GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Nov 2019, 22:13 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # xy is a 2 digit number whose reverse, yx, is x less than twice xy.

Author Message
TAGS:

### Hide Tags

VP  P
Joined: 07 Dec 2014
Posts: 1221
xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

### Show Tags

8 00:00

Difficulty:   55% (hard)

Question Stats: 65% (02:25) correct 35% (02:36) wrong based on 110 sessions

### HideShow timer Statistics

xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A. 8
B. 9
C. 11
D. 12
E. 13

(source:self)
Intern  B
Joined: 15 Sep 2014
Posts: 10
Location: India
GPA: 3.36
WE: Programming (Consulting)
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

### Show Tags

3
It can be written:
xy = 10x+y ; yx = 10y+x.

Also given,

10y+x = 2(10x+y) - x
=> 4y = 9x
x: y = 4:9
So, x+y will be a multiple of 13. Hence, E.
Director  D
Joined: 13 Mar 2017
Posts: 731
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

### Show Tags

3
gracie wrote:
xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A. 8
B. 9
C. 11
D. 12
E. 13

(source:self)

gracie this is a very good question. Thanks for posting it.

Integer xy = 10x+y
Integer yx = 10y+x

Now Integer yx = 2 * Integer xy - x
10y + x = 2*(10x+y) - x
8y = 18x
4y = 9x
x/y = 4/9

So sum x+y must be a multiple of 4+9 = 13...

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8453
Location: United States (CA)
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

### Show Tags

gracie wrote:
xy is a 2 digit integer whose reverse, yx, is x less than twice xy. What is the sum of x and y?

A. 8
B. 9
C. 11
D. 12
E. 13

We use the concept that the number 46, for example, can be expressed as (4)(10) + (6)(1) = 46. Thus, we see that the number “xy” = (10)(x) + (y)(1) = 10x + y.

Since the number “xy” = 10x + y, then its reverse “yx” = 10y + x.

Since “yx” is x less than twice “xy”:

2(10x + y) - x = 10y + x

20x + 2y - x = 10y + x

19x + 2y = 10y + x

18x - 8y = 0

9x - 4y = 0

Since x and y are single digits, the only way 9x - 4y = 0 is if x = 4 and y = 9. Thus, x + y = 4 + 9 = 13.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager  B
Joined: 03 Sep 2018
Posts: 252
Location: Netherlands
GMAT 1: 710 Q48 V40 GMAT 2: 780 Q50 V49 GPA: 4
Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.  [#permalink]

### Show Tags

Made a mistake here: yx is x less than twice xy means that

$$yx=2(xy)-x$$
_________________
Good luck to you. Re: xy is a 2 digit number whose reverse, yx, is x less than twice xy.   [#permalink] 04 Jan 2019, 02:13
Display posts from previous: Sort by

# xy is a 2 digit number whose reverse, yx, is x less than twice xy.  