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16 Jan 2019, 01:28
Kudos
Bookmarks
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!
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!
rajatvermaenator
16 Jan 2019, 01:47
Kudos
Bookmarks
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
Posted from my mobile device
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
Posted from my mobile device
rajatvermaenator
16 Jan 2019, 01:48
Kudos
Bookmarks
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.
Posted from my mobile device
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.
Posted from my mobile device
