- 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 - 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 questionHi 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?Rajesh99626 48484On Wed, Mar 30, 2011 at 2:46 PM, kamal lohia <kamallohia@...> 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
--- On

**Fri, 1/4/11, Rajesh Balasubramanian**wrote:*<rajesh@...>*

From: Rajesh Balasubramanian <rajesh@...>

Subject: Re: [2IIM CAT Prep] Challenging Number Theory question

To: ascent4cat@yahoogroups.com

Cc: "kamal lohia" <kamallohia@...>

Date: Friday, 1 April, 2011, 11:18 PMSpot 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 <kamallohia@...> 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,Cheers,**99626 48484****Weekend batches starting @ Chennai, Apr 3rd @ Velachery**