Official Quant thread for CAT 2013

MBA CAT 2024
29886
@j.gayu said:
can any one explain euler's theorem in detail manner??
This is not in much detail but shuld help
http://www.quantexpert.co.in/qenotes/quantnotes/numbers/50-remainder-theorem.html
29887
@vbhvgupta said:
A varies directly as the sum of the two quantities B and C. B in turn varies directly as x and C varies inveresly as x. when x=1 or 2 , A = 3. Find the value of A when x = 4.
A=k1*(B+C)
B=k2 *X
C=k3*1/X

So,
A=k1k2 * X + k1k3 *1/X

Substitute X=1 and A=3
3=k1k2+k1k3.................eq1
Substitute X=2 and A=3
3=2 k1k2 + 0.5 k1k3..........eq2
Solving these linear eq.s with variable as k1k2 and k1k3
=>k1k2=1 and k1k3=2
So,
A=X + 2/X
at X=4
A=4+2/4=4.5

29888
@vbhvgupta said:
Q 25
log 7623=3.8821
log x=-0.1179
logx+log 10000=-0.1179+4=3.8821
log10000x=3.8821
antilog log10000x=antilog 3.8821
=>10000x=7623
=>x=.7623....!!!

:drinking: :drinking: :drinking:
Bacardi+Smirnoff+Appy fizz= some start to weekend

29889
An iron water tank with a capacity of 10,000 gallons has a water supply inlet, which feeds water at the rate of 300 gallons per hour. This water inlet starts automatically when the water level goes below the 5000-gallon mark. If there is a hole formed at the bottom of the tank when the water tank is full, how long will it take for the whole tank to be emptied if the water goes out of the hole at the rate of 500 gallons per hour?
29890
@j.gayu said:
can any one explain euler's theorem in detail manner??
This too;)

http://totalgadha.com/mod/forum/discuss.php?d=1369

I had one PDF from TG for remainder methods alone some times back...does any one have that now?
29891
@shattereddream said:
An iron water tank with a capacity of 10,000 gallons has a water supply inlet, which feeds water at the rate of 300 gallons per hour. This water inlet starts automatically when the water level goes below the 5000-gallon mark. If there is a hole formed at the bottom of the tank when the water tank is full, how long will it take for the whole tank to be emptied if the water goes out of the hole at the rate of 500 gallons per hour?
35 hours? more of a IQ question:)
29892
@shattereddream said:
An iron water tank with a capacity of 10,000 gallons has a water supply inlet, which feeds water at the rate of 300 gallons per hour. This water inlet starts automatically when the water level goes below the 5000-gallon mark. If there is a hole formed at the bottom of the tank when the water tank is full, how long will it take for the whole tank to be emptied if the water goes out of the hole at the rate of 500 gallons per hour?
35 ?
29893

Q 34

29894
@vbhvgupta said:
Q 34
21 is only number in the options which are divisible by 7:)
29895
@vbhvgupta said:
Q 34
21... the answer is thr in just one line of the question..
29896
@mani0303 said:
35 hours? more of a IQ question
How yaar!I am getting 50/3 hrs
29897
@vbhvgupta said:
Q 34
Becoz of bad options , 21 is the answer
Detail:
Let their apples be a,b,2a and (b+2) in order
Now 2b/(a+b+2)=1/2 => b=a+2
and 2a/(a+2b+2)=2/5=>2a=b+1
Solve and get a=3,b=5
So total apples = 3+5+6+7=21
29898
@Buck.up said:
How yaar!I am getting 50/3 hrs
For the first 5000 liters,the outlet would take (5000/500) = 10 hrs,once the water level has reached 5000,both inlet and outlet would start working,so the net rate would be 200 litres/hr ie would be released...so,5000/200 = 25hrs

In total,the tank would be emptied in 35 hours
29899
@shattereddream said:
An iron water tank with a capacity of 10,000 gallons has a water supply inlet, which feeds water at the rate of 300 gallons per hour. This water inlet starts automatically when the water level goes below the 5000-gallon mark. If there is a hole formed at the bottom of the tank when the water tank is full, how long will it take for the whole tank to be emptied if the water goes out of the hole at the rate of 500 gallons per hour?
5000/500 + 5000/200 = 10+25 = 35
29900
@shattereddream said:
An iron water tank with a capacity of 10,000 gallons has a water supply inlet, which feeds water at the rate of 300 gallons per hour. This water inlet starts automatically when the water level goes below the 5000-gallon mark. If there is a hole formed at the bottom of the tank when the water tank is full, how long will it take for the whole tank to be emptied if the water goes out of the hole at the rate of 500 gallons per hour?
OA 35 @Narci @mani0303
29901
@vbhvgupta said:
Q 34
k1,k2,k3,k4...

k1/[k2+k4]=1/2....k3/[k1+k2+k4]=2/5

givin k3 2y apples ...we must give 5y apples to the rest...

k2=x apples...k4=x+2 apples..k1=x+1 apples...
total=3x+3=5y...

smallest such no=15.....y=3..x=4...
total=5+4+6+6=21....from options nly...as valu f x can also b=14..24.....34.....
29902
@mani0303 said:
This toohttp://totalgadha.com/mod/forum/discuss.php?d=1369I had one PDF from TG for remainder methods alone some times back...does any one have that now?
i have the ebook on number system by totalgadha
29903
@shattereddream said:
i have the ebook on number system by totalgadha
No dude..I could take it from online,but the one exclusively for remainders compiled by S/E engineer way back in 2004 is hard to get...I'd lost it now:(

One from the remainder:)

What is the remainder when (1!)^3 +(2!)^3 +(3!)^3 +(4!)^3 + -----------------------(1152!)^3 is divided by 1152?
29904
@mani0303 said:
No dude..I could take it from online,but the one exclusively for remainders compiled by S/E engineer way back in 2004 is hard to get...I'd lost it nowOne from the remainderWhat is the remainder when (1!)^3 +(2!)^3 +(3!)^3 +(4!)^3 + -----------------------(1152!)^3 is divided by 1152?
1152 = 2^7 X 3^2
So, (4!)^3 is divisible by 1152. Hence (1!)^3+(2!)^3 + (3!)^3 = 225 ??
29905
A and B start swimming simultaneously from two points P and Q respectively, on a river towards each other. A crosses a floating cork at a point S and B crosses the floating cork at a point T which is at a distance of 8 km from point S. A and B cross each other at a distance of 2 km from T. It is given that the direction of flow of the river is from P to Q and in still water, the ratio of speeds of A and B is 3 : 1. P, S, T and Q ( in that order) are on the same straight line and assume that A, B and the floating cork move along that line.
If PQ = 100 km, then find the distance between the floating cork and A when A reaches Q.