Official Quant thread for CAT 2013

@dilon1211 said:
@saurav205Suppose Nimai starts from point A and Nitai from point B. After travelling 400 mts Nimai is back at A but after travelling 700 mts Nitai is not at B or his initial position, but at A. According to me, they can never simultaneously reach their initial positions.Could you please point out where am I missing it ?
bhai they can reach their initial positions simultaneously after travelling 800 and 1400 m respectively, i quoted saurav bro earlier,check my post
@Asfakul said:
how to get starting point and end point ?/
all 3 digit nos in base 7 has to atleast have 49

100 of bas 7 equals 49
and
1000 equals 343
so from 49 to 342
@mohitjain said:
its the smallest!!my largest shayad 38..nt sure
Be Sure OA.. approach if any?
@Asfakul said:
how to get starting point and end point ?/
their is a bone of contention here

look what does question require
how many 3 digit numbers are there in base 7 which when converted to base 10 gives perfect square??
or how many 3 digit numbers in base 7 are perfect square

for 1 it will be 12 but for second it wont be 12 because number with unit digit 9 is never possible in base 7 so it will be 12-3=9( subtracting cases for 7,3,17

@albiesriram said:
and
sri ram bro oa for this 1????
for the first case is it 400
-997........998 with common difference 5 ?????
@abhishek.2011 said:
sri ram bro oa for this 1????for the first case is it 400-997........998 with common difference 5 ?????
NO 401. check again..

Now see .. When person A has travelled 7 one way journeys , person B would have travelled 4 one way journeys . At this moment , they would be at the same point . Till this point, they would have met 7 times as faster person would have crossed slower person 7 times.


Now when they start from the same point , just try and imagine : THIS WOULD BE A REWIND MOVIE OF WHAT HAD EARLIER TAKEN PLACE . They would start together and end at their respective positions after 14 and 8 rounds respectively. So all meeting points would repeat .

Hence there are 7 distinct meeting points :)
Hope all of you understood the logic :)

Team BV--Pratik Gauri

Find the number of non negative integral solutions of x1+x2+x3+4x4=20.?

@albiesriram said:
Be Sure OA.. approach if any?
deres no aaproach as such ..had 2 check d nos..
d composite odd nos less dan 38 are 9,15,21,25,27,33,35..nt gettin 38 by adding any of those!!
aftr dat we can get each even no. as sum of 2 composite
@albiesriram said:
NO 401. check again..
bhai the function will have repeated roots after an interval of 5 integers????? right ?
that was the only concept there? rest is just algebra 😃 i am not good today thats why commiting stupid errors :)
@pavimai said:
Find the number of non negative integral solutions of x1+x2+x3+4x4=20.?
22c2+ 18c2 + 14c2 + 10c2 + 6c2 + 2c2

536


@pavimai said:
Find the number of non negative integral solutions of x1+x2+x3+4x4=20.?
x1 + x2 + x3 = 20 - 4x4 and x4 = t = 0,1,2,3,4,5
number of required solutions = summation( 22-4t C2 )
@bodhi_vriksha Hi.


523_ _ _. How many such 6-digit nos. are divisible by 7, 8 and 9 together.

@abhishek.2011 said:
bhai the function will have repeated roots after an interval of 5 integers????? right ?that was the only concept there? rest is just algebra i am not good today thats why commiting stupid errors
@abhishek.2011 said:
sri ram bro oa for this 1????for the first case is it 400-997........998 with common difference 5 ?????
Well take a look at this

f(2+x)= f(2-x)
f(7+x)=f(7-x)

put 2+x = t

therefore,
f(t) = f(4-t);
f(t)=f(14-t)=f(14-(4-t)) = > f(t)=f(t+10)

t= 0 is a root, given.

So Roots must be 0 + or -10 upto the interval -1000 to 1000,= 201 roots

also ( 4- t ) is there . hence take all those roots which are similar of the type, (4 mod 10). = 200 roots.

in total 401 roots.

@pavimai said:
Find the number of non negative integral solutions of x1+x2+x3+4x4=20.?
22C2+ 18C2 + 14C2 +10C2 + 6C2 +1
@imrover said:
@bodhi_vriksha Hi.523_ _ _. How many such 6-digit nos. are divisible by 7, 8 and 9 together.
1
@mohitjain said:
1
sir, could you please elaborate on your approach?
@albiesriram said:
22C2+ 18C2 + 14C2 +10C2 + 6C2 +1
pls explain this one..
@albiesriram said:
384
:banghead: calc error