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What is y in terms of x ?

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by uptowngirl92 » Tue Jun 09, 2009 7:45 pm
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
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by ssmiles08 » Tue Jun 09, 2009 8:17 pm
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
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by abhinav85 » Fri Jun 12, 2009 7:28 am
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.
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by truplayer256 » Fri Jun 12, 2009 11:02 am
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.
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by ssmiles08 » Fri Jun 12, 2009 12:44 pm
abhinav85 wrote: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.
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by mehravikas » Thu Jun 25, 2009 6:51 pm
IMO - E
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