Official Quant thread for CAT 2013

MBA CAT 2024
10341
@maddy2807 ok thanks,what u think about first question that i posted.U have any shorter approach for that ?
10342
@jain4444 said:
@techsurge nice bet
The polynomial x^2-2x+7 divides the polynomial x^4+px^2+q. What is the value of q?
(x^2+7 -2x)*(x^2+7 +2x)=x^4+49+14*x^2-4*x^2=x^4+10*x^2+49

=> p=10, q=49


@jain4444 said:
The sum of the parent's ages is twice the sum of their children's ages. Five years ago, the sum of the parent's ages is four times the sum of their children's ages. In fifteen years, the sum of the parent's ages will be equal to the sum of their children's ages. How many children were in the family?bhai question says 4 times you took 5 times in your solution
That was the stupidest mistake I have ever made :banghead:
I feel like killing myself
10343
@nole said:
Ratio of incomes of a and b is 3:4,ratio of expenditure is 4:5.The ratio of savings can be.1)4:5 2)6:73)8:134)7:9I did it like this ratio of savings =(3x-4y)/(4x-5y). then i equated the ratio with each of the options to get the answer. the correct answer is 8/13. But is there any shorter approach?q2) If a-b varies directly with a+b,then a^2 - b^2 will vary directly with1) a^2 + b^22)ab3)a^2 + b^2 + 3ab4) more than one of the aboveI did it like this:a-b=k(a+b)multiplying both sides by a+ba^2-b^2=k(a+b)^2What to do next to reach the answer ? Answer is 4) more than one of the above.
I don't know of any shorter method other than the one you posted for the first one
You could assume arbitary values and try..but that would be lengthier than your method
10344
@jain4444
The polynomial x^2-2x+7 divides the polynomial x^4+px^2+q. What is the value of q?

is ans 49?
10345
@jain4444 said:

The polynomial x^2-2x+7 divides the polynomial x^4+px^2+q. What is the value of q?
(x^2 - 2x + 7)(x^2 + ax + b) = (x^4 + px^2 + q)

Comparing coefficients, we will get
-2 + a = 0 (coeff of x^3)
=> a = 2

b + 7 -2a = p, (coeff of x^2)
-2b + 7a = 0 (coeff of x)
So, b = 7
and p = 10

q = 7b = 49
10346
@nole said:
@maddy2807 ok thanks,what u think about first question that i posted.U have any shorter approach for that ?

I would hv gone thru the same method. matching options. No other technique
10347
@jain4444 said:
@techsurge nice bet let sum of parent's ages = N average age of children's = x number of children's = yN = 2*xy --------1(N - 10) = 4*(xy - 5y)---------2(N + 30) = xy + 15y ------3put 1 in (2) and (3)2xy - 10 = 4xy - 20y20y - 2xy = 10 15y - xy = 30=> y = 5The polynomial x^2-2x+7 divides the polynomial x^4+px^2+q. What is the value of q?
(x^2-2x+7)(x^2+2x-7)=x^4+10x^2+49
p=10,q=49
10348
Mr X,a very industrious person ,wants to establish his own unit.For this he needs an instant loan of Rs 5,00,000 and,every five years he requires an additional loan of Rs. 100,000.If he had to clear all his outstandings in 20 yrs,and he repays the principal of the first loan equally over the 20 yrs,find what amount he would have to pay as interest on his initial borrowing if the rate of interest is 10% p.a. simple interest ??
a 560,000 b 540,000 c 525,000 d 500,000
10349
@IIM-A2013 said:
Mr X,a very industrious person ,wants to establish his own unit.For this he needs an instant loan of Rs 5,00,000 and,every five years he requires an additional loan of Rs. 100,000.If he had to clear all his outstandings in 20 yrs,and he repays the principal of the first loan equally over the 20 yrs,find what amount he would have to pay as interest on his initial borrowing if the rate of interest is 10% p.a. simple interest ??a 560,000 b 540,000 c 525,000 d 500,000
is it 5,25,000? :neutral:
10350
@vijay_chandola
tell me the approach

10351
@vijay_chandola said:
He chooses 2 people by C(N, 2) ways.then the teacher can pass the baton to either of the students, ultimately the first one will get the baton.

I think C(N,2) is not correct. As question says teacher select the 1st student, Now choice for the second student totally lies with 1st one. Now when we do C(N,2) ,We already selected second student ,Which shud have been chosen by the 1st one , Thus voilating the condition. What Say ??
10352
@IIM-A2013 said:
@vijay_chandolatell me the approach
Yearly payable amount=25000.

Interest at the end of first year=5,00,000*10/100=50,000
at the end of second year=(5,00,000-25000)*10/100=47,500
at the end of second year=(4,75,000-25000)*10/100=45,000

=> making a series with d= -2500, n=20, a=50,000
=> Total value of interest=20/2*{2*50,000+19*(-2500)}=5,25,000
10353
@koshti said:
I think C(N,2) is not correct. As question says teacher select the 1st student, Now choice for the second student totally lies with 1st one. Now when we do C(N,2) ,We already selected second student ,Which shud have been chosen by the 1st one , Thus voilating the condition. What Say ??
He can choose any number of students right?

Is it specifically mentioned in the question that teacher selects only 'one student' ? :neutral:
I can;t find the question now :O

@jain4444 : see the below post and reply no. #10540 for C(N, 2) wali query :)
10354
@vijay_chandola said:
He can choose any number of students right? Is it specifically mentioned in the question that teacher selects only 'one student' ? I can;t find the question now
yeah question says that , here the question :

The professor plays a game of "pass the baton" with his class of N students. He randomly selects one student, say A, and that student again randomly selects another student (say B)and passes him the baton, then B selects another student and passes him the baton and the game ends. What is the probability that the first student who got the baton from the professor ends up with the baton in the end
10355
@koshti said:
yeah question says that , here the question : The professor plays a game of "pass the baton" with his class of N students. He randomly selects one student, say A, and that student again randomly selects another student (say B)and passes him the baton, then B selects another student and passes him the baton and the game ends. What is the probability that the first student who got the baton from the professor ends up with the baton in the end
1/(N-1)?

Favourable case:
'A' selects from N - 1 students = N - 1
'B' selects A = 1

Sample space:
'A' selects from N - 1 students = N - 1
'B' selects from N - 1 students = N - 1

probability = (N - 1)/((N - 1) * (N - 1)) = 1/(N - 1)
10356

Koshti: its NP2 not nc2 we have to do. That takes of the selection bit, since the baton has to be returned to the first person, either the second can be selected first and pass it to the first or the other way around. I do think that approach is logically consistent.
of course in the actual exam the best approach would be to take a sample set of say 4 students calculate exact probability and substitute value of N in the options.:P

10357

Well OA says 1/2(n-1) but im certain thats wrong, they've taken NC2 and not bothered with the arrangement, which is wrong.....unless of course WE are the ones misinterpreting the question..~_~

10358
The equation of four lines is given below:
x + 2y - 3 = 0, 3x + 4y - 7 = 0, 2x + 3y - 4 = 0 and 4x + 5y - 6 = 0
(1) Concurrent
(2) The sides of a parallelogram
(3) The sides of a square
(4) None of these
10359
@anantn said:
Koshti: its NP2 not nc2 we have to do. That takes of the selection bit, since the baton has to be returned to the first person, either the second can be selected first and pass it to the first or the other way around. I do think that approach is logically consistent.of course in the actual exam the best approach would be to take a sample set of say 4 students calculate exact probability and substitute value of N in the options.
Bro P(N,2) is what i Did.

P(N,2) = N!/(n-2)! = N*(N-1) . 😃

I think Answer given is wrong. It Shud be 1/(N-1)
10360

If the largest angle in a triangle is 70o, what is least possible value of the smallest angle of the triangle?

  1. 69o
  2. 1o
  3. 40o
  4. 39o
  5. 41o