Official Quant thread for CAT 2013

One day each member of Ram €™s family consumed some milk and some water. Though the quantities of milk and water varied for the family members, the total consumption of the two liquids was exactly 7 litres for each family member. If Ram had one-fourth of the total milk consumed and one-sixth of the total water consumed, then what was the ratio of the quantity of milk to that of water consumed by Ram on that day?
(a) 3 : 2 (b) 1 : 1 (c) 2 : 3 (d) Cannot be determined




P.S-Kindly show detailed method
@sumeet1489 said:
2009*2010*2011*2012+1 is a perfect square (wolframalpha se check kiya)so ans. must be 0 par ye pata kaise chalega ki ye perfect square hai
maine to chote se numbers ke liye check kia
2*3*4*5+1=121=11^2
3*4*5*6+1=361=19^2

bas phir upar wale ka naam leke 0

@krum bhai ye vaale question ka bhi kuchh karo

Consider the following equation; x^2 + y^2 + z^2 = (x 창€“ y)(y 창€“ z)(z 창€“ x)Which of the following statement is definitely true?Options:

1) The above equation has no integer solutions for x, y, z.
2) The above equation has finitely many distinct integer solutions for x, y, z.
3) The above equation has 2 distinct integer solutions for x, y, z.
4) The above has infinitely many integer solution for x, y, z.

PS: isme option 1 n 3 to eliminate kar liya maine but finite ya infinite hoga pata nahi chal raha
@krum said:
maine to chote se numbers ke liye check kia2*3*4*5+1=121=11^23*4*5*6+1=361=19^2bas phir upar wale ka naam leke 0
bhai..your methods are simply awesome..actually this is the way to approach the problem..
@gudda1122 said:
One day each member of Ram €™s family consumed some milk and some water. Though the quantities of milk and water varied for the family members, the total consumption of the two liquids was exactly 7 litres for each family member. If Ram had one-fourth of the total milk consumed and one-sixth of the total water consumed, then what was the ratio of the quantity of milk to that of water consumed by Ram on that day?(a) 3 : 2 (b) 1 : 1 (c) 2 : 3 (d) Cannot be determinedP.S-Kindly show detailed method
Answer is 1:1 I guess..and as far as I remember yeh CL ke kisi ek MOCK me aaya tha...
@staaalinnn said:
Answer is 1:1 I guess..and as far as I remember yeh CL ke kisi ek MOCK me aaya tha...
answer is correct bt method ......:(
@gudda1122 said:
One day each member of Ram €™s family consumed some milk and some water. Though the quantities of milk and water varied for the family members, the total consumption of the two liquids was exactly 7 litres for each family member. If Ram had one-fourth of the total milk consumed and one-sixth of the total water consumed, then what was the ratio of the quantity of milk to that of water consumed by Ram on that day?(a) 3 : 2 (b) 1 : 1 (c) 2 : 3 (d) Cannot be determinedP.S-Kindly show detailed method
Edit: By solving you will see that the equations satisfy when there are 5 members in the family.. Take 5 members then..form equations..you will get the answer easily.. Take the milk consumptions as a,b,c,d,e and water consumption as 7-a, 7-b, 7-c...and so on.. It will come out to be 1:1
A cylindrical overhead tank is filled by two pumps P1 and P2.P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours.Their is a pipe P3 which can empty the tank in 8 hours.Both the pumps are opened simultaneously.The Supervisor of the tank before going out on a work,sets a timer to open P3 when the tank is half filled so that tank is exactly filled up by the time he is back.Due to technical fault P3 opens when the tank is one third filled.If the supervisor comes back as per the plan what percent of the tank is still empty ???

25,12,10,not
@gudda1122 said:
answer is correct bt method ......
Let there be y persons in Ram €™s family and the total amount of milk consumed by the family be x.
As per the given information,
x/4 + (7y-x)/6 = 7
=> x + 14y = 84
Now y is an integer and 0 => 0 on solving this you'll get
=> 4 => y = 5 and x = 14
Hence, the ratio = 3.5 : 3.5 = 1 : 1
@sumeet1489 said:
@krum bhai ye vaale question ka bhi kuchh karoConsider the following equation; x^2 + y^2 + z^2 = (x – y)(y – z)(z – x)Which of the following statement is definitely true?Options:1) The above equation has no integer solutions for x, y, z.2) The above equation has finitely many distinct integer solutions for x, y, z.3) The above equation has 2 distinct integer solutions for x, y, z.4) The above has infinitely many integer solution for x, y, z.PS: isme option 1 n 3 to eliminate kar liya maine but finite ya infinite hoga pata nahi chal raha
finit soln acc to wolfram:

http://www.wolframalpha.com/input/?i=x%5E2%20%2B%20y%5E2%20%2B%20z%5E2%20%3D%20(x%20%E2%80%93%20y)(y%20%E2%80%93%20z)(z%20%E2%80%93%20x)&t;=crmtb01&f;=rc
@staaalinnn said:
Let there be y persons in Ram €™s family and the total amount of milk consumed by the family be x.As per the given information,x/4 + (7y-x)/6 = 7=> x + 14y = 84Now y is an integer and 0 => 0 => 4 => y = 5 and x = 14Hence, the ratio = 3.5 : 3.5 = 1 : 1
buddy i also have this method in cl solution but point is rather then taking no. of people why can't we take say Y liters of total water avail then equation would be like

x/4+y/6=7
but i am not getting answer from this if possible kindly explain me rationale behind taking n people

This is an IIFT question. I was unable to get solution without a calculator. hoping you guys can help

What is the value of

2 - sqrt (6407522209/3600840049)

options are

A 0.666039

B 0.666029

C 0.666009

D None of these

the solution just posted the value :P

the answer is A

So do share your approach

@ScareCrow28
@gudda1122
@staaalinnn
@sumeet1489
@krum ek baar nazar maar lo :mg:
@gudda1122 said:
One day each member of Ram €™s family consumed some milk and some water. Though the quantities of milk and water varied for the family members, the total consumption of the two liquids was exactly 7 litres for each family member. If Ram had one-fourth of the total milk consumed and one-sixth of the total water consumed, then what was the ratio of the quantity of milk to that of water consumed by Ram on that day?(a) 3 : 2 (b) 1 : 1 (c) 2 : 3 (d) Cannot be determinedP.S-Kindly show detailed method
let total milk - M
total water - W

=>M+W=7k

given that
M/4+W/6=7
=>3M+2W=84
=>M=(84-2W)/3

after little work, w=21 =>M=14

=>M/4=3.5 and W/6=3.5

so 1/1
@techsurge said:
This is an IIFT question. I was unable to get solution without a calculator. hoping you guys can helpWhat is the value of 2 - sqrt (640752209/3600840049)options are A 0.666039B 0.666029C 0.666009D None of thesethe solution just posted the value the answer is ASo do share your approach@ScareCrow28@gudda1122@staaalinnn@sumeet1489@krum ek baar nazar maar lo
buddy i think this question can be solved by using appox

like 640752209 can be written as 6400000 and similarly for 3600000
now when you will solve it you will get b
2-4/3=2/3 which is .666666.... now mark the answer which is closest to this value
not sure about this method :(
@techsurge said:
This is an IIFT question. I was unable to get solution without a calculator. hoping you guys can helpWhat is the value of 2 - sqrt (6407522209/3600840049)options are A 0.666039B 0.666029C 0.666009D None of thesethe solution just posted the value the answer is ASo do share your approach@ScareCrow28@gudda1122@staaalinnn@sumeet1489@krum ek baar nazar maar lo
Handsup! 😛 Exact nikalna time waste karna hoga..obviously calculate to ho he jaega but will consume other questions time also.. Atleast i feel that :P
@gudda1122 said:
One day each member of Ram €™s family consumed some milk and some water. Though the quantities of milk and water varied for the family members, the total consumption of the two liquids was exactly 7 litres for each family member. If Ram had one-fourth of the total milk consumed and one-sixth of the total water consumed, then what was the ratio of the quantity of milk to that of water consumed by Ram on that day?(a) 3 : 2 (b) 1 : 1 (c) 2 : 3 (d) Cannot be determinedP.S-Kindly show detailed method
let the total quantity of milk consumed be "x" and total number of people in his family be "n"
so then total water consumed =7n-x
according to the condition
x/4 +(7n-x)/6 =7
3x+2(7n-x)=84
x+14n=84
x=84-14n we can observe 0
ie0
only possibility is n=5
now substitute to get the value of x =14
now(14/4):(21/6)=1:1
@gudda1122 said:
buddy i also have this method in cl solution but point is rather then taking no. of people why can't we take say Y liters of total water avail then equation would be likex/4+y/6=7but i am not getting answer from this if possible kindly explain me rationale behind taking n people
dude I solved in this way in the mocks also...may be I got the answer by chance but the method I cited was the only method I knew at that moment..
and what I feel if you take y liters of water, then we cannot assume any of milk or water consumption as integers and probably the inequality that follows cannot be solved.this is just an opinion..
@ScareCrow28 bhai , koi to technique hogi, IIFT wale bewkoof thodi honge jo aisa bhayankar dikhne wala question bina calculator ke denge ??? :shocked:
@techsurge said:
This is an IIFT question. I was unable to get solution without a calculator. hoping you guys can helpWhat is the value of 2 - sqrt (6407522209/3600840049)options are A 0.666039B 0.666029C 0.666009D None of thesethe solution just posted the value the answer is ASo do share your approach@ScareCrow28@gudda1122@staaalinnn@sumeet1489@krum ek baar nazar maar lo
root (3600840049)=6007 was easy, but 6407522209 looks hard to me, i don't even remember how to calculate square root
@techsurge said:
@ScareCrow28 bhai , koi to technique hogi, IIFT wale bewkoof thodi honge jo aisa bhayankar dikhne wala question bina calculator ke denge ???
Question given for testing "Question selection" ability 😛 ...Lets see what others have to say