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

It is currently 12 Dec 2019, 09:24

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If the difference between a two digit positive integer and its reversa

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59712
If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 01:20
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (01:53) correct 38% (02:11) wrong based on 66 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 338
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 02:22
2
xy-yx=3(x+y)
10x+y-10y-x=3x+3y
x=2y

4digits(x={1,2,3,4};y={2,4,6,8}) satisfies above equation

OA:D
Senior Manager
Senior Manager
avatar
P
Joined: 07 Mar 2019
Posts: 456
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 02:33
2
If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Let the two digits number be 10a + b
Reverse is 10b + a

Now, 10a + b - 10b - a = 3(a + b)
9a - 9b = 3a + 3b
6a = 12b
a = 2b

'a' can have only four values for which 'b' would have four values. The numbers are:
a = 1, b = 2
a = 2, b = 4
a = 3, b = 6
a = 4, b = 8

Hence only four numbers are possible.

IMO Answer D.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5478
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 03:15
1
10a+b-10b-a=3(a+b)

3(a-b)=(a+b)
a=2b
possible pairs ( 1,2) ( 2,4) (3,6) (4,8)
IMO D ; 4


If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 963
Location: United States
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 04:32
1
Quote:
If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5


10A+B-(10B+A)=3(A+B)
9(A-B)=3(A+B)
A=2B
0<A≤9
A={2,4,6,8}; B={1,2,4,3}
(A,B)={2,1;4,2;6,4;8,3}: 4 pairs

Ans (D)
Senior Manager
Senior Manager
avatar
P
Joined: 22 Feb 2018
Posts: 344
CAT Tests
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 05:26
2
Imo. D

If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?
10a+b - (10b+a) = 3 (a+b)
9a-9b = 3a+3b
6a=12b
a/b=2/1
Let's check the respective numbers
21-12 = 3 *3
42-24 = 3 * 6
63-36 = 3 * 9
84-48 = 3 * 12

Sp, total 4 such pairs are possible.

Hence, D.
_________________
Thanks in the forum can be expressed by hitting KUDOS!!!
VP
VP
avatar
D
Joined: 20 Jul 2017
Posts: 1145
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 09:38
1
Let the two digit number be m = xy = 10x + y
And number obtained by reversing be n = yx = 10y + x

Difference = 10x + y - (10y + x) = 9x - 9y = 9(x - y)

Given, 9(x - y) = 3(x + y)
—> 3(x - y) = x + y
—> 2x = 4y
—> x = 2y
—> Possible values = 12, 24, 36, 48
—> Possible pairs of 2 digit number and its reversal = {(12,21). (24,42), (36,63), (48,84)}
—> 4 pairs

IMO Option D

Posted from my mobile device
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1217
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 15:53
1
10x+y-(10y+x)=3(x+y)→
x=2y
so 4 possible pairs are:
21&12
42&24
63&36
84&48
Director
Director
avatar
P
Joined: 18 May 2019
Posts: 549
GMAT ToolKit User Premium Member CAT Tests
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 21:43
1
Let the two digit positive number =ab
then its reverse is ba
ab-ba=3(a+b)
but ab=10a+b and ba=10b+a
10a+b-(10b+a)=3a+3b
9a-9b=3a+3b
6a-12b=0
6(a-2b)=0
This implies a=2b
since when b=0 a=0, b cannot be 0
only four other possible values exist which yield unique value for a, since the largest unit digit that a can take is 8 based on the given condition of a=2b.
The set of possible values of b={1, 2, 3, 4}

The answer is, therefore, option D in my view.
Intern
Intern
avatar
Joined: 26 Nov 2017
Posts: 1
CAT Tests
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 11 Nov 2019, 22:39
1
Answer is D(4)

x=2 y=1
x=4 y=2
x=6 y=3
x=8 y=4
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8680
Location: United States (CA)
Re: If the difference between a two digit positive integer and its reversa  [#permalink]

Show Tags

New post 19 Nov 2019, 19:27
1
Bunuel wrote:

Competition Mode Question



If the difference between a two digit positive integer and its reversal is three times the sum of its digits, how many such pairs are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Are You Up For the Challenge: 700 Level Questions


We can let a = tens digit and b = ones digit, and create the equation:

10a + b - (10b + a) = 3(a + b)

10a + b - 10b - a = 3a + 3b

6a = 12b

a = 2b

We see that a can be 2, 4, 6, or 8, so there are 4 such pairs.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

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.

GMAT Club Bot
Re: If the difference between a two digit positive integer and its reversa   [#permalink] 19 Nov 2019, 19:27
Display posts from previous: Sort by

If the difference between a two digit positive integer and its reversa

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne