official quant thread for cat08

[nbangalorekar]

just to ease off a bit.... lets discuss sumthng else (i hope other things pertaining to math can also be discussed on this thread... lest i get a coupla groans)
i was wondering if there exists a polynomial equation which can generate all primes...
n^2+n+41 will generate primes but only so long as n<41.
ne inputs puys...
i luv the concept of primes....one of the most intriguing aspect of math

[Udit Mohan]

(a,b,c) are coprime positive integers such that 1/a+1/b=1/c then which is true:
1) (a+b) is a square
2) (a+b) is never a square
3) (a+b) is a square for prcisely 4 values of a & b
4)none of the foregoing


1/a+1/b =1/c or, c=ab/(a+b)..
a b
odd odd --> not possible as c becomes fraction
even odd --> not possible as c becomes even
odd even --> not possible as c becomes even
even even --> not possible

then how 1/a+1/b=1/c is possible??

[neynetr]

Originally Posted by Udit Mohan

(a,b,c) are coprime positive integers such that 1/a+1/b=1/c then which is true:
1) (a+b) is a square
2) (a+b) is never a square
3) (a+b) is a square for prcisely 4 values of a & b
4)none of the foregoing


1/a+1/b =1/c or, c=ab/(a+b)..
a b
odd odd --> not possible as c becomes fraction
even odd --> not possible as c becomes even
odd even --> not possible as c becomes even
even even --> not possible

then how 1/a+1/b=1/c is possible??

hi...

i think therz a flaw in ur reasoning....

it says that a,b and c are coprime... it no where says that c needs to be a prime.... so c can be even.... right...??

or am i wrong in my reasoning...

puys plz correct me if im wrong....

meanwhile ill try solving it...!!!!

[Aarav]

Originally Posted by neynetr

hi...

i think therz a flaw in ur reasoning....

it says that a,b and c are coprime... it no where says that c needs to be a prime.... so c can be even.... right...??

or am i wrong in my reasoning...

puys plz correct me if im wrong....

meanwhile ill try solving it...!!!!

1/6 + 1/3 = 1/2. Put a = c -x and b = c-y. This will yield the result immediately. BTW, this question was asked in a RMO way back in 1993.

[devs]

Hi all,
plz solve this for me..

In a shop color tv,dvd & wasing machine(WM) r sold.List prices of a CTV,DVD & WM r 15000,3000 & 12000 respectvely.There is discount of 40% on CTV ,25% on WM.Profit obtained per item is the same for these two.
Profit of selling a WM is 25%.The ratio of Cost price of WM to DVD is 3:1 .What will be the Maximum % discount tht can be offered on the price of a DVD player so that there will be no loss?

[shivam_01]

Hi all,
plz solve this for me..

In a shop color tv,dvd & wasing machine(WM) r sold.List prices of a CTV,DVD & WM r 15000,3000 & 12000 respectvely.There is discount of 40% on CTV ,25% on WM.Profit obtained per item is the same for these two.
Profit of selling a WM is 25%.The ratio of Cost price of WM to DVD is 3:1 .What will be the Maximum % discount tht can be offered on the price of a DVD player so that there will be no loss?

hello is the answer 46 % if it cortect then i will post my approach...

[devs]

hi,

ans is not 46%..it is 20% or 40%...m not sure

[sarvshwet]

Originally Posted by devs

Hi all,
plz solve this for me..

In a shop color tv,dvd & wasing machine(WM) r sold.List prices of a CTV,DVD & WM r 15000,3000 & 12000 respectvely.There is discount of 40% on CTV ,25% on WM.Profit obtained per item is the same for these two.
Profit of selling a WM is 25%.The ratio of Cost price of WM to DVD is 3:1 .What will be the Maximum % discount tht can be offered on the price of a DVD player so that there will be no loss?

ans is 20% this is how:

we know the list price for the three items....
and the discounts for the 2

so we get:
selling price of CTV=15000 - 40%(15000)=9000

selling price of WM=12000 - 25%(12000)=9000

we know that profit on selling WM is 25%
hence CP=9000/1.25=7200
hence CP of dvd=7200/3=2400

hence max disc= 600=20% of 3k

[romy4allcse]

Originally Posted by devs

hi,

ans is not 46%..it is 20% or 40%...m not sure

ctv(15000) dis(40%) sp(9000)
=>as cpctv = cpwm =>cpctv(7200)
dvd(3000)
=> cpdvd = 7200/3 = 2400
wm(12000) dis(25%) sp(9000) profit(25%)
=> cost price of wm = 7200
so max discount on dvd one can offer to hav no gain no loss = 3000-2400 = 600
hence % dis = 600*100/3000 = 20 % ans.

[romy4allcse]

[quote=getintoiimb;1160435]puys pls help me with these qns !


2)ajit can do as much work in 2 days as baljit can do in 3 days and baljit can do as much in 4 days asdiljit in 5 days.a piece of work takes 20 days if all work together.how long would baljit take to do all the work by himself?

ans : 66 days

Ans : In case of ajit & baljit
%work done by ajit in one day = (100/2)(3/3) = (3/2)(100/3) = 3/2b
%work done by baljit in one day = 100/3 = b

In case of baljit & diljit
%work done by balit in one day = 100/4 = b
%work done by diljit in one day = 100/5 = (4/5)b
if they work together then work completed by them in one day = a + b + d
a = 3/2b
d = 4/5b
=> 3/2b + b + 4/5b = 33b/10
now (33b/10)*20 = 100
=> b = 50/33
hence b(days req. by baljit to complete this 100% work)
= 100*33/50
= 66 days