## Challenging Number Theory question

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• Hi all, Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at
Message 1 of 4 , Mar 29, 2011
Hi all,

Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .

There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.

Cheers,
99626 48484
Weekend batches starting @ Chennai, Apr 3rd @ Velachery
• The number is 1233 = 12² + 33². Let s say the four digit number = N = abcd = XY = 100X + Y = X² + Y² = (X - 50)² + (Y - 1/2)² = 50² + (1/2)² = 4(X -
Message 2 of 4 , Mar 30, 2011
The number is 1233 = 12² + 33².

Let's say the four digit number = N = abcd = XY = 100X + Y = X² + Y²
=> (X - 50)² + (Y - 1/2)² = 50² + (1/2)²
=> 4(X - 50)² + (2Y - 1)² = 10001 = 76² + 65²
=> X = 12, Y = 33 and the number is 1233.

Kamal Lohia
9953813320

From: Rajesh Balasubramanian <rajesh@...>
To: ascent4cat@yahoogroups.com
Sent: Wed, March 30, 2011 10:20:23 AM
Subject: [2IIM CAT Prep] Challenging Number Theory question

Hi all,

Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .

There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.

Cheers,
99626 48484
Weekend batches starting @ Chennai, Apr 3rd @ Velachery
• Spot on. This answer is correct. There is one more solution to this question. Any other attempts? Rajesh 99626 48484 ... Spot on. This answer is correct. There
Message 3 of 4 , Apr 1, 2011
Spot on. This answer is correct. There is one more solution to this question. Any other attempts?

Rajesh
99626 48484

On Wed, Mar 30, 2011 at 2:46 PM, kamal lohia wrote:

The number is 1233 = 12² + 33².

Let's say the four digit number = N = abcd = XY = 100X + Y = X² + Y²
=> (X - 50)² + (Y - 1/2)² = 50² + (1/2)²
=> 4(X - 50)² + (2Y - 1)² = 10001 = 76² + 65²
=> X = 12, Y = 33 and the number is 1233.

Kamal Lohia
9953813320

From: Rajesh Balasubramanian <rajesh@...>
To: ascent4cat@yahoogroups.com
Sent: Wed, March 30, 2011 10:20:23 AM
Subject: [2IIM CAT Prep] Challenging Number Theory question

Hi all,

Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html .

There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd.

Cheers,
99626 48484
Weekend batches starting @ Chennai, Apr 3rd @ Velachery

• the other solution is 8833 50-x= -38  from kamal s solution.   -Sindhu ... From: Rajesh Balasubramanian Subject: Re: [2IIM CAT Prep]
Message 4 of 4 , Apr 4, 2011
 the other solution is 8833 50-x= -38  from kamal's solution. -Sindhu --- On Fri, 1/4/11, Rajesh Balasubramanian wrote:From: Rajesh Balasubramanian Subject: Re: [2IIM CAT Prep] Challenging Number Theory questionTo: ascent4cat@yahoogroups.comCc: "kamal lohia" Date: Friday, 1 April, 2011, 11:18 PM Spot on. This answer is correct. There is one more solution to this question. Any other attempts? Rajesh99626 48484On Wed, Mar 30, 2011 at 2:46 PM, kamal lohia wrote: The number is 1233 = 12² + 33².Let's say the four digit number = N = abcd = XY = 100X + Y = X² + Y²=> (X - 50)² + (Y - 1/2)² = 50² + (1/2)²=> 4(X - 50)² + (2Y - 1)² = 10001 = 76² + 65²=> X = 12, Y = 33 and the number is 1233.Kamal Lohia9953813320 From: Rajesh Balasubramanian To: ascent4cat@yahoogroups.comSent: Wed, March 30, 2011 10:20:23 AMSubject: [2IIM CAT Prep] Challenging Number Theory question Hi all, Post the World cup freebies, here is a challenging quesiton on Number Theory. The question can also be found at our blog at http://iimcat.blogspot.com/2011/03/cat-number-theory-challenging-question.html . There is a 4-digit number 'abcd' that satisfies the following property. 'abcd' = ab ^2 + cd ^2. Find abcd. Cheers,99626 48484Weekend batches starting @ Chennai, Apr 3rd @ Velachery

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