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I have a big question !

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meobeou
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I have a big question ! [#permalink] New post   16 Jan 2019, 01:28
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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!
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rajatvermaenator
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GMAT 1: 710 Q49 V39
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Re: I have a big question ! [#permalink] New post   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

Answer: you already got it right so far.
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

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rajatvermaenator
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Schools: Carey Arizona "22 (WA$) McDonough '22 (A) Schulich "22 (A) Broad '22 (A$) Kelley '22 (A$)
GMAT 1: 710 Q49 V39
GPA: 3
WE:Engineering (Transportation)
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Re: I have a big question ! [#permalink] New post   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

Answer: you already got it right so far.
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.

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udaypratapsingh99
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GMAT 1: 660 Q47 V34
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Re: I have a big question ! [#permalink] New post   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 :thumbup:
GMAT Club Bot
gmatclubot
Re: I have a big question ! [#permalink]
16 Jan 2019, 01:55

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