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Some Mathematical Curios
by Total Gadha - Tuesday, 31 July 2007, 03:48 AM
  cat 2010 cat 2010 xat 2010 mba 2009 useful quant formulasPresented below are some of the findings that many CAT 2007 aspirants will find useful and many CAT 2008 aspirants will do well to add them in their armory early on. Unfortunately, I have not been able to provide the proofs for these results as the space, as well as the attention span of my readers, is at a premium. Perhaps, I will do so in my later chapters. Working as a teacher, I regularly come across useful results that can prove to be beneficial to one's mathematical health but which do not reach the students because they are not properly documented. Well, hereon, I promise to document every useful result/proof that crosses the eyes and grey cells of this Gadha. Feel free to ask any question that arises in your curious mind.



cat 2008 cat 2007 xat 2008 mba 2008 useful quant formulas

I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

 

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Re: Some Mathematical Curios
by Inder Negi - Tuesday, 31 July 2007, 08:13 AM
 

Hi TG,

its great ..really you are doing good job .thanks a ton for this .........

 

Re: Some Mathematical Curios
by Puneet Kabra - Tuesday, 31 July 2007, 08:26 AM
  Thx a ton...boss
Re: Some Mathematical Curios
by saurabh kakar - Tuesday, 31 July 2007, 12:10 PM
  Thanks a lot for this awesome rare info...time savers
Re: Some Mathematical Curios
by Charu Mahajan - Tuesday, 31 July 2007, 12:28 PM
 

Hi,

Thanks a ton...really helpful !!!

Charu

Re: Some Mathematical Curios
by Small Wonder - Tuesday, 31 July 2007, 12:32 PM
 

TG's magnum opus on display !

smile

Re: Some Mathematical Curios
by tripti pathak - Tuesday, 31 July 2007, 12:59 PM
  can u help me wid how to grasp wat thgs to find out in a problem like this

The equation |x-1| - |x-2| + |x-4| = m has exactly n real solutions for some real m. Then which among the following relations between m and n can not be true?

(a) m/n = 3/5    (b) m = n    (c) m/n = 3/2    (d) m/n = 5/3    (e)  m = n-1


i do not how to start wid such kind of problemss

Re: Some Mathematical Curios
by arun kumar - Tuesday, 31 July 2007, 02:33 PM
  sir ,
how do i find the coefficient of x^100 in (1+ x^2 + x^4..) (1 + x^3 + x^ 6.....) (1 + x^5 + x^10...).....
Re: Some Mathematical Curios
by Anand Kishore - Tuesday, 31 July 2007, 03:47 PM
 

hi TG,

how to find the coefficient of x^100 in (1+x^2+x^4...)(1+x^3+x^6..)(1+x^5+x^10...) using binomial Th. or any other short cut method is there for this ... Plz let me know Thanks

Re: Some Mathematical Curios
by dr naina singh - Tuesday, 31 July 2007, 09:41 PM
  thanks boss you r awesome. really u r doing great job.
Re: Some Mathematical Curios
by Total Gadha - Tuesday, 31 July 2007, 10:35 PM
  Hi Anand and Arun,

You will have to calculate the coefficient of x100 in (1 + x2 + x4 + x6 + ...)(1 + x3 + x6 + ...)(1 + x5 + x10 + ...) the hard way, although it's not so hard as it seems. Notice the exponents of the last multiplicand here- 1 + x5 + x10 + x15 + ... x100. The coefficient of x are 0, 5, 10, ... 100. Therefore, we need to find the coefficient of x100, x95, x90.... in (1 + x2 + x4 + x6 + ...)(1 + x3 + x6 + ...). In other words, we need to find the number of solutions to 2x + 3y = 100, 2x + 3y = 95, 2x + 3y = 90, and so on. This can be found straight away through the formula given for the number of whole number solution of ax + by = c in the same article. smile

Total Gadha
Re: Some Mathematical Curios
by tanmay saxena - Tuesday, 31 July 2007, 11:53 PM
 

hi really encouraging ... a lot of tstuff always neede in one place .. thx

theres a query

 

how is 7777...7777 - 37 times divided by 19 gives a remainder of 7 ?

 

kindly xplain !!!! smile

 

 

Re: Some Mathematical Curios
by divya kansal - Wednesday, 1 August 2007, 09:50 AM
 

Thanks TG,

Jus gr8 stuff...i was always flustered by these kind of questions..

And for calcuating coefficient of x^100 ,is it not a lengthy process to calculate ax + by = 100,95,90...and so on?

Also,do we have such kind of formulae for finding number of integral solutions in case of product of two or three numbers?

Thanks in advance!!! smile

Re: Some Mathematical Curios
by Kunal Gupta - Wednesday, 1 August 2007, 11:59 AM
  Same problem as that of tanmay...
Re: Some Mathematical Curios
by Total Gadha - Wednesday, 1 August 2007, 01:24 PM
  Hi Kunal and Tanmay,

Think!

Total Gadha
Re: Some Mathematical Curios
by shiva chepuri - Wednesday, 1 August 2007, 03:55 PM
  it is just terrific!!!!!!
no words ,absolutely remarkable article
keep it up!!!!
Re: Some Mathematical Curios
by don don - Wednesday, 1 August 2007, 04:01 PM
 

for the eq. 5x+19y=64

if you apply the concept for finding no.of whole no sol.

i.e[HCF of 64/19,64/5]=0\

HCF of 64/19,64/5 =64/95

but it has one whole no solution (9,1)

correct if i m wrong

Re: Some Mathematical Curios
by Anand Kishore - Wednesday, 1 August 2007, 04:25 PM
 

hi TG,

I was jst going through HCF & LCM basics from TG...  this ques. really perturbed me 4 long...

The HCF of two numbers is 12 and their sum is 288. How many pairs of such numbers are possible?
i.e 12x+12y=288 ==> x+y =24

if i go using your method... HCF (24,24) is 24 i.e 24+1 =25 such pairs exists ... plz correct me , ..m confused .. what i missed here .. thoughtful

Re: Some Mathematical Curios
by shashank shah - Wednesday, 1 August 2007, 05:54 PM
 

They r awesome TG....surprise

thnx 4 those blasting tips...smile

Re: Some Mathematical Curios
by mallik rao - Wednesday, 1 August 2007, 08:59 PM
  JUST check this one for : ax+by=c
2x+3y=5......the whole number solutions according to formula
[HCF of (5/2,5/3)]-->[5/6]=0...but (1,1) is a solution:
AND COEFFICIENT OF X^100 :181...I HAVE CHECKED FROM 2X+3Y=100...TO 2X+3Y=0
Re: Some Mathematical Curios
by Total Gadha - Wednesday, 1 August 2007, 10:55 PM
  Hi Don don and Mallik Rao,

I did some research today on indeterminate equation when c/a and c/b are not integers. It seems that we look for 'nearest integer' in place of 'greatest integer'. Unfortunately, the nearest integer has to be determine through some funda of continued fractions. Let me work on it tonight. I will correct the method soon. The number of solutions when c/a or c/b or both are integers is correct.

The solution for coefficient of x100 is correct. The coefficient is 184. I calculated again.

Total Gadha
Re: Some Mathematical Curios
by amit sharma - Thursday, 2 August 2007, 01:38 AM
  Hi TG ..

It was really very helpful
Thanks a lot !!
Re: Some Mathematical Curios
by gaurav gupta - Thursday, 2 August 2007, 10:48 AM
 

hi anand,

the sloutions are whole number sloutions,substract 2 from them as (0,24) and (24,0) are not possible in this case as numbers cannot be 0 here.therefore the ans should be 23

i hope its ok now.....

Re: Some Mathematical Curios
by Sri KLR - Thursday, 2 August 2007, 11:32 AM
 

Hi TG,

It's a wonderful article. It's very grey area for me and I am so happy to see shortcuts for everything....

Keep updating us in the Quant-Di discussion section whenever you write a new article. Most of the time I hang around there only and don't come to the main page at all. Today also I saw your mentioning there and navigated to this page. Else would have missed it !!

Re: Some Mathematical Curios
by Total Gadha - Thursday, 2 August 2007, 11:39 AM
  Hi Anand,

If HCF of two numbers is H, the numbers can be written as Hx and Hy where x and y are coprime, i.e. they have no factors in common. Here, you have to find the value of x and y in x + y = 24 which have no factors in common. So pairs like (20, 4) won't do as they have a common factor..

Total Gadha
Re: Some Mathematical Curios
by mallik rao - Thursday, 2 August 2007, 08:22 PM
  100:17   95:15     90:16    85:14  80:14     75:13
70:12  65:10   60:11   55:9   50:9  45:8    40:7
35:5   30:6    25:4    20:4   15:3   10:2  5:1  0:1
these are all the possible solutions... sum is only 181...can you tell  me where i went wrong
Re: Some Mathematical Curios
by Total Gadha - Friday, 3 August 2007, 02:05 AM
  17 16 16 14 14 13 12 11 11 9 9 8 7 6 6 4 4 3 2 1 1 
Re: Some Mathematical Curios
by Srikanth Nair - Friday, 3 August 2007, 08:45 AM
  Hey TG,
    Just two words "HATS OFF ". U amazing. Thanks a 10^10^10^.... in kilos. Ton is not enough. big grin
Regards,
Srikanth Nair
Re: Some Mathematical Curios
by Aditi Dvivedi - Friday, 3 August 2007, 12:47 PM
 

Hi TG,

Plz tell me how will we get 16 solutions for 2x + 3y = 95? When both c/a and c/b are non-integer we take [ HCF of c/a and c/b ]. Where am I going wrong ?

Re: Some Mathematical Curios
by Aditi Dvivedi - Friday, 3 August 2007, 12:59 PM
 

Hi TG,

Awesome article... Thanks a lot...

895 gives 32 as the last two digits.It has been mentioned wrong in the article.

 

Re: Some Mathematical Curios
by Gul Gul - Friday, 3 August 2007, 03:32 PM
  yep TG 895 gives 32 as the last two digits
Re: Some Mathematical Curios
by gaurav gupta - Friday, 3 August 2007, 09:13 PM
 

Hi TG,

  Thanx for solving anand's problem.it cleared mey misconceptions also...but tell me that would we include pairs containing zeros or not????

Re: Some Mathematical Curios
by arun r - Friday, 3 August 2007, 09:52 PM
  Hi TG,
          I did not understand how you arrived with the calculation of finding the no:of odd divisors.I only know to find the total no:of divisors of a number..Please explain..
Re: Some Mathematical Curios
by arun r - Friday, 3 August 2007, 09:57 PM
  Hai TG,
          I arrived at finding the no:of odd divisors.Anyway thanks.The materials you provided are awesome!!
Re: Some Mathematical Curios
by Total Gadha - Saturday, 4 August 2007, 06:16 AM
  Hi Aditi and Gullz,

Corrected. smile Thanks for pointing that out. smile

Total Gadha
Re: Some Mathematical Curios
by mallik rao - Saturday, 4 August 2007, 07:31 AM
  thanks alot TG...
Re: Some Mathematical Curios
by Arun Reddy - Saturday, 4 August 2007, 10:40 PM
 

Thanks a lot TG! for this nice article.

Could you please give answers for the questions given in this article,If possible solutions also.

Thanks again!

Re: Some Mathematical Curios
by ramrajvi parghi - Sunday, 5 August 2007, 06:37 PM
  hey TG! great collection man. I am deeply indebted to you, but i'd like one more favour from you. could you please post some fundas to solve the questions on "to find the greatest/smallest value of an expression" where the variable is bounded in some limits. i really mess up in these problems. one commonly employed method to solve these type of problems  is the arithmatic mean and geometric mean method, but i havent learnt how to use it properly. could you please help me out on this?
Re: Some Mathematical Curios
by Mission IMpossible - Monday, 6 August 2007, 12:43 PM
 

This is amazing stuff. Thanks TG. You are simplyyyyyyyyyyyy great.... smile

Re: Some Mathematical Curios
by Gul Gul - Tuesday, 7 August 2007, 10:56 AM
  TG in last problem... can u throw light on .... expansion of (x-a)^n. thnx
Re: Some Mathematical Curios
by shashank somani - Tuesday, 7 August 2007, 03:49 PM
  Hi TG
I have not been able to find the error which the other CAT potentials have spotted,
It looks correct to me...could you help me spot it. And it the observation only valid for 76 and 01.
Shashank
Re: Some Mathematical Curios
by Dhruv M - Tuesday, 7 August 2007, 03:49 PM
 

Good going TG. Thanks for all the effort you're putting in...it shows!!wide eyes

Re: Some Mathematical Curios
by Anil Sahu - Wednesday, 8 August 2007, 02:35 PM
 

great stuff guys. keep going. smile

i am sure this will be of gr8 help for all CAT aspirants.

Re: Some Mathematical Curios
by ashish bhardwaj - Wednesday, 8 August 2007, 09:59 PM
 

Good stuff, But TG if question is something like 77777777...... up to 200  times and Divisor is non prime number like 68 or 25 ......how can i find out the remainder in that case...

If anyone knows please do tell me ...

Re: Some Mathematical Curios
by Total Gadha - Wednesday, 8 August 2007, 11:16 PM
  Hi Ashish,

Remainder of 7777....(200 times) when divided by 68:

68 = 17 × 4

77777...(200 times) = 7777...77700 + 77 --> remainder with 4 = 1
77777...(200 times) = 777...77700000000 (divisible by 17 as the number of 7s is a multiple of 16) + 77777777 --> remainder with 17 = 6

The lowest number which gives remainder 1 with 5 and 6 with 17 is 57. Hence remainder = 57.

Remainder of 7777....(200 times) when divided by 25:

77777...(200 times) = 7777...77700 + 77 ---> remainder with 25 = 2

Total Gadha
Re: Some Mathematical Curios
by Aditi Dvivedi - Thursday, 9 August 2007, 09:59 AM
 

Hi TG,

I am still waiting for the reply....

Thanks in advance

Re: Some Mathematical Curios
by Vimalesh Kobla - Wednesday, 15 August 2007, 12:22 AM
  Hi TG,
   how did you find the coefficient of x^100?? in 2x+3y+5z=100 problem
Re: Some Mathematical Curios
by Total Gadha - Thursday, 16 August 2007, 07:49 AM
  Hi Vimalesh,

Check this out: http://totalgadha.com/mod/forum/discuss.php?d=914#8563

Total Gadha
Re: Some Mathematical Curios
by Vimalesh Kobla - Thursday, 16 August 2007, 08:51 PM
  Hi TG,
   Thanks a lot
Re: Some Mathematical Curios
by TG Team - Friday, 31 August 2007, 08:15 AM
  Hi TG
where is that link moved which was about total whole number solutions of the equations like ax+by=c and ax+by+cz=d. Some thing like HCF{c/a,c/b}+1
Please help soon.
Kamal Lohia
Re: Some Mathematical Curios
by Aditi Dvivedi - Friday, 31 August 2007, 12:06 PM
 

Hi TG,

I have posted one question on the above link...Please guide me..

Thanks

Re: Some Mathematical Curios
by Aditi Dvivedi - Friday, 31 August 2007, 12:08 PM
 

Hi TG,

I have posted one question on the above link...Please guide me..

Thanks

Re: Some Mathematical Curios
by nitesh agarwal - Saturday, 1 September 2007, 08:53 PM
 

Hi TG,

This is truly Gr8 stuff. Thanks for this.

Could you please expalin how we got

Last two digits for 90*7^275* 

as 90*7*...

i doubt if it is 90*43*..

as 7^275 will give (...01)*7^3.... could you please tell which one is correct

Re: Some Mathematical Curios
by Total Gadha - Monday, 3 September 2007, 03:48 PM
  Hi Nitesh,

It should not be 7275 but 7273. Have corrected the typo.

Total Gadha
Re: Some Mathematical Curios
by Bhupendra Kumar Jain - Friday, 7 September 2007, 07:53 PM
  Hi TG,

How come 15 has 4 odd divisors? I am confused please help.
Re: Some Mathematical Curios
by saket tripathi - Saturday, 8 September 2007, 02:07 PM
  1,3,5,15
Re: Some Mathematical Curios
by devarshi shukla - Monday, 10 September 2007, 08:58 PM
  hello TG........can u explain how the cofficient of x^100 in the expansion of (x^0+x^2+x^4+x^6+............)(x^0+x^3+x^6+x^12+......)(x^0+x^5+x^10+....) comes out to be 184 .
Re: Some Mathematical Curios
by kamal mehta - Saturday, 5 April 2008, 12:25 AM
  hi tg great work yaar .......can u explain how the cofficient of x^100 in the expansion of (x^0+x^2+x^4+x^6+............)(x^0+x^3+x^6+x^12+......)(x^0+x^5+x^10+....) comes out to be 184 .
Re: Some Mathematical Curios
by sabyasachi baral - Monday, 21 July 2008, 10:42 PM
  its ossum . nice article . i found lots of knowledge frm it
Re: Some Mathematical Curios
by sachin jindal - Thursday, 24 July 2008, 07:20 PM
  i think m/n=3/5

Re: Some Mathematical Curios
by Anil Shivappa - Wednesday, 30 July 2008, 05:51 PM
 

Hi TG...U r amazing...Doin a great job..

Am not able to understand hows the last two digits of 8^95 is 32..help me plz....

Re: Some Mathematical Curios
by niharika mishra - Saturday, 20 September 2008, 08:58 AM
 

 

Remainder of 7777....(200 times) when divided by 68:

68 = 17 × 4

77777...(200 times) = 7777...77700 + 77 --> remainder with 4 = 1
77777...(200 times) = 777...77700000000 (divisible by 17 as the number of 7s is a multiple of 16) + 77777777 --> remainder with 17 = 6

The lowest number which gives remainder 1 with 5 and 6 with 17 is 57. Hence remainder = 57.

Remainder of 7777....(200 times) when divided by 25:

77777...(200 times) = 7777...77700 + 77 ---> remainder with 25 = 2

 

how do u g8 57 as remainder ........plz explain the last step

Re: Some Mathematical Curios
by vipul nahar - Thursday, 23 October 2008, 01:52 PM
 

Hi TG,

Even after goin thrugh the series of replies for the value of coff. of x^100, one thing is yet to b cleared in ma mind. Could you pl clarify. my doubt is:

no of solutions will b [HCF(c/a,c/b)]+1 when c/a & c/b are integers rght?

but what if they are not integers? and here are v talkin abt only +ve no of solutions?..these are ma queries regardin findin out the no of solns for an indeterminate equation. pl clarify

Thanks in advance

Vipul.

 

 

Re: Some Mathematical Curios
by vaibhav garg - Thursday, 7 May 2009, 12:12 PM
 

hello,

can u plz explain sir 4444 or 6666 or 7777 (written p-1 times where p=5) but it is not divisible by 5?????

Re: Some Mathematical Curios
by Total Gadha - Sunday, 10 May 2009, 08:57 AM
  Hi Vaibhav,

Please read the theorem again.

Total Gadha
Re: Some Mathematical Curios
by sanjeeb panda - Sunday, 10 May 2009, 10:08 AM
 

Hello TG sir,

Please explain this concept with one more example.

 

Re: Some Mathematical Curios
by vaibhav garg - Sunday, 10 May 2009, 07:49 PM
  Thanxx a lot sir...missed the bracket part initailly...
Re: Some Mathematical Curios
by Ritwik Roy - Sunday, 10 May 2009, 09:45 PM
 

Hi TG

can you plz share the link of your article on how to find the number of whole number solutions of ax + by = c where c/a and c/b are not integers ?

In some thread I found it is nearest integer[ HCF of (c/a,c/b)] + 1...but it is failing for some scenarios like
2x+3y = 85

if we calculate nearest integer[ HCF of (c/a,c/b)] + 1 ..it will come as 14 +1 =15
But actually the answer will be 14 ...earlier you mentioned ...Unfortunately, the nearest integer has to be determine through some funda of continued fractions....any update on this ?

Another queations ..if we are asked to find out number of integral solutions of an equation..should we consider both postive and negative or only postive integral solution ?

Thanks

Ritwik

 

Re: Some Mathematical Curios
by kiran kashyap - Friday, 12 June 2009, 08:53 PM
 

hi.......

plz plz solve dis problm .......

find remainder when 888888888......................89times is divided by 470.....?

Re: Some Mathematical Curios
by Raj Malhotra - Tuesday, 1 September 2009, 12:09 PM
  Some body can solve this problem in a LUCID way. The ans is 278. But the approach was very very hard to understand..so plz help
Re: Some Mathematical Curios
by akhilesh pandey - Tuesday, 1 September 2009, 02:04 PM
 

sir i am not able to understand this method of finding out reminder when there is repetion of any such no 666666666666666666666666666666666 or 777777777777777777777777777777777777777 ... 98 or 67 times and reminder when divided by 19  or 17

 

Re: Some Mathematical Curios
by saurabh chauhan - Wednesday, 2 September 2009, 11:44 PM
  For this article...I just want to say WOW..!!!!!
Re: Some Mathematical Curios
by vikas sharma - Wednesday, 9 September 2009, 05:21 PM
 

Hi tg sir

cant we find no of whole no sol of eqn. ax+by+cz=n

by formula Cn+3-13-1  here 3 is for no of variables in eqn.(x,y,z)

if this is not sol then where its used i had read it somewhere.

pls reply asap

Re: Some Mathematical Curios
by vigneshsabari vignesh - Thursday, 10 September 2009, 11:05 PM
  this is awesome sir,I was wondering if u could send me some thing more like this,pls sir.
vignesh
Re: Some Mathematical Curios
by vigneshsabari vignesh - Thursday, 10 September 2009, 11:12 PM
  you have found out number of odd divisors of 15 as 4,but how did u find out? how do you find number of odd divisors of a number ?
Re: Some Mathematical Curios
by vigneshsabari vignesh - Thursday, 10 September 2009, 11:20 PM
  how do you find the coefficient of x^n in (1+x^2+x^4+.....)(1+y^3+y^6+...)(1+z^4+z^8+...)

Re: Some Mathematical Curios
by srinivasan ravi - Friday, 11 September 2009, 12:42 AM
  hi evryone,
pls explain me the method to find out the coefficient of x^100..thanks..
Re: Some Mathematical Curios
by Ashu Jain - Friday, 6 November 2009, 10:26 AM
 

Hi,

There are some exceptions to the part - " Any single digit number N written (p-1) times, where p is a prime number, is always divisible by p".

4444 is not divisible by 5

3333 is not divisible by 5

22 is not divisible by 3

44 is not divisible by 3

1 is not divisible by 2

3 is not divisible by 2

and so on.

I think the given concept works for p > 5

Re: Some Mathematical Curios
by Ashu Jain - Friday, 6 November 2009, 10:28 AM
 

Hi,

There are some exceptions to the part - " Any single digit number N written (p-1) times, where p is a prime number, is always divisible by p".

4444 is not divisible by 5

3333 is not divisible by 5

22 is not divisible by 3

44 is not divisible by 3

1 is not divisible by 2

3 is not divisible by 2

and so on.

I think the given concept works for p > 5

Re: Some Mathematical Curios
by kanika kalra - Saturday, 28 November 2009, 06:35 AM
  hii

i stil dunt get to calculate the coefficient of x100 in (1 + x2 + x4 + x6 + ...)(1 + x3 + x6 + ...)(1 + x5 + x10 + ...) hw to do dat!! plz help
Re: Some Mathematical Curios
by suraj saxena - Sunday, 16 October 2011, 09:32 PM
  Hi TG ,

can you tell the method through binomial of this problem .I guess in binomial there is a method.

Suraj
Re: Some Mathematical Curios
by suraj saxena - Tuesday, 18 October 2011, 04:58 PM
  Hi TG,

can you t6ell me how to find the number of digits in a calculation
625^2 * 32^2 * 7

sooraj
Re: Some Mathematical Curios
by TG Team - Tuesday, 18 October 2011, 05:28 PM
 

Hi Suraj smile

625² × 32² × 7 = 58 × 210 × 7 = 28 × 108 is a ten digit number (i.e. 28 followed by eight zeroes.)

Kamal Lohia 

Re: Some Mathematical Curios
by suraj saxena - Wednesday, 19 October 2011, 11:13 AM
  Hi TG

Question like no of digits in the pdt of 8digit and 9 digit no

or pdt of 7 , 10 and 12 digit no

is there any method or we have to estimate by taking least and largest no's

sooraj
Re: Some Mathematical Curios
by TG Team - Wednesday, 19 October 2011, 11:46 AM
 

Hi Suraj smile

If you can calculate product of 7-digit number and 8-digit number mentally, nothing like it. Otherwise obviously you can estimate.

For example: smallest 7-digit number is 1 00 00 00 and smallest 8-digit number is 1000 0000 after multiplication product become 1013 i.e. a 14-digit number and if we multiply smallest 8-digit number and smallest 9-digit number, product will contain 16-digits.

So that means when a 7-digit number and 8-digit number is multiplied, product contains 14 or 15 digits. That's estimation.

Now to decide between 14 or 15 digits, again we can estimate by looking at the number of digits when first digits of the numbers are multipled. Take some numbers and try yourself. You'll be able to grasp the trick easily. smile

Kamal Lohia

Re: Some Mathematical Curios
by priyanka j - Thursday, 20 October 2011, 11:23 PM
  Kamal Sir :-)

In d ques How many no.'s between 100 & 900 have some thr digits equal to 12 ?
Do we need to count like:
no start with 1 : 129,138,147,156,165,174,183,192
2 series : 219,228,237,246,255,264,273,282,291
3 series : 318,327,336,345,354,363,372,381,390,309
4 : 417,426,435,444,453,462,471,480,408
5 : 516,525,534,543,552,561,570,507
6 : 615,624,633,642,651,660,606
7 : 714,723,732,741,750,705
8 : 813,822,831,840,804

Obviously this is nt d way 2 slove. plz help :-)
Re: Some Mathematical Curios
by priyanka j - Thursday, 20 October 2011, 11:31 PM
  One more ques sir,
Whats d funda of
" total whole number solutions of the equations like ax+by=c and ax+by+cz=d is HCF{c/a,c/b}+1 ".
mentioned earlier in d forum, but i didn't found it...help me in dis also.

THANKS
Re: Some Mathematical Curios
by TG Team - Friday, 21 October 2011, 12:18 PM
 

Hi Priyanka smile

I hope you know how to find number of whole number solutions of a + b + c = 12.

If not then go through the lessons on Groupings and Distribution by Total Gadha.

And if you know that already, then apply this to get your answer.

Kamal Lohia 

Re: Some Mathematical Curios
by TG Team - Friday, 21 October 2011, 12:36 PM
 

Take some example by giving numerical values to the coefficients. That'll help. smile

Kamal Lohia

Re: Some Mathematical Curios
by priyanka j - Friday, 21 October 2011, 06:16 PM
  Thanks sir smile
But is there any other method......m not comfortable with Grouping & Distribution..... never able to understand it exactly......
Re: Some Mathematical Curios
by bhanu pattapu - Thursday, 27 October 2011, 08:34 AM
  Hi,

whether 22 is divisable by 3, we get a reminder 1

Re: Some Mathematical Curios
by Ruchit Patel - Thursday, 4 June 2015, 03:11 AM
  How 100 can be written as sum of successive positive integers in 2 ways?