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If (243)x(463)y = n, where x and y are positive integers,
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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/if243x463 ... 02054.html== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: DS  Units Digit
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27 May 2008, 20:51
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
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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> 7y=x 9*y*(7y) 63*y9*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 91=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
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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
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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
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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
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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
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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
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28 May 2008, 13:57
i too get C...
maybe its ^x and ^y



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Re: DS  Units Digit
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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
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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
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28 May 2008, 17:42
Is this from there question banks? == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



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