Official Quant thread for CAT 2013

@19rsb said:
Due to the recent global financial crisis, many companies in the field of IT Services offer jobs on contractual basis with a clause of fine for the leave taken by the employee. An ITS company employs an engineer for 290 days on a salary of Rs. 500 for eight hours work per day, and the engineer has to pay a fine of Rs.50 for each hour of his absence. The engineer may compensate his one-day absence by working 4 hours extra for two days. If the engineer receives Rs.1,32,400 at the end of the contract, how many hours was he absent from his job?(1) 110 hours(2) 112 hours(3) 114 hours(4) 118 hoursOA is 112hrs......share ur approach.........
he shud be paid Rs. 145000
Instead he is paid Rs.132400
12600 less
Amount he looses if he is absent on 1 day = 500+50*8=900
therefore he was absent on= 12600/900= 14days
total= 14*8=112 hrs.
@19rsb said:
Due to the recent global financial crisis, many companies in the field of IT Services offer jobs on contractual basis with a clause of fine for the leave taken by the employee. An ITS company employs an engineer for 290 days on a salary of Rs. 500 for eight hours work per day, and the engineer has to pay a fine of Rs.50 for each hour of his absence. The engineer may compensate his one-day absence by working 4 hours extra for two days. If the engineer receives Rs.1,32,400 at the end of the contract, how many hours was he absent from his job?(1) 110 hours(2) 112 hours(3) 114 hours(4) 118 hoursOA is 112hrs......share ur approach.........
Options se bhi ho jayega
difference 12600 ka hai
so [12600-(50*option)]mod4 = 0. ;)
50[252-option]mod4=0
[252-option]mod4 =0.
only 112 satisfy. ;)
@Torque024 said:
Options se bhi ho jayega difference 12600 ka hai so [12600-(50*option)]mod4 = 0. 50[252-option]mod4=0 [252-option]mod4 =0. only 112 satisfy.
yes it is better if u calculate fast.

Suppose there is sphere with diameter atleast 6 inches.Through this sphere drill a hole along diameter..The part of sphere lost in this process of drilling the hole looks like two caps joined to cylinder,where cylindrical part has length 6 inches.It turns out that volume of remaining portion does not depend upon diameter of spehere.Using this fact calculate volume of remaining part.

@gnehagarg said:
Suppose there is sphere with diameter atleast 6 inches.Through this sphere drill a hole along diameter..The part of sphere lost in this process of drilling the hole looks like two caps joined to cylinder,where cylindrical part has length 6 inches.It turns out that volume of remaining portion does not depend upon diameter of spehere.Using this fact calculate volume of remaining part.
27pi hai kya?
kisi se ho rha?

@kinkong said:
10% of salty sea water contained in a flask was poured out in a beaker.After this a part of water contained in beaker was vaporized by heating and due to this,the percentage of salt in beaker increased "M" times.If it is known that after the content of beaker was poured into the flask,the percentage of salt in the flask increased by x%.Find the original quantityof sea water in the flask. plz guys help karo...arun sharma ka hai ye ..plz.....

let total quantity of sea water in the flask be T
amount of salt in it be
S

after 10% is transferred, amount of water and salt left in flask =>

90/100(T-S) and 90/100(S)

amount of water and salt in beaker =>

10/100(T-S) and 10/100(S)

lets say z amount if water is now evaporated =>

S/T*M=S/10/(T/10-z)
=>S/T*M = S/(T-10z)
=>(T-10z)/T=1/M
=>1-10z/T=1/M
=>z=(1-1/M)T/10

so amount of water left in beaker = 10/100(T-S) - (1-1/M)T/10

now this is transferred into the flask

amount of water in flask = T-S - (1-1/M)T/10
amount of salt = S

given

(100+x)/100*S/T=S/[T-S - (1-1/M)T/10 + S]

=>(100+x)/100*1/T=1/[T- (1-1/M)T/10]
=>(1+x/100)*1/T=1/T*10M/(9M+1)
=>x/100=(10M-9M-1)/(9M+1)
=>x/100=(M-1)/(9M+1)

so x=100*(M-1)/(9M+1)

now what

@kinkong what is the OA anyway?
@krum said:
let total quantity of sea water in the flask be Tamount of salt in it be Safter 10% is transferred, amount of water and salt left in flask =>90/100(T-S) and 90/100(S)amount of water and salt in beaker =>10/100(T-S) and 10/100(S)lets say z amount if water is now evaporated =>S/T*M=S/10/(T/10-z)=>S/T*M = S/(T-10z)=>(T-10z)/T=1/M=>1-10z/T=1/M=>z=(1-1/M)T/10so amount of water left in beaker = 10/100(T-S) - (1-1/M)T/10now this is transferred into the flaskamount of water in flask = T-S - (1-1/M)T/10amount of salt = Sgiven(100+x)/100*S/T=S/[T-S - (1-1/M)T/10 + S]=>(100+x)/100*1/T=1/[T- (1-1/M)T/10]=>(1+x/100)*1/T=1/T*10M/(9M+1)=>x/100=(10M-9M-1)/(9M+1)=>x/100=(M-1)/(9M+1)so x=100*(M-1)/(9M+1)now what @kinkong what is the OA anyway?
Checked Arun Sharma..OA is ((9M+1)x%)/M-1
@Torque024 said:
27pi hai kya? kisi se ho rha?
approach
@gnehagarg said:
Suppose there is sphere with diameter atleast 6 inches.Through this sphere drill a hole along diameter..The part of sphere lost in this process of drilling the hole looks like two caps joined to cylinder,where cylindrical part has length 6 inches.It turns out that volume of remaining portion does not depend upon diameter of spehere.Using this fact calculate volume of remaining part.
is the answer 9*pi ?
@gautam22 said:
sir isme to integration lag rahi hai....
sir nhi madam h :P
@gautam22 said:
ok.....bina integration ke to nahi hoga ye......haina?
i guess simple geometry should suffice.....does not depend on "d" matlab jitne bhi terms me "d" h maybe v can ignore them....dats wat i think...i am waiting for neha to reply with the correct answer...the question seems good :)
@gnehagarg said:
Suppose there is sphere with diameter atleast 6 inches.Through this sphere drill a hole along diameter..The part of sphere lost in this process of drilling the hole looks like two caps joined to cylinder,where cylindrical part has length 6 inches.It turns out that volume of remaining portion does not depend upon diameter of spehere.Using this fact calculate volume of remaining part.
36pi?
Data sufficiency

In the game Cako, a player is awarded one tick for every third Alb captured, and one click for every fourth Berk captured. The total score is equal to the product of clicks and ticks. If a player has a score of 77, how many Albs did he capture?


(1) The difference between Albs captured and Berks captured is 7.


(2) The number of Albs captured is divisible by 4.


I think 1 se ho jayega but 2 se nai. Anyone confirm this.
@gautam22 said:
sir jo small caps hain unka radius fixed nahi hai sir change kar raha hai......bina integration ke kaise kar diya
bro i think ki sphere fixed h...n length of cylinder bhi fixed h=6. To agar hole ke dia ko d' le liya to wahi hoga caps ka.....if my calc is ryt then d' wala term to cancel hi ho jata h...except woh term jisme d n d' dono sath me ate h...
@Torque024 said:
Data sufficiencyIn the game Cako, a player is awarded one tick for every third Alb captured, and one click for every fourth Berk captured. The total score is equal to the product of clicks and ticks. If a player has a score of 77, how many Albs did he capture?(1) The difference between Albs captured and Berks captured is 7.(2) The number of Albs captured is divisible by 4.I think 1 se ho jayega but 2 se nai. Anyone confirm this.
Agreed
77, 1 albs both satisfy the case , hence 2 is incomplete
for 77 => 231,232,233 and 1 => 3,4,5 hence 2 se nahi hona chahiye
@Torque024 said:
Data sufficiencyIn the game Cako, a player is awarded one tick for every third Alb captured, and one click for every fourth Berk captured. The total score is equal to the product of clicks and ticks. If a player has a score of 77, how many Albs did he capture?(1) The difference between Albs captured and Berks captured is 7.(2) The number of Albs captured is divisible by 4.I think 1 se ho jayega but 2 se nai. Anyone confirm this.
help me with this...
score=77=no. of ticks *clicks
now 77 = 1*77 or 7*11 or 11*7 or 77*1
dono conditions se nhi ho raha yeh to fit :0
wats the answer?
@gautam22 said:
sir mera bhi yahi aa raha hai par maine integration lagayi hai.......aapne kisi aur tareeke se kara hai kya?
bhai maine cap ke volume ka formula yahan se liya hai
mathforum.org/dr.math/faq/formulas/faq.sphere.html


@gnehagarg what is the OA?

@techsurge @surajmenonv
Mai aise kr rha
t*c = 77
(t,c)=(11,7),(7,11),(77,1),(1,77)
alb=3n,3n+1,3n+2
berk=4m,4m+1,4m+2,4m+3
for 11,7
alb= 33,34,35
berk= 28,29,30,31
35-28=7 will satisfy the condition
So alb=35, berk=28
Or koi combination se diff 7 nai aa rha tha
So 1, sirf 2 se possible nai
@gautam22 said:
@krum sir vo jo aapne 7 nikala tha vo aa to 7 hi raha hai exact par ek baat hai ki jab hum side 7 consider karenge tab vo equilateral triangle ban jayega.....par angles honge(63,58.5,58.5).......thoda isko dekho
han yaar, par 3 angles the , teeno approx 7 de rahe the, par teeno same nai the, lagta hai side is to angle wala ratio nai lagega wahan
@Torque024 said:
@techsurge@surajmenonvMai aise kr rha t*c = 77(t,c)=(11,7),(7,11),(77,1),(1,77)alb=3n,3n+1,3n+2berk=4m,4m+1,4m+2,4m+3for 11,7alb= 33,34,35berk= 28,29,30,3135-28=7 will satisfy the condition So alb=35, berk=28Or koi combination se diff 7 nai aa rha tha So 1, sirf 2 se possible nai
ohhh yup...i totally missed it conceptually.....no of albs sirf no of ticks*3 nhi honge but it can be 3k, 3k+1, 3k+2..
\m/