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

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If the tens digit x and the units digit y of a positive [#permalink] New post 07 Mar 2012, 14:32
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A
B
C
D
E

Difficulty:

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Question Stats:

66% (02:04) correct 34% (00:45) wrong based on 98 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Mar 2012, 14:40, edited 1 time in total.
Edited the OA
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Re: PT #11 PS 3 Q 15 [#permalink] New post 07 Mar 2012, 14:39
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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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Re: If the tens digit x and the units digit y of a positive [#permalink] New post 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] New post 07 Mar 2012, 21:48
Expert's post
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, 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] New post 20 Jun 2012, 02:37
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: PT #11 PS 3 Q 15 [#permalink] New post 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 + 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 18 Jun 2014, 03:37
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Re: If the tens digit x and the units digit y of a positive [#permalink] New post 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] New post 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
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