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by GMATGuruNY » Tue Dec 03, 2013 7:26 am
rainmaker wrote:Please explain your answer:

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
If m = abc, then the units digit of m is equal to the units digit of the following product:
(units digit of a)(units digit of b)(units digit of c).

Since we are concerned only about the units digits, the question stem above can be rephrased as follows:
If (3^x)(3^y) = n, where x and y are positive integers, what is the units digit of n?
Simplfying the question stem, we get:
n = (3^x)(3^y)
n = 3^(x+y).

To determine the units digit of n, we need to know the value of x+y.
Final rephrase: What is the value of x+y?

Statement 1: x+y = 7
SUFFICIENT.

Statement 2: x=4
INSUFFICIENT.

The correct answer is A.
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by jaspreetsra » Mon Jan 12, 2015 12:35 am
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

Good Question.

IMO: A
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by Brent@GMATPrepNow » Mon Jan 12, 2015 10:01 am
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
Important aside: The units digit of (243)^x is the same as the units digit of 3^x (since we are only concerned with the last digit, the other digits are of no consequence). Similarly, the units digit of (463)^y is the same as the units digit of 3^y.

So, we can reword the target question as, "If (3^x)(3^y) = n (where x and y are positive integers), what is the units digit of n?"

Since we now have the two powers (3^x and (3^y) written with the same base, we can combine them to get 3^(x+y)

This means we can further reword the target question as, "If 3^(x+y) = n (where x and y are positive integers), what is the units digit of n?"

Okay, now the statements:

Statement 1: x+y=7
Given this, our target question becomes "What is the units digit of 3^7?"
Since we can answer the target question with certainty, statement 1 is sufficient

Statement 2: x=4
Given this, we are unable to determine the value of 3^(x+y).
So, statement 2 is not sufficient, and the answer is A.

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by bpdulog » Tue Apr 03, 2018 1:25 am
LalaB wrote:IMHO A

we know, that

3^1=3(9 is a unit digit)
3^2=9(9 is a unit digit)
3^3=27 (7 is a unit digit)
3^4=81 (1 is a unit digit)
3^5=243(3 is a unit digit)

so , now we r moving to stmnt 1

x+y=7

since we know that x and y are positive integers, then x colud be equal to 3;5;4;2 ,then y will be equal to 4;2;3;5 respectively.

so if x =3 ,and y =4 then the units digit of n will be 7 (since 3^3=27 (7 is a unit digit)
3^4=81 (1 is a unit digit) 7*1 =7)

if x=5 then y=2 ,so the units digit of n will be 7 again (since 3^2=9(9 is a unit digit) and 3^5=243(3 is a unit digit) ; 9*3=27)

A is sufficient

B is not sufficient, since we have no info about y.

imho ,the trick of this question is the tendency of choosing C.
Hmm..I think you are right conceptually but the you are wrong in that the units digit of n will not be 7. This is what the #s come out to in excel:


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