manhattan, but Manh say A is OA
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 09:05
sondenso wrote:
I am not a fan of Manhattan, but Manh say A is OA


Can you post the explanation?

I don't see why A is suff.


We could have 1,6, or 2,5.

3*3 =9 (units digit w/o x and y) --> with X and Y scenario 1: we have a U digit of 4.

Second: we have a U digit of 0.


....????
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 09:22
C is the answer.

The question seems to be so illogically framed.
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Re: DS - Units Digit  [#permalink]

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New post Updated on: 28 May 2008, 14:48
ldpedroso 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



C should be the official answer because if you look at the coefficients of x and y, they both end in a 3, and according to stmt (1) x+y=7. Therefore x or y could equal (order doesn't matter):
1 and 6 ---> 1*3= units place of 3 AND 6*3 = units place of 8 So, 3*8 = 24 --> units place of 4 for n
2 and 5 ---> 2*3 = units place of 6 AND 5*3 = units place of 5 So, 6*5 = 30 --> units place of 0 for n
3 and 4 ---> 3*3 = units place of 9 AND 4*3 = units place of 2 So, 9*2 = 18 --> units place of 8 for n
So NOT SUFFICIENT

However, I noticed that if the original equation was addition (243x + 463y = n) instead of multiplication, then A would be the answer --> because the units of 243x and 463 would add up to 11 with a units place of 1. It might be a typo.
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Originally posted by brokerbevo on 28 May 2008, 09:40.
Last edited by brokerbevo on 28 May 2008, 14:48, edited 1 time in total.
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 10:21
sondenso wrote:
I am not a fan of Manhattan, but Manh say A is OA


if the problem statement is missing a plus sign... then the answer is A
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 13:57
i too get C...

maybe its ^x and ^y
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 15:36
Sorry, it's (243)^x*(463)^y = n

The OA is A. Here's teh OE

We know from the question that x and y are integers and also that they are both greater than 0. Because we are only concerned with the units digit of n and because both bases end in 3 (243 and 463), we simply need to know x + y to figure out the units digit for n. Why? Because, to get the units digit, we are simply going to complete the operation 3x × 3y which, using our exponent rules, simplifies to 3(x + y).

So we can rephrase the question as "What is x + y?"

(1) SUFFICIENT: This tells us that x + y = 7. Therefore, the units digit of the expression in the question will be the same as the units digit of 37.

(2) INSUFFICIENT: This gives us no information about y.
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 17:29
ldpedroso wrote:
Sorry, it's (243)^x*(463)^y = n

The OA is A. Here's teh OE

We know from the question that x and y are integers and also that they are both greater than 0. Because we are only concerned with the units digit of n and because both bases end in 3 (243 and 463), we simply need to know x + y to figure out the units digit for n. Why? Because, to get the units digit, we are simply going to complete the operation 3x × 3y which, using our exponent rules, simplifies to 3(x + y).

So we can rephrase the question as "What is x + y?"

(1) SUFFICIENT: This tells us that x + y = 7. Therefore, the units digit of the expression in the question will be the same as the units digit of 37.

(2) INSUFFICIENT: This gives us no information about y.


that's a different question...
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Re: DS - Units Digit  [#permalink]

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New post 28 May 2008, 17:42
Is this from there question banks?

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Re: If (243)x(463)y = n, where x and y are positive integers,  [#permalink]

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Re: If (243)x(463)y = n, where x and y are positive integers,   [#permalink] 27 Feb 2019, 13:01
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