Number System - Questions & Discussions

monnu · March 18, 2010, 9:20am

Joining this thread .. It will sure help me to get grip over Number system.

regards,
Brij

avinav2712 · March 18, 2010, 9:22am

Joining this thread .. It will sure help me to get grip over Number system.

regards,
Brij

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mail2neha_k · March 19, 2010, 3:59am

Hi Pk,

As the cyclic form will give only two possibility as 9 or 1 as last digit depending on the power (if odd then 9, if even then 1)

So let us work on power. After the 5! all the sum will have last digit as 0, so we have to work only upto 4!
1!=1, 2!=2, 3!=6, 4!=24 sum of all will give 33. So we are concerned only with 3 as last digit of power which is ODD. So the answer will be 9.
Please confirm

Hi! To solve these kind of questions check out the pattern...,

Here 5789^( 1!+2!+3!+4!+5!+.....)

is given,

so pattern of 9 { 9 1 } 2digits

also after 5! each term will end into zero for ex.6! 6*5=30 *4*3*2*1...,

therefore we are concerned with only upto 4!

dividing 1!.., 2!..,3!...,4!...,

we get remainder as 1

therefore the last digit should be 9

mail2neha_k · March 19, 2010, 4:23am

avinav2712 Says
You don't need to post to subscribe to a thread. You can click "Subscribe to this thread", which you can find in "Thread Tools" on the top of this page.

Hi Abhinav!

You seem to be regular pagalguy.com user...,

can you tell me how to find last year quantitative threads for various chapters

like geometry & mensuration..,probability etc.

also same for LR & DI...,verbal ??

Thanks & regards,

avinav2712 · March 19, 2010, 4:34am

Hi Abhinav!

You seem to be regular pagalguy.com user...,

can you tell me how to find last year quantitative threads for various chapters

like geometry & mensuration..,probability etc.

also same for LR & DI...,verbal ??

Thanks & regards,

mail2neha_k · March 19, 2010, 2:12pm

Try searching for appropriate threads. Learn how to search here:

http://www.pagalguy.com/discussions/official-quant-thread-for-cat-2010-25047731
2. http://www.pagalguy.com/discussions/cat-2010-lr-di-thread-25048796
4. http://www.pagalguy.com/discussions/quant-marathon-25014041
5. http://www.pagalguy.com/discussions/vedic-mathematics-25006767
6. http://www.pagalguy.com/discussions/quant-by-arun-sharma-25023813
7. http://www.pagalguy.com/discussions/doubts-in-permutation-combination-25010050
8. http://www.pagalguy.com/discussions/time-speed-distance-questions-discussions-25001217
9. http://www.pagalguy.com/discussions/time-speed-work-alligations-and-mixtures-problems-25009280
10. http://www.pagalguy.com/discussions/geometry-25000856

I guess these should suffice :)

PS: My name is Avinav :D

Thanks Avinav! 😃

kinji.at.pg1 · March 26, 2010, 6:30am

mail2neha_k Says
Thanks Avinav! :)

Please use the thanks button at the below of the post. 😃

girish_deore · April 9, 2010, 6:32pm

Can someone plz help in solving this question?

1234512345..............................(25 times)

remove 10 entries so that the number will be big enough....

kinji.at.pg1 · April 11, 2010, 5:17am

Can someone plz help in solving this question?

1234512345..............................(25 times)

remove 10 entries so that the number will be big enough....

I presume the question is remove the 10 digits so the resultant number becomes the lasrgest number possible.

The Maximum Digit in this number is 5

Therefore remove the first four digits (1234)from left hand side, we get and again remove (1234) leaving out the 5 and again leave out 5 and remove the next two digits 12.

Therefore number becomes 553451234512345....

This should be the maximum number possible.

niketjain · April 11, 2010, 3:57pm

can some1 plzz help me in dis question?
find the last two digits of the no N,
where N =20025*20026*200027*200035?

is there just one way to en up multiplying 25*26*27*35?
or is there any oder easy method also.

maskedmenace · April 11, 2010, 4:23pm

can some1 plzz help me in dis question?
find the last two digits of the no N,
where N =20025*20026*200027*200035?

is there just one way to en up multiplying 25*26*27*35?
or is there any oder easy method also.

50*Even ends in 00
50*odd ends in 50

25*26*27*35 => 50*13*27*35 => 50*odd => 50

avinav2712 · April 11, 2010, 4:41pm

can some1 plzz help me in dis question?
find the last two digits of the no N,
where N =20025*20026*200027*200035?

is there just one way to en up multiplying 25*26*27*35?
or is there any oder easy method also.

To find out the last two digits of any expression, you need to find its remainder when divided by 100.

Thus, taking the last two digits and finding their remainder with 100,

(25*26*27*35) mod 100
1*26*27*35 mod 4 (Dividing numerator and denominator by 25)

1*2*(-1)*(-1) mod 4 (Remainders of 1, 26, 27 and 35 when divided by 4)
Thus, 2 mod 4

Now, since we had divided by 25, we need to multiply the remainder by 25 to get the remainder when divided by 100.

Thus, the remainder is 2*25 = 50

sweety.k5 · April 13, 2010, 6:17am

To find out the last two digits of any expression, you need to find its remainder when divided by 100.

Thus, taking the last two digits and finding their remainder with 100,

(25*26*27*35) mod 100
1*26*27*35 mod 4 (Dividing numerator and denominator by 25)

1*2*(-1)*(-1) mod 4 (Remainders of 1, 26, 27 and 35 when divided by 4)
Thus, 2 mod 4

Now, since we had divided by 25, we need to multiply the remainder by 25 to get the remainder when divided by 100.

Thus, the remainder is 2*25 = 50

Hi guys,

Could you please suggest may a method to solve three variables equations:
Eg.
x+y+z=80
4x-2y-z=138
I think we can solve by equating them to "k".But could not proceed properly.
Please explain the method.

kaivalya_psy · April 13, 2010, 6:25am

start removing 10 digits serially starting from the unit digits...

monnu · April 13, 2010, 4:20pm

can some one tell to find the remainder when divisor is composite number like:
Find remainder when 2^1990 is divided by 1990 ?

kaivalya_psy · April 13, 2010, 4:51pm

they would obviously be 50... bcoz of one 2 in 26 and many 5's

akrosh007 · April 13, 2010, 5:25pm

can some one tell to find the remainder when divisor is composite number like:
Find remainder when 2^1990 is divided by 1990 ?

==>hey is it 1974...?
==>2^n mod n=(2n+4) mod n....for n even
=(2n+2) mod n.....for n odd:lookround:
confrm..m not sure abt this method

monnu · April 13, 2010, 5:37pm

==>hey is it 1974...?
==>2^n mod n=(2n+4) mod n....for n even
=(2n+2) mod n.....for n odd:lookround:
confrm..m not sure abt this method

answer is 1024 (2^10) ... but i want method to reach the ans.

kinji.at.pg1 · April 15, 2010, 5:05am

Monnu Says
answer is 1024 (2^10) ... but i want method to reach the ans.

See Brij, use the Euler's theorem or if that doesn't work, Break the divisor into number of coprimes (preferrably two) and use Chinese remainder theorem.

kinji.at.pg1 · April 15, 2010, 5:09am

Hi guys,

Could you please suggest may a method to solve three variables equations:
Eg.
x+y+z=80
4x-2y-z=138
I think we can solve by equating them to "k".But could not proceed properly.
Please explain the method.

if you can get hold of TIME Material, you can use Special Equations, but before using that, use the method you have suggested yourself. If it doesn't work, use special equations. Special Equation takes some time to master and apply so use it judiously. In actual exam, use options to eliminate also 😃