Official Quant thread for CAT 2013

MBA CAT 2024
25348
@amresh_maverick said:
Sumit committed a mistake in finding the LCM of three distinct positive integers greater than 1 namely A, B and C, and found it to be 840, which is a common multiple of A, B and C all, but is not the lowest. The HCF of A, B and C is 1. Find the maximum possible value of A + B + C. OA : 563
ans is
A = 280
B= 280
c = 3

so the maximum sum 563 of A + B + C
25349
@amresh_maverick
Q) there are 10 stations between station A and Station B. 4 new stations have been added now. what are the number of ways in which new tickets can be issued considering only 1 way of the journey ?


Answer - there are now 10+2+ 4 = 16 stations (12 old stations and 4 new stations)...

from every new station the number of tickets that can be issued is = 15.
total new tickets from the 4 new stations = 15*4= 60.

from every old station the number of new tickets that can be issued is 4.
total number of new tickets that can be issued from the 12 old stations are 12*4 = 48...

total = 48+60 = 108....

25350

albiesriram ------ refer to the post above.....

25351
@ayushbhalotia said:
@amresh_maverickQ) there are 10 stations between station A and Station B. 4 new stations have been added now. what are the number of ways in which new tickets can be issued considering only 1 way of the journey ? Answer - there are now 10+2+ 4 = 16 stations (12 old stations and 4 new stations)...from every new station the number of tickets that can be issued is = 15.total new tickets from the 4 new stations = 15*4= 60.from every old station the number of new tickets that can be issued is 4.total number of new tickets that can be issued from the 12 old stations are 12*4 = 48...total = 48+60 = 108....
I think I have not understood the question, plz correct my understanding

Let two of the new station be A and B . So, the no of ticket from A to B is 1 and we do not have to count from B to A as we need to consider only 1 way of the journey .??

Am I right in my understanding ?
25352
@amresh_maverick said:
I think I have not understood the question, plz correct my understandingLet two of the new station be A and B . So, the no of ticket from A to B is 1 and we do not have to count from B to A as we need to consider only 1 way of the journey .??Am I right in my understanding ?
no no bro... !!! A and B are two stations along with 10 others.... so these 12 stations are old stations... now 4 new stations are added.... so the question is how many new tickets can be allotted from/to these new stations from the old stations ....
25353
@amresh_maverick said:
Sumit committed a mistake in finding the LCM of three distinct positive integers greater than 1 namely A, B and C, and found it to be 840, which is a common multiple of A, B and C all, but is not the lowest. The HCF of A, B and C is 1. Find the maximum possible value of A + B + C.
Given :
A,B & C >1
actual LCM
HCF of A,B & C =1 , i.e., A,B and C are co-prime to each other.
max. possible values are 2,3,135.
2.3.135=810 (actual LCM)
therefore 2+3+135=140.
So my ans. would be 140.
25354
@pankaj1988 said:
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
speed of C=30 km/hr.
25355
@pankaj1988 said:
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
Given:
All A , B and C meets at the same time.
Therefore A and B meets after covering the same distance.
90xt=60x(t+3)
=>t=6 hrs.
90xt +60x(t+3) + Cxt=1260
=>x=30 Km/hr.
25356
@amresh_maverick said:
Min value of (x+y^2+z^3) (1/x+1/y^2+1/z^3) for +ve x,y,z
am>=hm

9
25357
The number of points with integer co-ordinates within the circle with radius 6 and center at origin is:
a)24
b)85
c)109
d)114
25358
@saurabhlumarrai said:
The number of points with integer co-ordinates within the circle with radius 6 and center at origin is:a)24b)85c)109d)114
c)109?
25359
@saurabhlumarrai said:
The number of points with integer co-ordinates within the circle with radius 6 and center at origin is:a)24b)85c)109d)114
x^2 + y^2

So,considering the first quadrant alone,we would get 6 + 6 + 6 + 6 + 5 + 4 = 34 points lie in it...
so,(33 - 11)*4 + 21 = 88 + 21 = 109


25360
@saurabhlumarrai said:
The number of points with integer co-ordinates within the circle with radius 6 and center at origin is:a)24b)85c)109d)114
x^2+y^2 =

when x^2+y^2 = 1^2

(0,1);(0,-1);(1,0) and (-1,0)

when x^2+y^2 = 2^2 = 4

(0,2);(2,0);(0,-2) and (-2,0)

when x^2+y^2 = 3^2 = 9

(0,3);(3,0);(0,-3) and (-3,0)

when x^2+y^2 = 4^2 = 16

(4,0);(0,4);(-4,0) and (0,-4)

when x^2+y^2 = 5^2 = 25

(5,0);(0,-5);(-5,0);(0,5);(3,4);(3,-4);(-3,4);(-3,-4);(-4,3);(-4,-3);(4,3) and (4,-3)

when x^2+y^2 = 6^2

(6,0);(0,6);(-6,0) and (0,-6)

so total = 4*3 + 12 = 24 integral points??

@mani0303 @iLoveTorres how are you guys getting 109?? pls elaborate...

25361
@Logrhythm I think u have done to find number of points that lie in the different concentric circles lie inside the given circle...BTW,the question is asked for number of points lie 'inside' the circle...
25362
@mani0303 said:
@Logrhythm I think u have done to find number of points that lie in the different concentric circles lie inside the given circle...BTW,the question is asked for number of points lie 'inside' the circle...
ahh, actually no....what i have done is found the integral points that lie "on" those concentric circles....which is not asked here....

can you explain your method? i did not get what u did and neither am i able to deduce a logic on my own on how to solve this question..
25363
@Logrhythm said:
ahh, actually no....what i have done is found the integral points that lie "on" those concentric circles....which is not asked here....can you explain your method? i did not get what u did and neither am i able to deduce a logic on my own on how to solve this question..
Just usual stuff..like for 1st quadrant,if x = 0,y can take 0 - 5;x = 1,y can take 0 - 5 so on

In those 33 points in the first quad,subtract 11 points which lie in the x and y axes

but to find all points inside the circle,we have multiple by 4 ie 22*4 and finally add those points - 21 that lie in the axes
25364
@mani0303 thanks...got it..
25365
1.Find the no. of non-negative integral solutions to the system of equations x+y+z+t=20
and x+y+z=5

2.Find the no. of integral solutions to |x|+|y|+|z|=15
25366
@maroof10 said:
1.Find the no. of non-negative integral solutions to the system of equations x+y+z+t=20and x+y+z=52.Find the no. of integral solutions to |x|+|y|+|z|=15
if x+y+z+t=20 and x+y+z=5 this are separate questions then the answer would be
1)C(23,3)
2)C(7,2)
if they are one question then t=15 therefore answer would be C(7,2)
25367
@maroof10 said:
1.Find the no. of non-negative integral solutions to the system of equations x+y+z+t=20and x+y+z=52.Find the no. of integral solutions to |x|+|y|+|z|=15
@maroof10 said:
1.Find the no. of non-negative integral solutions to the system of equations x+y+z+t=20and x+y+z=52.Find the no. of integral solutions to |x|+|y|+|z|=15
1) C(7,2) = 21
2)I think one formula is there for this...guess it's 4a^2 + 1 = 901...