unit digit

[nidhis.1408]

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

can someone please explain this problem.

[user123321]

The thing you need to know is....to get units digit in a product, you just need to multiply unit's digit of each individual number in the product.

1) x+y = 7
since x & y are +ve integers,
x y unit's digit
1 6 4
2 5 0
3 4 8
.
.
so unit's digit can be anyone of above. hence insufficient.

2) x = 4
then 243 * 4 * 463 * y = n
still we dont know anything about y
say if y = 1 then unit's digit = 6
if y = 2 then unit's digit = 2
So unit's digit cannot be determined uniquely. hence insufficient.

if both used then x = 4, y = 3
so product is 243*4*463*3 => unit's digit is 8
hence sufficient.

IMO C

user123321

[neelgandham]

If (243)x(463)y = n, where x and y are positive integers, what is the units digit of n?

Assumption: (243)x(463)y = 243*x*463*y, Unit's digit of n = Unit's digit of 9*x*y
So the question can be rephrased as; What is the Unit's digit of 9*x*y ?

(1) x + y = 7

(x,y) = (6,1) Unit's digit of 9*x*y = 9*6*1 = 4
(x,y) = (1,6) Unit's digit of 9*x*y = 9*6*1 = 4
(x,y) = (5,2) Unit's digit of 9*x*y = 9*5*2 = 0
(x,y) = (2,5) Unit's digit of 9*x*y = 9*2*5 = 0
(x,y) = (4,3) Unit's digit of 9*x*y = 9*4*3 = 8
(x,y) = (3,4) Unit's digit of 9*x*y = 9*3*4 = 8

Hence, Insufficient !

(2) x = 4

9*x*y = 9*4*y = 36*y
Unit's digit of 36*y = 6 if y = 1
Unit's digit of 36*y = 2 if y = 2
Unit's digit of 36*y = 8 if y = 3
Unit's digit of 36*y = 4 if y = 4
Unit's digit of 36*y = 0 if y = 5
Unit's digit of 36*y = 6 if y = 6
Unit's digit of 36*y = 2 if y = 7
Unit's digit of 36*y = 8 if y = 8
Unit's digit of 36*y = 4 if y = 9

Hence, Insufficient!

From 1 and 2, x = 4, y = 3 and Unit's digit of 9*x*y = 9*4*3 = 8

Answer C

[shankar.ashwin]

You need both X and Y to answer this, neither statement gives this. Together we can find out X and Y. C IMO