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# I have a big question !

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

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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: 32
Location: United States
Concentration: Operations, Finance
GMAT 1: 650 Q48 V31
GPA: 3
WE: Engineering (Other)
Re: I have a big question !  [#permalink]

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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: 32
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
Senior Manager
Joined: 12 Jan 2019
Posts: 263
Re: I have a big question !  [#permalink]

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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
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Re: I have a big question !   [#permalink] 16 Jan 2019, 01:55
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# I have a big question !

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