please help with reversed digits problem

[Dixie-grl]

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

What am I doing wrong?

yx=n
xy=n+9

xy=yx+9

xy-yx=9

y(x-x) = 9 ??? undefined!

[Meggieski]

Ok so an easier way to solve this is to plug in some numbers. If the different is only 9, you know that the two digits cannot possibly be too large or too far away from each other.
2 and 9 reversed is 9 and 2.. much bigger than a difference of 9!

Lets take 1 and 2.. if you reverse them you have 2 and 1 which is 9 bigger.
Plugging in works here very well. You only have ten digits so just try a few. After one try you will realize that using 2 and 9 would never work. So youd try smaller ones and bingo.. the answer. This works for 1,2 2,3 3,4 and so on...its just recognizing a pattern.

Your math didnt work because if you multipy xy (say 1 and 2) you dont get 12.. which is n.


I guess if you're using bigger numbers this wouldnt work.. but for small ones with two digit places its pretty easy. It would be cool to see a math way of solving this.

The answer was E.

[crack_the_gmat]

IMO E

Let xy=23 then on reversing the digits 32=23+9

Now x=2 and y=3 let us substitute the values of x in each of the answer choices and see which one gives us the value of y as 3.

A 10-x----10-2=8 but y is not 8 so A is out
B 9-x-----9-2=7 but y is not 7 so B is out
C x+9------2+9=11 definitely out
D x-1----------2-1=1 but y is not 1 and so D is out
E x+1--------2+1=3 and the value of y is 3.Hence,E is the answer

[neuroticA]

its easy to solve this kind of problems by equations

original number N=10X +Y
After reversing the number becomes 10Y + X

Now 10Y+X happens to be 9 greater than the original number N
so 10x+y=10y+x+9
9x=9y+9
or x =y+1
or y=x-1
Answer should be D

[Meggieski]

neurotica,

But if you use real numbers it cannot be D. It logically works for 12 23 34 45 and so on. Try it out. The answer would work if the result was 9 less than n.

[ssky]

Answer is E.

xy=n which means 10x+y=n
Now when you flip them it will be
yx=n+9 meaning 10y+x=n+9

Solve them and you'll get x+1

[Retake_GMAT]

10x +y is n
10y+x = 10x + y + 9
9x -9y + 9=0
9 ( x-y+1) =0
x-y +1 =0
y=x+1

Ans E