What is y in terms of x ?

[uptowngirl92]

If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x ?

(A) 10 - x

(B) 9 - x

(C) x + 9

(D) x - 1

(E) x + 1

[ssmiles08]

IMO E

n = xy (where x and y are two different digits)

it can also be written as 10x+y = n

reverse of n = 10y + x

the question stem deduced is: 10y + x = 10x + y + 9

9y - 9x = 9

y - x = 1

y = 1 + x

[abhinav85]

I Think IMO is B.

becoz if you go by the ques it says that

tens digit x and the units digit y that means 10x + y
and when we reverse this we get 10y + x + 9

futher simplify it we get

10x + y = 10y + x + 9
9x = 9y + 9
x = y + 9

y = 9 - x.

[truplayer256]

I Think IMO is B.

becoz if you go by the ques it says that

tens digit x and the units digit y that means 10x + y
and when we reverse this we get 10y + x + 9

futher simplify it we get

10x + y = 10y + x + 9
9x = 9y + 9
x = y + 9

y = 9 - x.

How is x=y+9 equal to y=9-x? It should really be equal to y=x-9 and that's not even an answer choice. The mistake that you made is that you added the 9 to the number whose digits were reversed instead of adding the 9 to the original integer n. I guess you were confused with the wording.

[ssmiles08]

I Think IMO is B.

becoz if you go by the ques it says that

tens digit x and the units digit y that means 10x + y
and when we reverse this we get 10y + x + 9

futher simplify it we get

10x + y = 10y + x + 9
9x = 9y + 9
x = y + 9

y = 9 - x.

Hey abhinav85,

What you did was n = reverse + 9

The question stem is saying that (reverse of N) = N + 9

So it is (10y + x) = (10x + y) + 9

Also when you are dividing by 9, you need to divide everything by 9, not just x and y.

[mehravikas]

IMO - E