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

It is currently 22 Feb 2019, 07:01

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If a and b are two-digit numbers that share the same digits, but in re

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

Hide Tags

 
Intern
Intern
avatar
Joined: 31 Jan 2018
Posts: 9
If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

New post 03 Feb 2018, 21:26
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (02:16) correct 39% (02:13) wrong based on 134 sessions

HideShow timer Statistics

If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

New post 03 Feb 2018, 21:56
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9

Can some please help explain how the answer?



Let a be xy that is 10x+y and b will be 10y+x..
1) a-b=10x+y-10y-x=9(x-y)=45..... x-y=5..
Number a could be 61,72,83 or 94
Insuff
2) a is MULTIPLE of 9
Number could be 81,72,54 etc
Insufficient

Combined ..
Only 72 fits in both cases..
Sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53069
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

New post 03 Feb 2018, 22:56
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9


Similar question to practice: https://gmatclub.com/forum/if-a-and-b-a ... 94795.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

New post 03 Feb 2018, 23:07
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9


Let \(a=10x+y\) and \(b=10y+x\), where \(x\) & \(y\) are digits of the two digit number \(a\) & \(b\). To know the value of \(a\) we need the value of \(x\) & \(y\)

Statement 1: \(a-b=10x+y-10y-x=45\)

\(=>9(x-y)=45=>x-y=5\). Two variable one equation. Insufficient

Statement 2: \(a\) is multiple of \(9\), hence sum of digits must be multiple of \(9\)

\(=> x+y=9\) or \(x+y=18\). Again two variable, one equation. Insufficient

Combining 1 & 2: \(x-y=5\) & \(x+y=9\), solving we get \(x=7\) & \(y=2\)

for \(x+y=18\), we will not get \(x\) as integer, hence \(x+y=18\) is not possible.

Therefore \(a=72\). Sufficient

Option C
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

New post 09 Feb 2018, 06:54
ggpapas wrote:
If a and b are two-digit numbers that share the same digits, but in reverse order, the what is the value of a?

(1) a-b = 45
(2) The number a is a multiple of 9


Let a = xy, b = yx

Statement I:

\(a - b = 45,\)
\(x - y = 5\). The values of \((x,y) = (6,1) (7,2) (8,3) (9,4)\).. Insufficient.

Statement II:

Not sufficient as the numbers can be \(18, 27, 36,45, 54, 63....\)

Combine I & II:

\((x,y) = (7,2)\)... Sufficient.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Intern
Intern
avatar
B
Joined: 29 May 2018
Posts: 1
Concentration: Leadership, Technology
CAT Tests
Re: If a and b are two-digit numbers that share the same digits, but in re  [#permalink]

Show Tags

New post 03 Jan 2019, 11:45
Was it mentioned that both numbers should be positive?
why cant a be -27?
a=-27 and b=-72
a-b=45
a is a multiple of 9

i chose E thinking on this line.
what am i doing wrong?
GMAT Club Bot
Re: If a and b are two-digit numbers that share the same digits, but in re   [#permalink] 03 Jan 2019, 11:45
Display posts from previous: Sort by

If a and b are two-digit numbers that share the same digits, but in re

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.