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555-605 (Medium)|   Algebra|         
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eybrj2
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If the tens digit x and the units digit y of a positive Updated on: 07 Mar 2012, 15:40
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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75% (01:33) correct 25% (01:41) wrong based on 1223 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
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E
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Bunuel
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If the tens digit x and the units digit y of a positive 07 Mar 2012, 15:39
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eybrj2
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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\(n=10x+y\) and \(n'=10y+x\) --> \(n'-n=(10y+x)-(10x+y)=9\) --> \(y=x+1\).

Answer: E.
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If the tens digit x and the units digit y of a positive 07 Mar 2012, 22:07
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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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If the tens digit x and the units digit y of a positive 07 Mar 2012, 22:48
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damham17
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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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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If the tens digit x and the units digit y of a positive 20 Jun 2012, 03:29
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Bunuel
eybrj2
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.
Show more

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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If the tens digit x and the units digit y of a positive 20 Jun 2012, 03:37
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stne
Bunuel
eybrj2
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 ?
Show more

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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If the tens digit x and the units digit y of a positive 20 Jun 2012, 03:44
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Bunuel
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Bunuel
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.
Show more

Its clear now , great. Thank you
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If the tens digit x and the units digit y of a positive 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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If the tens digit x and the units digit y of a positive 06 Aug 2014, 21:26
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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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If the tens digit x and the units digit y of a positive 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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If the tens digit x and the units digit y of a positive 22 Jul 2022, 05:00
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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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If the tens digit x and the units digit y of a positive 13 Apr 2026, 07:39
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