Author
Message
TAGS:
Senior Manager

Joined: 31 Oct 2011

Posts: 331

Followers: 1

Kudos [? ]:
189
[0 ] , given: 18

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

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

Last edited by

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

Edited the OA

Math Expert

Joined: 02 Sep 2009

Posts: 23398

Followers: 3611

Kudos [? ]:
28860
[1 ] , given: 2854

Re: PT #11 PS 3 Q 15 [#permalink ]
07 Mar 2012, 14:39
1

This post received KUDOS

1

This post was BOOKMARKED

Intern

Joined: 06 Mar 2012

Posts: 21

Concentration: International Business, Finance

GMAT Date : 08-04-2012

WE: Consulting (Accounting)

Followers: 0

Kudos [? ]:
24
[0 ] , given: 2

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.

_________________

make each day your masterpiece

Math Expert

Joined: 02 Sep 2009

Posts: 23398

Followers: 3611

Kudos [? ]:
28860
[0 ] , given: 2854

Re: If the tens digit x and the units digit y of a positive [#permalink ]
07 Mar 2012, 21:48

Manager

Joined: 27 May 2012

Posts: 213

Followers: 0

Kudos [? ]:
47
[0 ] , given: 209

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 ?

_________________

- Stne

Math Expert

Joined: 02 Sep 2009

Posts: 23398

Followers: 3611

Kudos [? ]:
28860
[0 ] , given: 2854

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.

_________________

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. What are GMAT Club Tests ? 25 extra-hard Quant Tests Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager

Joined: 27 May 2012

Posts: 213

Followers: 0

Kudos [? ]:
47
[0 ] , given: 209

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

_________________

- Stne

CEO

Joined: 09 Sep 2013

Posts: 2837

Followers: 207

Kudos [? ]:
43
[0 ] , given: 0

Re: If the tens digit x and the units digit y of a positive [#permalink ]
18 Jun 2014, 03:37

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).

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.

_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern

Status: Preparing for GMAT

Joined: 10 Dec 2013

Posts: 24

Location: India

Concentration: Marketing, Leadership

GMAT 1 : 530 Q46 V18

WE: Other (Entertainment and Sports)

Followers: 0

Kudos [? ]:
5
[0 ] , given: 61

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.

Current Student

Joined: 11 Jun 2014

Posts: 57

Concentration: Technology, Marketing

GMAT 1 : 770 Q50 V45

WE: Information Technology (Consulting)

Followers: 1

Kudos [? ]:
19
[0 ] , given: 3

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