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If the tens digit x and the units digit y of a positive [#permalink ]
07 Mar 2012, 14:32

Question Stats:

65% (02:05) correct

35% (00:44) wrong

based on 94 sessions
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

Last edited by

Bunuel on 07 Mar 2012, 14:40, edited 1 time in total.

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Re: PT #11 PS 3 Q 15 [#permalink ]
07 Mar 2012, 14:39
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Re: If the tens digit x and the units digit y of a positive [#permalink ]
07 Mar 2012, 21:07

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 ]
07 Mar 2012, 21:48

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Re: PT #11 PS 3 Q 15 [#permalink ]
20 Jun 2012, 02:29

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 ]
20 Jun 2012, 02:37
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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Re: PT #11 PS 3 Q 15 [#permalink ]
20 Jun 2012, 02:44

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 + 1n=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 ]
18 Jun 2014, 03:37

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Re: If the tens digit x and the units digit y of a positive [#permalink ]
06 Aug 2014, 10:28

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 ]
06 Aug 2014, 20:26

n is 10x+y reversed it is, 10y+x 10y+x - (10x+y) = 9 9y-9x=9 --> y-x=1 --> y=x+1

Re: If the tens digit x and the units digit y of a positive
[#permalink ]
06 Aug 2014, 20:26