Official Quant thread for CAT 2013

MBA CAT 2024
6061
@techsurge said:
yup OA b)@rkshtsurana 's approach is rightalthough options can eliminate the sameQ) Bhanu and Ria start running simultaeously on a linear track with same speeds and cover first 280 m in t seconds. After covering every 280 m , Bhanu decreases its speed by fraction of half and Ria decreases her speed by fraction of 2/3 . bhanu takes 1.5 t minutes less than the time taken by Ria to cover the entire distance. Find the distance which in metres is an integral multiple of 280A) 2800B) 1400C) 1680D) 2240

let their initial time taken be = x

bhanu will take double of time to cover next 280 from previous one and ria will take 3 times of time to cover next 280 from previous one and so on

now we need to make a difference of 90 minutes in between them

let x = 1

bhanu = 1 + 2 + 4 + 8 + 16 = 31
ria = 1 + 3 + 9 + 27 + 81 = 121

we have a difference of 90 after 5

so , answer should be 280*5 = 1400
6062
@techsurge said:
yup OA b)@rkshtsurana 's approach is rightalthough options can eliminate the sameQ) Bhanu and Ria start running simultaeously on a linear track with same speeds and cover first 280 m in t seconds. After covering every 280 m , Bhanu decreases its speed by fraction of half and Ria decreases her speed by fraction of 2/3 . bhanu takes 1.5 t minutes less than the time taken by Ria to cover the entire distance. Find the distance which in metres is an integral multiple of 280A) 2800B) 1400C) 1680D) 2240
1400???
6063
@krum said:
how many 3 digit natural numbers have less than 5 prime factors?
900
smallest number with 5 primes =2*3*5*7*11 > 1000
could be wrong
6064
How many numbers between 1 and 1000 are such that n^2+3n+5 is divisible by 121?
6065

Find number of real solutions of

log_base9_(2x^2+3x+1) = log_base3_(x-3)

6066
@techsurge said:
Find number of real solutions of log_base9_(2x^2+3x+1) = log_base3_(x-3)
only 1 sol
6067
@techsurge said:
Find number of real solutions of log_base9_(2x^2+3x+1) = log_base3_(x-3)
1 ?
6068

@rachit_28 said:
1 ?
@FoolNFinal said:
only 1 sol
6069

@techsurge said:
Find number of real solutions of log_base9_(2x^2+3x+1) = log_base3_(x-3)
2x^2 + 3x + 1 = x^2 - 6x + 9
x^2 + 9x - 8 = 0

it ll have one + ve root and one -ve root
both roots will be discarded because x - 3

so 0 ?

6070
@krum said:how many 3 digit natural numbers have less than 5 prime factors?
no such no. exists
6071
@viewpt said:
@krum said:how many 3 digit natural numbers have less than 5 prime factors?so such no exists
kya baat kr rhe ho..jo bhi three digit primes hnge..unka toh 1 he prime factor hga..
6072

@techsurge said:
Find number of real solutions of log_base9_(2x^2+3x+1) = log_base3_(x-3)
0?
6073
@techsurge said:
Find number of real solutions of log_base9_(2x^2+3x+1) = log_base3_(x-3)
Only 1; ~.8
6074
@krum said:
2x^2+3x+1=(x-3)^3=>2x^2+3x+1=x^3-27-9x^2+27x=>x^3-11x^2-24x+28=01 sol?
bhai cube kaha se aagya :P
6075
@viewpt said:
@krum said:how many 3 digit natural numbers have less than 5 prime factors?so such no exists
all 3 digit numbers i.e 900
6076
@krum said:
2x^2+3x+1=(x-3)^3
=>2x^2+3x+1=x^3-27-9x^2+27x
=>x^3-11x^2-24x+28=0

1 sol?

6077

@rkshtsurana said:
kya baat kr rhe ho..jo bhi three digit primes hnge..unka toh 1 he prime factor hga..
prime factors.. not coprime i guess..
6078
@Torque024 said:
Only 1; ~.8
6079
@krum said:
all 3 digit numbers i.e 900
question samajh nai aya..fir se btao.
6080
@krum said:
2x^2+3x+1=(x-3)^3=>2x^2+3x+1=x^3-27-9x^2+27x=>x^3-11x^2-24x+28=01 sol?
wo square hai cube ki jagah..
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Q: A grasshoper at a meter distance froma wall. with everey jump te covers half of the remaining distance. find the no. of jumps required to reach to the wall?