From Number System:

Ques. -> Suppose one wishes to find distinct positive integers x,y such that (x+y)/xy is also a positive integer. Identify the correct alternative.

Options->

1.Not possible
2.Possible & (x,y) pair is unique
3.Possible and finite no of pairs
4.Possible and infinite pairs

What should be the answer?

x+y=xy => y=x/x-1 as consequtive integers are coprime so only one case possible ie when x=2 => y=1,so option 2

If f1(x)=1/1+x and fn(x)=1/1+fn-1(x). then f100(a)=.....

all 8 or less digit numbers formed by using 0 1 2 = 3^8-1

now for 9 digit numbers
9-digit number can start with only 1 => 1*3^8 = 3^8 such numbers

so total numbers less than 2*10^8 = (3^8-1 + 3^8 )/3 = 3^7-1+3^7 (as we need to take integral value)

=> 2*3^7-1 such numbers

Culdip bhai...why are we dividing by three while calculating the total numbers ?

Let's try this:

what's GCD of 701701.....(701 repeated 72 times) and 701701....(701 repeated 114 times)

:)

Gcd (72,114)=2..So 701701.:)

mani0303 Says

111....20 times

yaha pe 100 and 60 ki GCD kyu le rhe hai ??

Find the GCD of (11111.....100 ones , 1111.....60 ones).
Good morning puys.

A pedestrian and a cyclist left nagpur to buti bori at the same time.Having reached buti bori, the cyclist turned back and met the pedestrian an hour after the start.After their meeting,the pedestrian continued his trip to buti bori and the cyclist turned back and also head to buti bori.Having reached buti bori, the cyclist turned back again and met the pedestrian 30 mins after their first meeting.Determine what time it takes the pedestrian to cover distance between nagpur and buti bori.

P S: an arun sharma q but no solution given..
puys please post the approach for this one

If x is a number of five digit which when divided by 8,12,15 and 20 leaves respectively 5,9,12, and 17 as remainders, then find x such that it is the lowest such number.?
a] 10017 b] 10057 c] 10097 d] 10137

Puys, please post the approach also.

Edit : Had added 1 extra 0 in option a

Each one of them leaves remainder of -3..So the no will be of the form 120k-3..10000 leaves a remainder of 60 with 12o...So the least no would be 10000 + 60 -3 = 10057

vinay_sharma Says

editing...............

applying derangement formula...we get 6!(1-1/2!+1/3!-1/4!+1/5!-1/6!)

4 is written 3400 times side by side to give you a big number.i.e 444.....44(3400 times). What is the remainder when 37 divide this number?

A.7 b. 26 c. 33 D.4

4444444.....3400 times mod 37 can be written as 4(111111....3400 times) mod 37...and 111 mod 37=0...So the ans is 4*1..is it correct ?