Official Quant thread for CAT 2013

MBA CAT 2024
7001
@krum @grkkrg ..bro plz explain in detail how
y=x^2 is many to one function, and
y=rootx is one to many..??
7002
@Shray14 said:
@krum@grkkrg ..bro plz explain in detail howy=x^2 is many to one function, andy=rootx is one to many..??
y = x^2
x = -2 => y = 4
x = 2 => y = 4
Many to one

y = root(x)
x = 4
y = 2
y = -2
One to many :)

7003
@grkkrg said:
y = x^2x = -2 => y = 4x = 2 => y = 4Many to oney = root(x)x = 4y = 2y = -2One to many
and then if simplify y=root(x) to y^2=x then it will be many to one? in terms of y??
7004
@Shray14 said:
and then if simplify y=root(x) to y^2=x then it will be many to one? in terms of y??
In technical terms:
y here is a dependent variable
x is an independent variable

So x determines what the value of y is. Not the other way.

In the first case
y = root(x) means that y derives its value from x (whatever that may be)
i.e. one to many mapping from x to y

But in the second case, we have two possibilities:
1) x is dependent and y is independent
In this case x derives its value from y. (this gives many to one mapping from y to x)
2) y is dependent and x is independent
In this case we have to re arrange it to y = root(x)
(this gives one to many mapping from x to y)

So if you consider y to be the dependent variable, then both y = root(x) and y^2 = x are one to many mappings.

Hope it makes sense. :)
7005
@grkkrg said:

Finally got it bro...thanks
7006
the probability that in a household LPG will last 60 days or more is 0.8 and that it will last at most 90 days is 0.6. The probability that the LPG will last 60 to 90days is.. Aaj ka IIFT paper,koi solve karo bhai. CL and TF giving different keys for this.
7007
@aj23 said:
the probability that in a household LPG will last 60 days or more is 0.8 and that it will last at most 90 days is 0.6. The probability that the LPG will last 60 to 90days is.. Aaj ka IIFT paper,koi solve karo bhai. CL and TF giving different keys for this.
0.4 ?

Probability that the LPG will last for less than 60 days = 0.2
Probability that the LPG will last for more than 90 days = 0.4

Required probablity = 1 - 0.2 - 0.4 = 0.4
7008
@ajeetaryans said:
Ashish is studying late into the night and id hungry . He opens his mother's snack cupboard without switching on the lights . Knowing that his mother has kept 10 packets of chips and biscuits in the cupboards . He pulls out 3 packets from the cupboards and all of them turn out to be chips . what is the probability that the snack cupboard contains 1 packets of biscuits and 9 packets of chips ?
10 chips and 0 biscuit
9 chips and 1 biscuit
8 chips and 2 biscuit
7 chips and 3 biscuit
6 chips and 4 biscuit
5 chips and 5 biscuit
4 chips and 6 biscuit
3 chips and 7 biscuit

9C3/(10C3+9C3+8C3+7C3+6C3+5C3+4C3+3C3)
147/(273+120)
147/(393)
7009

@aj23 said:
the probability that in a household LPG will last 60 days or more is 0.8 and that it will last at most 90 days is 0.6. The probability that the LPG will last 60 to 90days is.. Aaj ka IIFT paper,koi solve karo bhai. CL and TF giving different keys for this.
Prob that cylinder will last for 60 days or more = 0.8
Prob that cylinder will last less than 60 days = 0.2
Prob that cylinder will last at most 90 days = 0.6

Hence, we get the distribution

0-60--->0.2
60-90--->0.4
90+----->0.2
7010
A thief steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap.He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of mixture again,and fills it with water. When the liquid soap is checked at a station it is found that the ratio of liquid soap now left in the container to that of the water in it is 36:13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody during the entire period?
a 7 gal b 14 gal c 21 gal d 28 gal
please tell
7011
@grkkrg said:
The owner of Cheap and Best, a kirana shop, bought some apples at 4 per rupee and an equal number at 5 per rupee. He then sold the entire quantity at 9 for 2 rupees. What is his percentage profit or loss?a) 1.23% lossb) 6.66% lossc) 3.33% profitd) No profit no lossďťże) None of these
(4x/9)-(x/4+x/5)/(x/4+x/5)

4x/9-(9x/20)/(9x/20)
-x/180*20/9x
1.23% loss

7012
@ajeetaryans said:
the answer sheets of 5 engineering students can be checked by any one of 9 professors . what is the probability that all the 5 answer sheets are checked by exactly 2 professors ?
2^5*9C2/(9^5)
7013
@IIM-A2013 said:
A thief steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap.He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of mixture again,and fills it with water. When the liquid soap is checked at a station it is found that the ratio of liquid soap now left in the container to that of the water in it is 36:13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody during the entire period?a 7 gal b 14 gal c 21 gal d 28 galplease tell
28??
7014
@IIM-A2013 said:
A thief steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap.He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of mixture again,and fills it with water. When the liquid soap is checked at a station it is found that the ratio of liquid soap now left in the container to that of the water in it is 36:13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody during the entire period?a 7 gal b 14 gal c 21 gal d 28 galplease tell
( x*(x-4)^2/x^2)/(x- x*(x-4)^2/x^2)=36/13

==>[(x-4)^2/x]/[(x^2-(x-4)^2)/x]=36/13
==>(x-4)^2/(2x-4)*4=36/13

x=28
7015
@rubikmath said:
@scrabbler@scrabblerused the same method . but y are u counting backwards from B ?
Forward is much harder - more ramifications possible. Backward, if you take one step at a time you can cover all possible cases with no chance of missing any. There is some formal theory behind this I believe (the stagecoach problem I had mentioned), but I cannot recollect it...

Try it for a standard grid, say a 5x3 rectangular one with no diagonal routes.... We know the answer will be 8C3 there, but it is a good way to practice this approach.

regards
scrabbler
7016
@sonamaries7 said:
2- [ rt(640522209)/rt(3600840049)]? 0.66630390.6660290.666009none of the above @scrabbler ,@rubikmath@ayushnasa : pencil chor, yeh solve kar

@sonamaries7 said:
@ayushnasa ,@rubikmath : typo ...2- [ rt(6407522209)/rt(3600840049)]..(7 key me prob hai meri ) is the qs...ab bolo

Would go with (b). Got approx 0.66605...

regards
scrabbler
7017

Please suggest a quick way to find the least value among 420/88, 433/92 and 456/97.

7018
@anytomdickandhary said:
Sum[ (r+c-d)!/ {(r-d)!(c-d)!d!} ] where 0

Nicely done :)
@anytomdickandhary said:
@scrabbler ...hello! its been long time.

Indeed...have been most irregular 😃 and I will be on here only sporadically till December-end...:( hopefully from Jan will be regular again!

regards
scrabbler
7019
@ajeetaryans said:
6/55 12/73 14/557/50these are option pls chill sir,jain4444 solve my problem
Am getting 14/55....slightly long method....looking for a shorter appraoch.

regards
scrabbler
7020
@gnehagarg said:
2^5*9C2/(9^5)
(2^5-2) karna padega....the 2^5 includes two cases where "only 1 prof corrects", questions asks for "exactly two profs"...

regards
scrabbler