Number System - Questions & Discussions

catwoman_09 · September 1, 2009, 3:37pm

help me in solving the following sum:

a natural number N when divided by 10 leaves a remainder of R and quotient of Q. the number N is equal to the sum of the product QR and the sum(Q+R). If N is a multiple of 9 and is less than 10000, ho0w many values can N assume?

a)110
b)112
c)999
d)1000

is it 112

catwoman_09 · September 1, 2009, 3:46pm

Let N=10Q + R
N = QR + Q +R

Therefore

10Q+R = QR +Q+R
Therefore 9Q = QR
R = 9
Put
Q = 0,1,2......

N = 9,19,29,.......9999
= 1000 different value.

Is the answer Correct?

how can N be 19,29,.... it has to be a multiple of 9..........

xpect_ton_hurts · September 1, 2009, 3:49pm

is it 112

yup, u r correct once agn...do post the solution...

kac8l591 · September 1, 2009, 3:50pm

catwoman_09 Says
how can N be 19,29,.... it has to be a multiple of 9..........

Yes this is wrong I didnot consider the case that N is a multiple of 9

catwoman_09 · September 1, 2009, 3:52pm

help me in solving the following sum:

a natural number N when divided by 10 leaves a remainder of R and quotient of Q. the number N is equal to the sum of the product QR and the sum(Q+R). If N is a multiple of 9 and is less than 10000, ho0w many values can N assume?

a)110
b)112
c)999
d)1000

my explanation
10Q+R = QR +Q+R
9Q = QR
R = 9
so d values of N can be of d form 9*(10k+1)
k can be 0,1,2,.....111
hence number of diff values of N=112.......

jain_ashu · September 1, 2009, 7:23pm

If the product of four positive integers is 10! What is the smallest possible value their sum can have?

a. 175
b. 176
c. 180
d. 181

I am getting 175 but it took too much time with hit and trial method. Any short method for this.

jain_ashu · September 1, 2009, 7:36pm

In a national hockey single elimination tournament, 303 teams are participating. How many games will be played before a team becomes the national champion?

a. 152
b. 302
c. 77
d. 303

naga25french · September 1, 2009, 7:58pm

In a national hockey single elimination tournament, 303 teams are participating. How many games will be played before a team becomes the national champion?

a. 152
b. 302
c. 77
d. 303

it should be b) 302

sample it for smaller value

u get if n team plays , n-1 matches are played.. so 302

suhansarkar · September 1, 2009, 8:03pm

the answer should be 302
to eliminate 302 team you need 302 matches

ankurb · September 1, 2009, 8:04pm

If the product of four positive integers is 10! What is the smallest possible value their sum can have?

a. 175
b. 176
c. 180
d. 181

I am getting 175 but it took too much time with hit and trial method. Any short method for this.

a+b+c+d >=45(approx)
numbers have to be around 44
40,42,45,48 = 175
used hit and trial only.

suhansarkar · September 1, 2009, 8:11pm

it should be b) 302

sample it for smaller value

u get if n team plays , n-1 matches are played.. so 302

dont think we need smaller samples...302 matches are required for 302 teams to loose ...:-P

naga25french · September 1, 2009, 8:16pm

If the product of four positive integers is 10! What is the smallest possible value their sum can have?

a. 175
b. 176
c. 180
d. 181

I am getting 175 but it took too much time with hit and trial method. Any short method for this.

45^4 = 2025^2 = 41xxxxxx > 10 !

so there is one possibility where in sum is less than 180

this rule out option 3 and 4

now write 10 ! = 6* 4 * 5 * 6 * 7 * 8 * 9 * 10

make this expression as product of four numbers in 40's

40 * 42 * 45 * 48

so sum = 175

i cant term this hit and trial .. dunno what method to term

pgaucha · September 2, 2009, 7:19am

In a national hockey single elimination tournament, 303 teams are participating. How many games will be played before a team becomes the national champion?

a. 152
b. 302
c. 77
d. 303

less than one to be a champion

b.302

orangejawan · September 2, 2009, 8:52am

Hello Aspirants ,,,

This is my 1st post as mee not comfortable with NumberSystem... Please help me out..... I have started my journey so help me outttt

1 : What is the remainder when 32^32^32 is divided by 9??

pgaucha · September 2, 2009, 8:53am

Hello Aspirants ,,,

This is my 1st post as mee not comfortable with NumberSystem... Please help me out..... I have started my journey so help me outttt

1 : What is the remainder when 32^32^32 is divided by 9??

answer is 4......
refer total gadha it helped me alot

mani_23 · September 2, 2009, 9:23am

Hello Aspirants ,,,

This is my 1st post as mee not comfortable with NumberSystem... Please help me out..... I have started my journey so help me outttt

1 : What is the remainder when 32^32^32 is divided by 9??

its 4
(32^32^32)/9
= ((125^10^32).(25^32))/9
= ((8^10^32).(7^32))/9
= ((64^5^32).(49^16))/9
= ((1^5^32).(4^16))/9
= ((1).(4^15)(4))/9
= ((64^5)(4))/9
4

2nd method is by Euler :32^32^32/9

sol- using Euler theorem:-

32 n 9 are co prime

Euler number of 9=6
6*5=30
32^30=1mod9

thus,
32^32^32
=(32^2)^32
=(5^2)^32 (using rem theorem)
=25^32
=7^2 (using rem theorem as well eulers theorem)
=49

49=4mod9

hence rem=4

sachy24 · September 2, 2009, 10:05am

In a national hockey single elimination tournament, 303 teams are participating. How many games will be played before a team becomes the national champion?

a. 152
b. 302
c. 77
d. 303

answer is 302

sachy24 · September 2, 2009, 10:06am

Hello Aspirants ,,,

This is my 1st post as mee not comfortable with NumberSystem... Please help me out..... I have started my journey so help me outttt

1 : What is the remainder when 32^32^32 is divided by 9??

Answer is 4....

bhupi3149 · September 2, 2009, 10:12am

99.......99 (2009 times) = n

whats the sum of digits of n^2

bhupi3149 · September 2, 2009, 10:22am

answer is 4.

i tried it by euler number

32^32^32/9

euter number for 9 is 6

32^32/6 will leave 4 as remainder

(32^6*x)*32^4/9
1*4=4

is it right