official quant thread for cat08

[amitkrsingh]

Originally Posted by roni_here

i dont know the answer yaar ...and anyways i am more interested in the approach ......

what will be the remainder when 123123123... 300 digits is divided by 504?

504 = 9*8*7(Coprimes)
123123123...%9 = 6
123123123...%8 = 3
123123123...% 7 = 0
So,
123123123... = 9a+6=8b+3= 7c

Smallest no. which satisfies all this criteria is 483 which is the answer. There may be calculation mistake(made it last time also).

[hellion]

Originally Posted by Hi2All

In a club there are certain no. of males and females. If 15 females are absent then no. of males will be twice that of females. If 45 males are absent then female strength will be 5 times that of males. Find no. of males actually present.

No of males -> m No of females->f

m = 2(f-15)
f = 5(m-45)
m = 2[5m-240]
m = 53.333

Don't know where i have gone wrong

[implex]

Originally Posted by linksuresh

i too feel that it shd be option c) 8
not too sure why implex its d...
waiting for his reply....

its option d as per solution key
now i have solved myself, it should be option c)

[implex]

New Problem!

[implex]

For those who might be interested, the above problem is from AOPS forum and the solution there is by me only! So no plagiarism !

[implex]

96 Find the number of positive integer triplets(a,b,c) that satisfy abc=4(a+b+c) with a<b<c
a) 4 b) 5 c) 6 d)7 e) none of these

97) Find the number of ordered integer pairs (x,y) which satisfy 1/x+1/y=1/2
a) 6 b) 10 c) 12 d) 5 e) none of these

98 ) Find the number of solutions in real numbers x^4+|x|=10
a) 0 b) 1 c) 2 d) 4 e) 8

[Hi2All]

Four persons can cross a bridge in 3,7,13,17 minutes.Only 2 can cross at a time.Find the minimum time taken by the 4 to cross the bridge.

[selebratinglife]

Originally Posted by implex

97) Find the number of ordered integer pairs (x,y) which satisfy 1/x+1/y=1/2
a) 6 b) 10 c) 12 d) 5 e) none of these

(4,4)(1,-2)(-2,1)(3,6)(6,3) are the possible ordered pairs of (x,y) hence 5.

[implex]

Originally Posted by Hi2All

Four persons can cross a bridge in 3,7,13,17 minutes.Only 2 can cross at a time.Find the minimum time taken by the 4 to cross the bridge.

17+3+13+3+7=40
this is the minimum time
(17,3) go
(3) returns
(13,3) go
(3) returns
(3,7) go

[implex]

Originally Posted by selebratinglife

(4,4)(1,-2)(-2,1)(3,6)(6,3) are the possible ordered pairs of (x,y) hence 5.

yeah right but what's the approach!!