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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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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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Last edited by Bunuel on 07 Mar 2012, 15:40, edited 1 time in total.
Edited the OA



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Re: PT #11 PS 3 Q 15 [#permalink]
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07 Mar 2012, 15:39



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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.



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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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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 xy=1 y= x1 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 yx=1 y= x+1 why two different answers ?
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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 xy=1 y= x1 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 yx=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]
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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 xy=1 y= x1 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 yx=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]
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18 Jun 2014, 04:37
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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 voiceovers.



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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
9y9x=9 > yx=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
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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 => 9y9x=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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Re: If the tens digit x and the units digit y of a positive [#permalink]
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02 Dec 2016, 03:41




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