## Re: [ascent CAT] number system

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• Hi I think using the concepts of congruency and modulo will be much helpful here. these, as you might be knowing, help you in calculating these remainders in
Message 1 of 9 , Nov 9, 2005
Hi

I think using the concepts of congruency and modulo will be much
these remainders in just 1 step, and there are also very powerful
short theorems in these topics.
in case you are not aware of these topics, you can get them in any
standard number theory textbook. you may also refer
http://mathworld.wolfram.com

bye.... all the best for CAT exams!
--
Siddharth Tallur
B.Tech Electrical Engineering
IIT Bombay

On 10/24/05, Mridul Sharma <it_edu2002@...> wrote:
>
> Hi Khushi,
>
> Answers to ur problems are as below,
>
> khushi shukla <ss11rd03@...> wrote:
>
>
>
> Remainder wen 6 to the power 45 + 6 to the power 3 is divided by 215
>
> a)0 b) 6 c)4 d)none of these
>
>
>
> (6^3)^15 + 6^3 can be written as (215+1)^ + (215+1) so when divided by 215
> will give remainder 1+1=2
>
>
>
> remainder wen 3 to the power 440 is divided by 15
>
> a)6 b) 4 c) 2 d)0
>
>
>
> 3^439/5 can be written as 3 .3^438/5 = 3.(3^2)^219=3.(10-1)^219 when divided
> by 5 gives remainder -3 that means +2 since we cancelled 3 thus remainder
> should be 6
>
> for any value of `P` prime number greatr tan 3 ,p to the power 2 +17
> divided by 24
>
> a)0 b) 1 c) 2 d)none of these
>
>
>
> This question requires clarity are u talking (p^2)+17 or p^2+17
>
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--
Siddharth Tallur
B.Tech Electrical Engineering
IIT Bombay
• dear friends, i have a math question which is very interesting. i have been trying to get an answer but almost all efforts went in vain , so i seek your
Message 2 of 9 , Sep 26, 2006
dear friends,
i have a math question which is very interesting. i have been trying to get an answer but almost all  efforts went in vain , so i seek your humble assitance to get the exact answer to this question which goes as follows:
in a particular no system the product of 44 and 11 is 1034. what is the value of 3111 in decimal system?

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• it will be for base system 5 , so value of 3111= 156 soln : (4n+4)*(n+1)=n^3+3*n+4
Message 3 of 9 , Oct 14, 2006
it will be for base system 5 , so value of 3111= 156
soln : (4n+4)*(n+1)=n^3+3*n+4

On 9/26/06, samir joshi < sam_shill_143@...> wrote:

dear friends,
i have a math question which is very interesting. i have been trying to get an answer but almost all  efforts went in vain , so i seek your humble assitance to get the exact answer to this question which goes as follows:
in a particular no system the product of 44 and 11 is 1034. what is the value of 3111 in decimal system?

Find out what India is talking about on - Yahoo! Answers India
Send FREE SMS to your friend's mobile from Yahoo! Messenger Version 8. Get it NOW

• Hi dear , This can be the solution for ur problem: Lets say that number syatem is based on base n. Notations number in base n= (no.)n nmber in base 10 =
Message 4 of 9 , Oct 15, 2006
Hi dear ,
This can be the solution for ur problem:

Lets say that number syatem is based on base n.

Notations
number in base n= (no.)n
nmber in base 10 = (no.)10

(44)in base n = (4n+4) in base 10
(11) in base n = (n+1)   in base 10
(1034) in base n = (1.n^3 + 3.n + 4 ) in base 10.

(4n + 4) (n+1) = (n^3 + 3.n + 4)
4n^2 + 8n + 4 = n^3 + 3n +4

Solving this would give
n = 5,0,-1

A base can't be -ve negative and 0

So our numbers are  in base 5.

[3111] in base 10 = [44421] in base 5(n)

Thanks and Regards
Anand

From: ascent4cat@yahoogroups.com [mailto:ascent4cat@yahoogroups.com] On Behalf Of samir joshi
Sent: Tuesday, September 26, 2006 7:59 PM
To: ascent4cat@yahoogroups.com
Subject: [Ascent CAT] number system

dear friends,
i have a math question which is very interesting. i have been trying to get an answer but almost all  efforts went in vain , so i seek your humble assitance to get the exact answer to this question which goes as follows:
in a particular no system the product of 44 and 11 is 1034. what is the value of 3111 in decimal system?

Find out what India is talking about on - Yahoo! Answers India
Send FREE SMS to your friend's mobile from Yahoo! Messenger Version 8. Get it NOW

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• how many natural numbers less than 1700 can be expressed as the difference of the two perfect squares in atleast one way. a.)1174 b.)1274 c.)1374 d.)974
Message 5 of 9 , Aug 20, 2007
how many natural numbers less than 1700 can be expressed as the
difference of the two perfect squares in atleast one way.
a.)1174
b.)1274
c.)1374
d.)974
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