Number System - Questions & Discussions

MBA CAT 2022
1613
number=10x+y
now 10x+y=x^2+y^2-11
and 10x+y=2xy +5
so, x^2+y^2-11=2xy +5

x^2+y^2-2xy=16
x-y=4,-4
now check the options...options here are confusing

15,95 should be the answer...while 2nd option is again telling 95:-P
don't get confused...

Got d Same ans....15 n 95....
Dis is a very minor thing but really confusing.....both 4 n -4 have to b considered.......
For ex:normally we write Square root of 36 is equal to 6 not 6 n -6
But if we have
X^2 = 36....then x= 6, -6
1614

Minimum number N which gives remainders of 4, 6 and 9 when divided successively by 13, 11 and 15.



Can anyone tell me the methodology to solve these type of questions???

1615
Minimum number N which gives remainders of 4, 6 and 9 when divided successively by 13, 11 and 15.



Can anyone tell me the methodology to solve these type of questions???

What's d ans ??? 1369??
1616
Minimum number N which gives remainders of 4, 6 and 9 when divided successively by 13, 11 and 15.



Can anyone tell me the methodology to solve these type of questions???



1369 should be the answer.

The equation becomes

13(11(15x+9)+6)+4

Put x=0 so as to find the lowest number.
1617
What's d ans ??? 1369??


yes ans is 1369 .... but how to found if 'successively' is not used. And Qn is like this, find a number 'N' when divided by 7, 17& 19 gives remainder 3,4 & 13. Except hit and trial method .
1618
on the edge Says
yes ans is 1369 .... but how to found if 'successively' is not used. And Qn is like this, find a number 'N' when divided by 7, 17& 19 gives remainder 3,4 & 13. Except hit and trial method .


Hi

We use Chinese Remainder Theorem for this type of questions.

We take each pair of number and remainder one by one.

So first we have to find a number when divided by 19 gives a reminder 13.

req number, n = 19K +13.

Now take second pair ie. when divided by 17 gives remainder 4.
for this divide find remainder of n when divided by 17
remainder, r = 2K+13
now r should give a remainder 4 when divided by 17,
so 2k+13 can 4,21,28,......

take the first value of k which gives integral value.
so k = 4.

therefore, n = 89

now the our required number will be lcm(17,19)*integral value (say k) + 89

req number = 323K + 89

now again find remainder when divided by 7 = (323K + 89)%7 = K+5

this can be equal to 3,10, 17, 24,....

so smallest value of k is 5.

so our required number is 1704.

Hope I did not make any mistakes.

Thanks
Varun.
1619

Are itna sannata kyun hai bhai??:D
Qn for practice: Find the smallest number N! which has 30 zeros and also divisible by 7.
And this one from test series (8888... 100times ) divided by 625 what is the remainder, i got ans correct but any fast method to solve it??

1620
Are itna sannata kyun hai bhai??:D
Qn for practice: Find the smallest number N! which has 30 zeros and also divisible by 7.
And this one from test series (8888... 100times ) divided by 625 what is the remainder, i got ans correct but any fast method to solve it??


THE ANSWER TO 2ND PART should be 138...i just did direct division and it took around 20 seconds...

btw what method you applied?
1621
THE ANSWER TO 2ND PART should be 138...i just did direct division and it took around 20 seconds...

btw what method you applied?


Ya it is the correct ans... Actually i am doing by making (888...100 times) to 8/9*(10^101 -1) and dividing by 625 and applying euler's theorem but here 10 is not coprime to 625, so it is getting lengthy:banghead:. But i was unable to understand direct division method what was the logic ?

And the ans to first part is 91.
1622
Ya it is the correct ans... Actually i am doing by making (888...100 times) to 8/9*(10^101 -1) and dividing by 625 and applying euler's theorem but here 10 is not coprime to 625, so it is getting lengthy:banghead:. But i was unable to understand direct division method what was the logic ?

And the ans to first part is 91.


bhai direct divide kar...after 2 steps 138 aana shuru ho jayega...
1623

Where can i get wilson's theorem, Euler's theorem, Chinese remainder theorem and others methods in solving number system problems ?
Does Arun Sharma or Quantam CAT have it? Pl. help.

1624
Where can i get wilson's theorem, Euler's theorem, Chinese remainder theorem and others methods in solving number system problems ?
Does Arun Sharma or Quantam CAT have it? Pl. help.


First of all you must see the various threads in PAGALGUY itself definitely there would be threads on number system.
You could also visit TOTALGADHA it contains very good tutorial on number system .Also you could download their e book on number system it is available over the net.
1625

Qn for practice: Find the smallest number N! which has 30 zeros and also divisible by 7.

120!-124! Has 28 Zeros
125!-129! - has 31 Zeros (125 will have 5^3 and hence 3 Zeros )
So there wont be any factorial which will have 30 zeros in the end??


1626

Reminder when 122333444455555....... 100 terms divided by 7 ??

1627
Qn for practice: Find the smallest number N! which has 30 zeros and also divisible by 7.

120!-124! Has 28 Zeros
125!-129! - has 31 Zeros (125 will have 5^3 and hence 3 Zeros )
So there wont be any factorial which will have 30 zeros in the end??




Ans. I calculated by hit and trial method is 91 which is divisible by 7 and 91! have 30 zeros as: 1. No. of 5s(18+3) and no. of zeros(9) so total 30zeros. Hope i am not wrong.
1628
Qn for practice: Find the smallest number N! which has 30 zeros and also divisible by 7.

120!-124! Has 28 Zeros
125!-129! - has 31 Zeros (125 will have 5^3 and hence 3 Zeros )
So there wont be any factorial which will have 30 zeros in the end??




yes you are right.There is no N! which has 30 zeros.
1629
on the edge Says
Ans. I calculated by hit and trial method is 91 which is divisible by 7 and 91! have 30 zeros as: 1. No. of 5s(18+3) and no. of zeros(9) so total 30zeros. Hope i am not wrong.


How come 91! HAS 30 ZEROS??????????????.YOU ARE TOTALLY WRONG.
1630

Find the number of non - negative integral solutions to the system of equations x+y+z+u+t=20 and x+y+z=5.
(a)228 (b)336 (c)448 (d)528


actually i have some problem in this type of questions...so can u guys plz solve dis?

1631
on the edge Says
Ans. I calculated by hit and trial method is 91 which is divisible by 7 and 91! have 30 zeros as: 1. No. of 5s(18+3) and no. of zeros(9) so total 30zeros. Hope i am not wrong.


brother in these types of questions you dont need to add...you have to take common...suppose there are 10 5's and 12 2's....so number of zeroes will be 10...
1632
Find the number of non - negative integral solutions to the system of equations x+y+z+u+t=20 and x+y+z=5.
(a)228 (b)336 (c)448 (d)528


actually i have some problem in this type of questions...so can u guys plz solve dis?


Here is another question

Find the number of nonnegative
integral solutions to the following system of
equations
x + y + z + w + r=16
x + y + z=6
(1) 142 (2) 500 (3) 420 (4) 308

Solution
The given two equations can be reduced to x + y + z = 6 (1)
w + r = 10 (2)
Number of nonnegative
integral solutions of (1) are = (6+3-1)C(3-1) = 8C2------->28

Number of nonnegative
integral solutions of (2) are = (10+2-1)C(2-1) =11C1-------->11

28 solutions of equations (1) and there are (11) solution of equation (2) therefore total number of solutions = 28 11 = 308. Ans.(4)

Although i have got the solution of this problem but unable to understand it.