official quant thread for cat08

[nbangalorekar]

Originally Posted by implex

New Problem!

since k,a,b, etc r all positive they are all greater than 1.
let us take different cases.
for k=1; a1*b1= 7 only 2 solns r possible.
for k=2; a1*b1+a2(b1+b2)=7
take different cases ranging frm
a1=1 to a1 = 5 (it cant be more than 5) u will have 8 possible solutions.
for k=3; a1b1+a2(b1+b2)+a3(b1+b2+b3): u can either have:
a1, b1,b2,a2,a3 all equal to 1 n b3 = 2
or a1=2 n rest all equal to one. thus 2 solns.
k cant be >3 coz then one of the variables have to be 0 n thus not satisfying the condition.
so in all we have 2+8+2 = 12 solutions.
so answer is option 'e' none of these ..... unless im missing out sumting..

[selebratinglife]

Originally Posted by implex

New Problem!

a1,b1,a2,b2 are as follows..also a3,b3 if applicable
1,1,1,1,1,2
1,1,1,5
1,2,1,3
1,1,3,1
1,3,1,1
2,1,1,1,1,1
2,2,1,1
2,1,1,4
3,1,2,1
3,1,1,3
4,1,1,2
5,1,1,1
7,1
1,7

14 cases..Lemme know if I'm missing any combination.

[pavanpadekal]

Originally Posted by implex

x=2y/(y-2) this will give only 5 solns for integers!!

y-2=+-2y
y-2=+-2
y-2=+-1
y-2=+-4

Can someone explain how this was arrived at.


I got only so much.stuck.
(y-2)^2=4y^2/x^2
y-2=+-2y/x
y-2=+-2y/1
y-2=+-2y/2
y-2=+-2y/3
y-2=+-2y/4
y-2=+-2y/5
y-2=+-2y/6


Please do help a person trying to learn!

[getintoiimb]

Hi puys!
pls solve these for me with steps.

1)125 toffees cost Rs 75.find the cost of one million toffes if there is a discount of 40% on the selling price for this quantity?

ans : Rs 360000

2)in order to maintain the price line a trader allows a discount of 10% on the marked price of goods in his shop..however he still makes a gross profit of 17% on the cost price.find the profit per cent he would have made on the seleeing price had he sold at the marked price?

ans : 23.07%

3)a man buys 50 kg of oil at Rs 10 per kg and another 40 kg of oil at Rs 12 kg and mixes them.he sells the mixture at the rate of Rs 11 per kg.what will be hi gain percent if he is able to sell the whole lot?

ans : 100/98 %

4)a dealer buys eggs at Rs 36 per gross.he sells the eggs at a profit of 12(1/2)% on the CP.what is the SP per egg?
how much is a gross?i.e like one dozen is 12 how much is a gross?

ans : 28 paise

5)a manufacturer makes a profit of 15% by seliing a colour tv for Rs 5750.if the cost of manufacturing increases by 30% and the price paid by the retailer is inceased by 20%,find the profit percent made by the manufacturer?

ans : 6(2/13)%

6)a watch dealer pays 10% on a wathc that costs Rs 250 abroad.for ho0w much should he mark it if he desires to make a profit of 20% after giving a discount of 25% to the buyer?

ans : Rs 440

7)a shopkeeper buys an article for Rs 400 and marks it for sale at a price that gives him 80% profit on his cost.he however gives a 15% discount on the MP to his customer.calc the actual % profit made by the shopkeeper

ans : 53%

8 )a trader purchases apples at Rs 60 per hundred.he spends 15% on the transportation.what should be the SP per 100 to earn a profit of 20%?

ans : Rs 82.8

Thanks !

[Hi2All]

1)When I was married 10 years ago my wife is the 6th member of the family. Today my father died and a baby born to me. The average age of my family during my marriage is same as today. What is the age of Father when he died?

2)A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?

Please help me with a solution to this problem..

[vivs_d]

Originally Posted by Hi2All

1)When I was married 10 years ago my wife is the 6th member of the family. Today my father died and a baby born to me. The average age of my family during my marriage is same as today. What is the age of Father when he died?

10 years ago, let the name of the members be a,b,c,d,e,f. where 'a' refers to grandfather of the newborn kid. kid is represented by 'g'

now according to given situation

a+b+c+d+e+f-60 = b+c+d+e+f+g [but g=0 as the kid is newborn.]
a=60......... ans
dadaji ki age 60 yrs.



(one obvious assumption i have taken is that the protagonist's wife is the last member in the family, till the kid is born so that the total family members are six at both the times. )

[implex]

sol to question 95!!
I had already posted it somewhere so just made an image from there

[implex]

Originally Posted by selebratinglife

Is it 2?Consider f(x)=x^4+|x|-10=0,f(1) is negative and f(2) is +ve . Also f(-1) is -ve and f(-2) +ve

yeah it is 2
x^4=|x|^4
let |x|=t , t>=0
we get f(t)= t^4+t-10
clearly f(t) is an increasing function for all t
f(1) <0 and f(2) >0
so one solution for t
this means two solution for x

[amitkrsingh]

Find few solutions below:-

Originally Posted by getintoiimb

Hi puys!
pls solve these for me with steps.

1)125 toffees cost Rs 75.find the cost of one million toffes if there is a discount of 40% on the selling price for this quantity?

ans : Rs 360000

125 toffes cost - 75
10^6 toffes cost- 75*8000
But there is 40% discount. So,
SP= 75*8000*(3/5)=36 *10^4

2)in order to maintain the price line a trader allows a discount of 10% on the marked price of goods in his shop..however he still makes a gross profit of 17% on the cost price.find the profit per cent he would have made on the seleeing price had he sold at the marked price?

ans : 23.07%
SP=0.9*MP
SP/CP=1.17
MP/CP=1.17/0.9=13/10

Profit % = (1-C/M)*100= 300/13= 23.07%

3)a man buys 50 kg of oil at Rs 10 per kg and another 40 kg of oil at Rs 12 kg and mixes them.he sells the mixture at the rate of Rs 11 per kg.what will be hi gain percent if he is able to sell the whole lot?

ans : 100/98 %

SP = 990
CP= 500+480 = 980
Gain %= 100/98

[linksuresh]

Originally Posted by Hi2All

2)A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?

my ans = minimum time needed - 35 mins

Time PPl who know the secret
0th 1
5 3 (1 who told the secret+2 others who hrd it)
10 9 (2*3+3)

hence if u see carefully u see at the end of Nth 5 min slot there wud be 3^N who would have heard the secret.

hence 3^n >= 768
n > 6 => hence n=7 for being sure more than 768 have heard it...

5*N = 5*7 = 35 mins for being sure 768 have heard it (we are told only at the end of 5mins how many know, hence we cannot say how many ppl are told in 1st min of the 5mins slot... else we cud have said smth like 31 mins... but... )