Official Quant thread for CAT 2013

@viewpt said:
TPQ: A writes all the nos. frm 1 to 1000 on paper in order. Find the 2883rd digit written by him?
76?
@mohitjain said:
thoda explain kijiye..m gettin radius as rt3+1/rt3
Check out the attachment! Samajh ajana chahiye barring my drawing skills :banghead:
@iLoveTorres said:
76?
How is 76 even a digit? 😉

regards
scrabbler

@viewpt said:
TPQ: A writes all the nos. frm 1 to 1000 on paper in order. Find the 2883rd digit written by him?
we know
1 digit no = 9
2 digit numbers = 90 ... digits 2*90 = 180
3 digit numbers = 900....digits 3*900 = 2700
so it ll be a digit of 3 digit number
let us make evything into 3 digit..tthat is add 00 in front of single digit no and 0 in front of 2 digit numbers...so
numbers of 0 add = 2*9 + 1*90 = 108
so ultimately digit we need to find is 2883+ 108 = 2991
now we ll divide 2991 by 3 = 997..so 7 is the last digit...
so 7
@DeAdLy said:
xplain maro..main confusa gaya hun thoda..
1 digit numbers have 9 digits (1-9)
2 digit numbers have 180 digits (10-99 means 90 numbers => 90*2 = 180 digits)
3 digit numbers have 2700 digits (100-999 means 900 numbers => 900*3 = 2700 digits)
total digits till here = 2889
we need 2883rd hence go 7 digits back or simply remove 2889-2883 = 6 digits from last

last few digits wld be -> 996,997,998,999

abb yahan se 7 aa gaya...
@viewpt said:
TPQ: A writes all the nos. frm 1 to 1000 on paper in order. Find the 2883rd digit written by him?
1 digit nos = 9
2 digit = 90*2 = 180
3 digit = 900*3 = 2700
Total = 2889

Hence 2883rd digit = 7 ( 7_998_999)
@mohitjain said:
thoda explain kijiye..m gettin radius as rt3+1/rt3
if u'll connect centres u'll get equilateral tri.

of side 2 . hence altitude= rt3/2(2)= rt3
now from the centre of the bigger circle to the centre of top concentric circle distance is= 2/3(rt(3)= 2/rt3
hence radius of bigger circle= 2/rt3+1= (2+rt3)/rt3
hence the area= pi*[(2+rt3)/rt3]^2
@scrabbler said:
How is 76 even a digit? regardsscrabbler
bhai typo ho gaya.. jus like in morning aapka 1176 ko 49c2 bol diya tha don kno what is happening to my typing skills
@viewpt A writes all the nos. frm 1 to 1000 on paper in order. Find the 2883rd digit written by him?

total no. of 1 digit no.s --> i.e from 1 to 9 =9.
total no. of 2 digit no.s --> [(99-10) + 1]*2= 90
total no. of three digit no. till 899 = 3[(899-100) + 1] =2400
Total = 2400+180+9 = 2589

now. 2883 - 2589 = 98 =>899 +98 = 997 i.e last digit is 7...



@Logrhythm said:
There are three pipes, A, B and C, opening into a tank. Each pipe can be used to fill or empty the tank at the same respective rate. The ratio of the rates of the three pipes at which they either fill or empty the tank is 2 : 3 : 4. Pipes A and B, working together, take 3 hours to fill the tank when both are used as inlet pipes. In the first, second and third hours of operation, the pipes, A, B and C respectively are used as emptying pipes, while the other two pipes are used as filling pipes. What is the fraction of the tank to be filled at the end of the three hours ?
3/5th of the tank gets filled

Approach :
let the rates be 2a,3a,4a
a and b fill the tank in 3 hours.
volume = (2a+3a)3 = 15a
first hour (c is outlet pipe)
volume filled = 5a - 4a= a
2nd hour ( a outlet pipe)
volume filled = 7a-2a =5a
3rd hour (b outlet pipe)
volume filled = 6a - 3a =3a
total volume filled = a+5a+3a = 9a
fraction = 9a/15a = 3/5
OA kya hai??
@scrabbler Really nice one mate
@iLoveTorres said:
bhai typo ho gaya.. jus like in morning aapka 1176 ko 49c2 bol diya tha don kno what is happening to my typing skills
😃 Chalo believe karta hoon is baar....waise mera bhi 7 aaya, post karne gaya aur aapka answer dekha aur 😲 ho gaya :D

regards
scrabbler

for this problem

All possible 6 digit numbers, in each of which the digits occur in non - increasing order (from left to right) are written in increasing order. What is the 500th number in this sequence ?OPTIONS

1) 632100
2) 622110
3) 633110
4) 642100

@saurav205 said:
3/5th of the tank gets filledApproach :let the rates be 2a,3a,4aa and b fill the tank in 3 hours.volume = (2a+3a)3 = 15afirst hour (c is outlet pipe) volume filled = 5a - 4a= a2nd hour ( a outlet pipe)volume filled = 7a-2a =5a3rd hour (b outlet pipe)volume filled = 6a - 3a =3atotal volume filled = a+5a+3a = 9afraction = 9a/15a = 3/5OA kya hai??
bhai left puchchca hai hence 6a/15a= 2/5=40%
@scrabbler said:
Chalo believe karta hoon is baar....waise mera bhi 7 aaya, post karne gaya aur aapka answer dekha aur ho gaya regardsscrabbler
aaapke believing pe hi toh humari knowledge jinda hai :P
@viewpt said:
bhai left puchchca hai hence 6a/15a= 2/5=40%
My bad..

@ravi6389 said:
for this problemAll possible 6 digit numbers, in each of which the digits occur in non - increasing order (from left to right) are written in increasing order. What is the 500th number in this sequence ?OPTIONS1) 632100 2) 622110 3) 633110 4) 642100
OA) 3
Q. (21) ^ 21^21^21^21......(21 times) remainder by 25 ?

P.S - After a long time posting here, Feel so good here..so a question from my side

@ravi6389 said:
for this problemAll possible 6 digit numbers, in each of which the digits occur in non - increasing order (from left to right) are written in increasing order. What is the 500th number in this sequence ?OPTIONS1) 632100 2) 622110 3) 633110 4) 642100
633110??
@viewpt said:
TPQ: A writes all the nos. frm 1 to 1000 on paper in order. Find the 2883rd digit written by him?
7 aayega.
1 to 9 : 9 numbers
10 to 99 : 90*2 =180 digits
100 to 999 = 900 *3 digits
so total comes out as 2889 digits. going back 6 places comes to 997.
hence 7.

OA??