If the tens digit x and the units digit y of a positive

Question

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

Bunuel · Accepted Answer

n=10x+y  and  n'=10y+x  -->  n'-n=(10y+x)-(10x+y)=9  -->  y=x+1 .

Answer: E.

damham17 · Answer

I plugged in with the numbers 23 and 32.

x=2, y=3 therefore y must be x+1. 
____
Bunuel,

I followed your solution up until the last portion. Could you explain how you solved the equation into y=x+1? Thanks.

Bunuel · Answer

Welcome to GMAT Club.

First of all let me say that plug-in method is fine for this question and your approach is correct.

As for my solution:  n'-n=(10y+x)-(10x+y)=9  -->  9y-9x=9  -->  y-x=1  -->  y=x+1 .

Hope it's clear.

stne · Answer

Can anybody clear this for me

suppose I take first number as 10y + x and reverse it to get 10x + y

Then according to the equation (10x + y) - (10y + x ) = 9 
 9x -9y= 9 
x-y=1
y= x-1

so why are we getting two different answers.
 
 if I take first number to be 10x + y and reverse it to get 10y +x 
then (10y + x) - (10x +y)= 9y- 9x=9 
y-x=1
y= x+1

why two different answers ?

Bunuel · Answer

You cannot arbitrary assign which will be the "first" number and which will be the "second", since the stem explicitly clears that.

Positive integer  n  has the tens digit x and the units digit y, so  n=10x+y ;

Reversed integer, say  n' , has the tens digit y and the units digit x, so  n'=10y+x ;

We are also told that " the resulting integer (so  n' ) is 9 more than  n ", which means  n'-n=(10y+x)-(10x+y)=9  -->  y=x+1 .

Hope it's clear.

stne · Answer

Its clear now , great. Thank you

suhaschan · Answer

Bunuel!!!! Your solutions make us all speechless. You are like the "Salman Khan" (The Hedge fund analyst who is the founder of Khan Academy- Free & quality education for all) of Gmat club. And what makes you even more special is that your solutions effectively convey what a hundred videos do, without any audio voice-overs.

sshrivats · Answer

n is 10x+y
reversed it is, 10y+x

10y+x - (10x+y) = 9

9y-9x=9 --> y-x=1 --> y=x+1

stonecold · Answer

NOTE=> This Question Should have specified that n is a two digit positive integer.
Nevertheless let us proceed =>
N=xy=> 10x+y (x,y are tens and units digit)
N'=yx=10y+x
hence N'=N+9
=> 9y-9x=9
y=1+x

Hence E

GmatPoint · Answer

Since y and x are the units and tens digits respectively of n,

n = 10x + y .....(i)

If the digits are reversed, then the value of n increases by 9.

Thus, n + 9 = 10y + x....(ii)

Subtracting (i) from (ii),

9 = 9y - 9x
y - x = 9

y = x + 1

Thus, the correct option is E.

bumpbot · Answer

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If the tens digit x and the units digit y of a positive

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