Official Quant thread for CAT 2013

MBA CAT 2024
27048




@ananyboss said:
Hi,I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !
=>(7*42 + 7*35 )- 13*40 .......to make calc easy u may take 49 common and then add 6+5...
=>49*11-520 ......for multiplying by 11. write the digits like this.

_49
49 .... and add. basically what i am trying to tell is ...this can be done mentally once u are used to it :)

539- 520= 19?


27049
@ananyboss
An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !

for first 7 persons there is surplus of 2 means extra 14 marks and for last 7 persons deficit of 5 means -35 marks
so for 7 person to have an average of 40 (all this surplus and deficit must balance out ) so 40+14+ (-35) =19 marks
27050
@raopradeep
@raopradeep said:
@ananybossAn average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !for first 7 persons there is surplus of 2 means extra 14 marks and for last 7 persons deficit of 5 means -35 marks so for 7 person to have an average of 40 (all this surplus and deficit must balance out ) so 40+14+ (-35) =19 marks
Thanks, This is what I am looking for !
Can you brief this ?
For the 7 person to have an avg of 40 !! ?
27051
how many three digit numbers are there whose sum is not greater than 16 ?
27052
@jain4444 said:
how many three digit numbers are there whose sum is not greater than 16 ?
a + b +c a + b+c +t =16
No of sol = 19C3

Need to remove those where digits are more than 9
Let a = a' + 10
a' + 10 +b +c +t=16
a' + b+c +t=6
No of sol = 9C3 *4

Also, need to remove where a =0 (no is abc)
b +c +t =16
No of sol =18C2

Need to remove those where digits are more than 9
Let b = b' + 10
10 +b' +c +t=16
b'+c +t=6
No of sol =8C2

Total such numbers = 19C3 - 9C3*4-18C2-8C2*3
@jain4444 sir

PS: kuch gadbad hai
27053

Hi,


I have just started the prep for 2013.This question has been nagging my mind since i came across it.

Find the area of largest square that can be fit into a semi-circle of area 50 pi.

I browsed a bit and got to know the approach,thou initially was not able to solve it all by myself..:(

The approach which was explained in the yahoo answers was using the circle equation x^2 + y^2 = r^2.I would like to know the other approach that can be used?can we use similar triangles concept here?cos,i started it off like that but couldnt get to the right ans...:(


Thanks in Advance!
27054
@AbhiFMS said:
Hi,I have just started the prep for 2013.This question has been nagging my mind since i came across it.Find the area of largest square that can be fit into a semi-circle of area 50 pi.I browsed a bit and got to know the approach,thou initially was not able to solve it all by myself..The approach which was explained in the yahoo answers was using the circle equation x^2 + y^2 = r^2.I would like to know the other approach that can be used?can we use similar triangles concept here?cos,i started it off like that but couldnt get to the right ans...Thanks in Advance!
is it 2000 ?

80 ?
27055
@jain4444 said:
how many three digit numbers are there whose sum is not greater than 16 ?
a+b+ca+b+c+k=16

1000
a+b+c+k=16
19C3

19C3-3*(9C3-8C3)
27056
@AbhiFMS said:
Hi,I have just started the prep for 2013.This question has been nagging my mind since i came across it.Find the area of largest square that can be fit into a semi-circle of area 50 pi.I browsed a bit and got to know the approach,thou initially was not able to solve it all by myself..The approach which was explained in the yahoo answers was using the circle equation x^2 + y^2 = r^2.I would like to know the other approach that can be used?can we use similar triangles concept here?cos,i started it off like that but couldnt get to the right ans...Thanks in Advance!
Please see the attached...(using Pythagoras instead of Co-Geo).

regards
scrabbler
27057

@rnishant231 : yes right!,that was quick:)Approach used pls?
27058
@jain4444 641 ??
27059

@scrabbler :ok,i get it!thank you.
27060
@AbhiFMS said:
@rnishant231 : yes right!,that was quickApproach used pls?
Pls check the attachment..
27061
@AbhiFMS 80
27062

@scrabbler said:
Please see the attached...(using Pythagoras instead of Co-Geo).regardsscrabbler
Please see the attached.nowBD=R sin xOB=R cosxArea of ABCD: 2Rcos x* R sin x= R^2 sin2xMaximum when sin2x=1i.e. 2x=90x=45Area(Max)=R^2R^2=25*pi/ pi/2R^2=50Hence Area(Max)=50...@scrabbler
27063
@rnishant231 : "Square Of max. are will be symmetrical at its centre"-thank you for clarifying,was doubtful on this point prev.
27064
@ananyboss said:
Hi,I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !

Marks of 1st 7 person + marks of last seven person = Marks of all 13 person + Marks of 7th person.

So Marks of 7th person. = 13*40 - 7*42 - 7*35 = 19
27065
@scrabbler said:
Please see the attached...(using Pythagoras instead of Co-Geo).regardsscrabbler
the answer is 80 ??
27066
@AbhiFMS said:
Hi,I have just started the prep for 2013.This question has been nagging my mind since i came across it.Find the area of largest square that can be fit into a semi-circle of area 50 pi.I browsed a bit and got to know the approach,thou initially was not able to solve it all by myself..The approach which was explained in the yahoo answers was using the circle equation x^2 + y^2 = r^2.I would like to know the other approach that can be used?can we use similar triangles concept here?cos,i started it off like that but couldnt get to the right ans...Thanks in Advance!
80 ?

pi*r^2/2 = 50*pi
r = 10

side of square = x

x^2 + (x/2)^2 = 10^2
5x^2/4 = 100
x^2 = 80
27067
@heylady said:
Please see the attached.nowBD=R sin xOB=R cosxArea of ABCD: 2Rcos x* R sin x= R^2 sin2xMaximum when sin2x=1i.e. 2x=90x=45Area(Max)=R^2R^2=25*pi/ pi/2R^2=50Hence Area(Max)=50...@scrabbler

if x = 45 , then we ll have base side of square = double the other side as per the figure..
which is not possible.
pls see...