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

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Senior Manager
Joined: 31 Oct 2011
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If the tens digit x and the units digit y of a positive [#permalink]

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07 Mar 2012, 15:32
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35% (medium)

Question Stats:

60% (02:11) correct 40% (01:01) wrong based on 232 sessions

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Mar 2012, 15:40, edited 1 time in total.
Edited the OA
Math Expert
Joined: 02 Sep 2009
Posts: 39753
Re: PT #11 PS 3 Q 15 [#permalink]

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07 Mar 2012, 15:39
Expert's post
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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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Joined: 06 Mar 2012
Posts: 29
Re: If the tens digit x and the units digit y of a positive [#permalink]

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 39753
Re: If the tens digit x and the units digit y of a positive [#permalink]

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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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Joined: 27 May 2012
Posts: 291
Re: PT #11 PS 3 Q 15 [#permalink]

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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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- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 39753
Re: PT #11 PS 3 Q 15 [#permalink]

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20 Jun 2012, 03:37
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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Joined: 27 May 2012
Posts: 291
Re: PT #11 PS 3 Q 15 [#permalink]

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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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- Stne

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Posts: 16024
Re: If the tens digit x and the units digit y of a positive [#permalink]

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18 Jun 2014, 04:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Location: India
Concentration: Marketing, Leadership
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Re: If the tens digit x and the units digit y of a positive [#permalink]

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06 Aug 2014, 11:28
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]

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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]

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11 May 2016, 04:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Posts: 2185
Re: If the tens digit x and the units digit y of a positive [#permalink]

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24 Nov 2016, 01:37
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]

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01 Dec 2016, 10:55
Shouldnt this question specify that they want y in terms of x of the starting number? take 23 and 32. y=x+1 works for 23 but not for 32. Confusing question?..
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Posts: 39753
Re: If the tens digit x and the units digit y of a positive [#permalink]

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02 Dec 2016, 03:41
iliavko wrote:
Shouldnt this question specify that they want y in terms of x of the starting number? take 23 and 32. y=x+1 works for 23 but not for 32. Confusing question?..

No, the question is clear.

$$n=10x+y$$ and $$n'=10y+x$$ --> $$n'-n=(10y+x)-(10x+y)=9$$ --> $$y=x+1$$.
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Re: If the tens digit x and the units digit y of a positive   [#permalink] 02 Dec 2016, 03:41
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# If the tens digit x and the units digit y of a positive

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