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

 It is currently 18 Mar 2019, 14:58

### 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

# I have a big question !

Author Message
Intern
Joined: 16 Jan 2019
Posts: 1
I have a big question !  [#permalink]

### Show Tags

16 Jan 2019, 01:28
1
If ab is a two digit number and ba represents a number when unit and ten's place digit of ab are exchanged then

Concept 1 : ab-ba is always divisible by 9.

Logic :

ab - ba = (10a +b) - (10b + a) = 9 (a - b )

Concept 2 : ab + ba is always divisible by 11.

Logic :

ab + ba = (10a +b) + (10b + a) = 11 (a + b)

Concept 3 : (ab)² - (ba)² is always divisible by 99.

Logic :

(ab)² - (ba)² = ( ab - ba ) * (ab + ba ) = 9 (a - b ) * 11 (a + b) = 99 (a - b) (a + b)

Concept application problem :

a and b represent nonzero digits, and (ab)² - (ba)² is a perfect square. What is that perfect square?

A) 169
B) 289
C) 576
D) 1089
E) 3025

Lee!
Intern
Joined: 15 Nov 2018
Posts: 25
Location: United States
Concentration: Operations, Finance
GMAT 1: 650 Q48 V31
GPA: 3
WE: Engineering (Other)
Re: I have a big question !  [#permalink]

### Show Tags

16 Jan 2019, 01:47
a and b represent nonzero digits, and (ab)² - (ba)² is a perfect square. What is that perfect square?

A) 169
B) 289
C) 576
D) 1089
E) 3025

All you need is a multiple of 99 which is a perfect square.
Which is 1089. The number should be divisible by 11 among the answers

Posted from my mobile device
Intern
Joined: 15 Nov 2018
Posts: 25
Location: United States
Concentration: Operations, Finance
GMAT 1: 650 Q48 V31
GPA: 3
WE: Engineering (Other)
Re: I have a big question !  [#permalink]

### Show Tags

16 Jan 2019, 01:48
a and b represent nonzero digits, and (ab)² - (ba)² is a perfect square. What is that perfect square?

A) 169
B) 289
C) 576
D) 1089
E) 3025

All you need is a multiple of 99 which is a perfect square.
Which is 1089. The number should be divisible by 11 among the answers and at the same time their sum should be divisible by 9.

Posted from my mobile device
Manager
Joined: 12 Jan 2019
Posts: 98
Re: I have a big question !  [#permalink]

### Show Tags

16 Jan 2019, 01:55
meobeou wrote:
If ab is a two digit number and ba represents a number when unit and ten's place digit of ab are exchanged then

Concept 1 : ab-ba is always divisible by 9.

Logic :

ab - ba = (10a +b) - (10b + a) = 9 (a - b )

Concept 2 : ab + ba is always divisible by 11.

Logic :

ab + ba = (10a +b) + (10b + a) = 11 (a + b)

Concept 3 : (ab)² - (ba)² is always divisible by 99.
Logic :

(ab)² - (ba)² = ( ab - ba ) * (ab + ba ) = 9 (a - b ) * 11 (a + b) = 99 (a - b) (a + b)

Concept application problem :

a and b represent nonzero digits, and (ab)² - (ba)² is a perfect square. What is that perfect square?

A) 169
B) 289
C) 576
D) 1089
E) 3025

Lee!

D) 1089
as it is divisible by 99.

By the way, nice conceptual explanation. Thanks a Lot
Re: I have a big question !   [#permalink] 16 Jan 2019, 01:55
Display posts from previous: Sort by

# I have a big question !

Moderator: HKD1710

 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®.