Official Quant thread for CAT 2013

Three drunkards agree to pool their vodka and decided to share it with a fourth drunkard (who had no vodka) at a price equal to 5 roubles a litre. The first drunkard contributed 1 litre more than the second and the second contributed a litre more than the third. Then all four of them divided the vodka equally and drank it. The fourth drunkard paid money, which was divided in the ratio of each drunkard's contribution towards his portion. It was found that the first drunkard should get twice as much money as the second. Assume that all shares are integral.

How much money did the second drunkard get (in roubles)?
(a) 8 (b)20 (c)15 (d)Data insufficient.

Please solve it .

@saurav.kgp said:
Three drunkards agree to pool their vodka and decided to share it with a fourth drunkard (who had no vodka) at a price equal to 5 roubles a litre. The first drunkard contributed 1 litre more than the second and the second contributed a litre more than the third. Then all four of them divided the vodka equally and drank it. The fourth drunkard paid money, which was divided in the ratio of each drunkard's contribution towards his portion. It was found that the first drunkard should get twice as much money as the second. Assume that all shares are integral.How much money did the second drunkard get (in roubles)?(a) 8 (b)20 (c)15 (d)Data insufficient.
15
@ishu1991 said:
A triangle has sides 13, 14, 15. It is rotated through 180 degrees about its centroid to form an overlapping triangle. What is the area of the union of the two triangles?(a) 84 (b) 56 (c) 126 (d) none of the foregoing

1.
A swimmer jumps from a bridge over a canal and swims 1 km upstream. After that first kilometer, he passes a floating cork. He continues swimming for another half an hour and then turns around and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant speed. How fast does the water in the canal flow?
@meenu05 said:
Please solve it .
is answer 11
@joyjitpal said:
1.A swimmer jumps from a bridge over a canal and swims 1 km upstream. After that first kilometer, he passes a floating cork. He continues swimming for another half an hour and then turns around and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant speed. How fast does the water in the canal flow?
1 km/hr

Please solve it .

in an attempt to find the prime number between(and including) 101 and 1000,all the numbers from 101 to 1000 are written on a sheet of paper.the first three steps of the process involve crossing out all multiplesof 2,3 and 5.After these three steps,how many numbers are left uncrosed?
a)230
b)235
c)240
d)245
@saurabhlumarrai said:
in an attempt to find the prime number between(and including) 101 and 1000,all the numbers from 101 to 1000 are written on a sheet of paper.the first three steps of the process involve crossing out all multiplesof 2,3 and 5.After these three steps,how many numbers are left uncrosed?a)230b)235c)240d)245
450+300+180-150-90-60+30=660
900-660=240??
@ishu1991 answer b = 11 or lesser than 1331 .
@saurabhlumarrai said:
in an attempt to find the prime number between(and including) 101 and 1000,all the numbers from 101 to 1000 are written on a sheet of paper.the first three steps of the process involve crossing out all multiplesof 2,3 and 5.After these three steps,how many numbers are left uncrosed?a)230b)235c)240d)245
240
@saurabhlumarrai said:
in an attempt to find the prime number between(and including) 101 and 1000,all the numbers from 101 to 1000 are written on a sheet of paper.the first three steps of the process involve crossing out all multiplesof 2,3 and 5.After these three steps,how many numbers are left uncrosed?a)230b)235c)240d)245
240
@ishu1991 said:
The distance AB is 12. The circle center A radius 8 and the circle center B radius 6 meet at P (and another point). A line through P meets the circles again at Q and R (with Q on the larger circle), so that QP = PR. Then the length of QP is(a) (120)^1/2 (b) (130)^1/2 (c) (160)^1/2 (d) none of the foregoing
it is 130^1/2
find the sum of the following series

S = 7/6 + 13/12 +21/20 +31/30 +.........+ 9901/9900


@ishu1991 said:
The overlap is a hexagon, and there are six congruent triangles outside the hexagon, each similar to the original triangle and 1/3 the (linear) size (because the centroid divides the median in the ratio 2:1). So the area of the union is 4/3 times the area of the triangle. We have the semiperimeter s = 21, so by Heron's formula the triangle has area (21路8路7路6)^1/2 = 84.this is the solution i have bt i have a doubt in it please clear it
i also have a doubt... union means area of the triangle + the 3 extra triangles we got right?

area of the triangle itself is 84.. answer has to >84 and
@meenu05 said:
Please solve it .
log32/log81=log2/log11*5/4*logb/loga

log2^5/log3^4=log2/log11*5/4*logb/loga

5log2/4log3=log2/log11*5/4*logb/loga

log11/log3=lob/loga

given a is 3 b is 11
@ChirpiBird said:
it is 130^1/2
yes u ar ryt plss explain
@meenu05 said:
Please solve it .
@meenu05 11
@joyjitpal said:
find the sum of the following seriesS = 7/6 + 13/12 +21/20 +31/30 +.........+ 9901/9900
(6+1)/6 + (12+1)/12.... so on..
or u get two series..
1+ 1/2*3 + 1 + 1/3*4.... so on

1+1+1 /// 98 times ... and 1/2*3 can be written as 1/2-1/3

or 98 + 1/2-1/3 + 1/3- 1/4 + 1/4 - 1/5 ...... + 1/99- 1/100
terms get cancel out..
98 + 1/2-1/100
98 + 98/200
98 +49/100
... aise hi karna h na???