Official Quant thread for CAT 2013

@Deb.csen
A

@Deb.csen said:
Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that two of sara's friend are connected with each other. On her birthday, Sara decides to invite her friends and the friens of her friends. How many people did she invite for her birthday party?A. >= 105B. C. D. >= 100 and >=105 and plz solve this with explanation..
answer kya hai ??
@pulkitgurditta said:
answer kya hai ??
pata nai h bhai..
@ishu1991 said:
@Deb.csenA
How say ur explanation..

The sum of n terms of a series is 3n^2 + 5n. Find the value of n if nth term is 152.

@Deb.csen said:
Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that two of sara's friend are connected with each other. On her birthday, Sara decides to invite her friends and the friens of her friends. How many people did she invite for her birthday party?A. >= 105B. C. D. >= 100 and >=105 and plz solve this with explanation..
B. ?
@vbhvgupta said:
The sum of n terms of a series is 3n^2 + 5n. Find the value of n if nth term is 152.
nth term = Sn - Sn-1 = 3*n^2+5n - 3*(n-1)^2+5(n-1) = 16*n-8 = 152
=> n= 10

how many 4 digit no's are there that does not contain more than 2 distinct digits?


@Deb.csen said:
Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that two of sara's friend are connected with each other. On her birthday, Sara decides to invite her friends and the friens of her friends. How many people did she invite for her birthday party?A. >= 105B. C. D. >= 100 and >=105 and plz solve this with explanation..
i guess ans is E.
my explanation wil be first consider the minimum situation i.e if two of her friends are friends with each other so they wil have all the friends in common so effectively they can be counted as 27(25 common friends and 2 themselves) and the remaining 3 friends will have all distinct friends so they are effectively 78 so its 105. And for maximum scenario consider the two friends to have all friends to be distinct so it effectively is 25*3(friends friend of sara)+24*2(friends friend of sara who are friends themselves)+5(friends)=123.

@Deb.csen said:
Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that two of sara's friend are connected with each other. On her birthday, Sara decides to invite her friends and the friens of her friends. How many people did she invite for her birthday party?A. >= 105B. C. D. >= 100 and >=105 and plz solve this with explanation..
dis was in xat 2013. according to tf key answer is B. i guess it would be E.
sara has 5 frnz. each of them have 25 frnz. among those 25, sara is also there. so there are actually 25 - 1 = 24 frnz. since 2 frnz are connectd with each other so each of them is in the friend list of the other. so there are actually 24 - 2 = 23 new friends. so total is = 5 + 24 + 24 + 24 + 23 +23 = 123.
and if all are connected to each other it will be = 5 + (25-5)x5 = 105

P.S -in the actual question it was stated "at least two of her friends are connected.." so 123 will be the max value.
@mailtoankit said:
Tn = Sn-Sn-1 = 3n^2 + 5 - 3(n-1)^2 - 5(n-1) = 16n - 8 = 152

ans 24?.
It is a A.P with common difference 6.

@vijay_chandola said:
nth term = Sn - Sn-1 = 3*n^2+5n - 3*(n-1)^2+5(n-1) = 16*n-8 = 152=> n= 10
@mailtoankit said:
Tn = Sn-Sn-1 = 3n^2 + 5 - 3(n-1)^2 - 5(n-1) = 16n - 8 = 152 n = 10 ?
why u used this formula..what is the logic behind this???
@vbhvgupta said:
why u used this formula..what is the logic behind this???
Some of the numbers till (n-1)th term = Sn-1 (let say)\
Some of the numbers till nth term = Sn

==> when we add nth term in the Sn-1, we get Sn
Sn-1 + nth term = Sn
@vbhvgupta said:
why u used this formula..what is the logic behind this???
nth term ke summation main se (n-1)th term ke summation ko subtract karoge to nth term milegi na.
@vbhvgupta said:
why u used this formula..what is the logic behind this???
Tn = Sn - Sn-1 = 3n^2 + 5 - 3 (n-1)^2 - 5(n-1) = 6n + 2 =152
n = 25?...is it correct....first one was wrong@iLoveTorres

Mr. Mehera is planning for higher education expenses of his two sons aged 15 and 12. He plans to devide Rs. 15lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs. 21 lakhs each when they reach the age of 21. He is looking for plans that wil give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should be

A. 5% and 7.5% respectively
B. 8% and 12% respectively
C. 10% and 15% respectively
D. 15% and 22.5% respectively
E. 20% and 30% respectively

solve this and xplain..

@Deb.csen said:
Mr. Mehera is planning for higher education expenses of his two sons aged 15 and 12. He plans to devide Rs. 15lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs. 21 lakhs each when they reach the age of 21. He is looking for plans that wil give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should beA. 5% and 7.5% respectivelyB. 8% and 12% respectivelyC. 10% and 15% respectivelyD. 15% and 22.5% respectivelyE. 20% and 30% respectivelysolve this and xplain..
We can say the elder son will get 21L after 6 years of SI on 15/2 L
So 15/2(6r/100+1)=21 =>r=30
So elder son shud get 30%

The option (e)
@Deb.csen said:
Mr. Mehera is planning for higher education expenses of his two sons aged 15 and 12. He plans to devide Rs. 15lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs. 21 lakhs each when they reach the age of 21. He is looking for plans that wil give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should beA. 5% and 7.5% respectivelyB. 8% and 12% respectivelyC. 10% and 15% respectivelyD. 15% and 22.5% respectivelyE. 20% and 30% respectivelysolve this and xplain..
E.20% and 30% respectively

P.S: explain koi aur karega...... XAT quant se hai ye sawal...
@mailtoankit said:
Tn = Sn - Sn-1 = 3n^2 + 5 - 3 (n-1)^2 - 5(n-1) = 6n + 2 =152n = 25?...is it correct....first one was wrong@iLoveTorres
yup, correct

Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram's car at the rate of 25 kmph, while shyam walked at 5 kmph. After sometime, Hari got off and started walking at the rate of 5kmph and Ram went back to pick up shyam. All three reached the destination simultaneously. The number of hours required for the trip was:
A. 8
B. 7
C. 6
D. 5
E. 4

Solve this with explanation...