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

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eybrj2
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If the tens digit x and the units digit y of a positive [#permalink] New post   Updated on: 07 Mar 2012, 15:40
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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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E

Originally posted by eybrj2 on 07 Mar 2012, 15:32.
Last edited by Bunuel on 07 Mar 2012, 15:40, edited 1 time in total.
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Re: PT #11 PS 3 Q 15 [#permalink] New post   07 Mar 2012, 15:39
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eybrj2 wrote:
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


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

Answer: E.
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damham17
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   07 Mar 2012, 22:07
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.
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   07 Mar 2012, 22:48
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damham17 wrote:
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.


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.
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Re: PT #11 PS 3 Q 15 [#permalink] New post   20 Jun 2012, 03:29
Bunuel wrote:
eybrj2 wrote:
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


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

Answer: E.


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 ?
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Re: PT #11 PS 3 Q 15 [#permalink] New post   20 Jun 2012, 03:37
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stne wrote:
Bunuel wrote:
eybrj2 wrote:
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


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

Answer: E.


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 ?


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.
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Re: PT #11 PS 3 Q 15 [#permalink] New post   20 Jun 2012, 03:44
Bunuel wrote:
stne wrote:
Bunuel wrote:
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

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

Answer: E.


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 ?


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.


Its clear now , great. Thank you
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   06 Aug 2014, 11:28
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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.
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   06 Aug 2014, 21:26
n is 10x+y
reversed it is, 10y+x

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

9y-9x=9 --> y-x=1 --> y=x+1
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   24 Nov 2016, 01:37
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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
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   22 Jul 2022, 05:00
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.
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post   03 Sep 2023, 05:58
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Re: If the tens digit x and the units digit y of a positive [#permalink]
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