Official Quant thread for CAT 2013

MBA CAT 2022
2081
@soham2208 said:
Why w and y are not equal ?
because from the equation we can conclude that w=x=z

So wy cant be equal and only possiblities are 1,4 or 4,1 in all cases sum is 5^2= 25
2082
@Torque024 said:
The length, breadth and height of a cuboid are given by unique linear functions L(x), B(x) and H(x) respectively (Here, 'x' is a real number). The volume of this cuboid is given by the cubic function V(x) = – x^3 – 4x^2 + 31x + 70. Which of the following values of 'x' is permissible? (1) 7 (2) – 3 (3) – 8 (4) 6 (5) 4
V(x) = – x^3 – 4x^2 + 31x + 70
v(x)=(x+2)(x+7)(5-x)

permissible value= 4

5)4
2083
@mbajamesbond said:
P is a group of four numbers 1, 2, 3 and 1. In every step, 1 is added to any two numbers in group P. In how many such steps is it possible to make all the four numbers in group P equal?a3 b5 c7 dNot possible
oa D Not possible
2084
@Torque024 said:
The length, breadth and height of a cuboid are given by unique linear functions L(x), B(x) and H(x) respectively (Here, 'x' is a real number). The volume of this cuboid is given by the cubic function V(x) = – x^3 – 4x^2 + 31x + 70. Which of the following values of 'x' is permissible? (1) 7 (2) – 3 (3) – 8 (4) 6 (5) 4
4 ? not sure
2085
@Torque024 said:
The length, breadth and height of a cuboid are given by unique linear functions L(x), B(x) and H(x) respectively (Here, 'x' is a real number). The volume of this cuboid is given by the cubic function V(x) = – x^3 – 4x^2 + 31x + 70. Which of the following values of 'x' is permissible? (1) 7 (2) – 3 (3) – 8 (4) 6 (5) 4
V(x) = (5-x)*(x + 7)*(x+2)

=> x -2 as length, breadth, height should be positive => option 5 ?
2086
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?
A) 503 B) 640 C) 724 D) 758 E) 1013
2087
@Torque024 said:
The length, breadth and height of a cuboid are given by unique linear functions L(x), B(x) and H(x) respectively (Here, 'x' is a real number). The volume of this cuboid is given by the cubic function V(x) = – x^3 – 4x^2 + 31x + 70. Which of the following values of 'x' is permissible? (1) 7 (2) – 3 (3) – 8 (4) 6 (5) 4
4 ??
2088
@krum said:
like this@wovfactorAPS iska bhi graphical approach bata dijiyeTwo points A and B are selected on a straight line segment of length 10cm. What is the probability that length(AB)>4cm .1)5/242)9/253)3/84)4/15
@pankaj1988 explained it clearly

a square with X AND Y as its axis

x-y>=4 and y-x>=4 ..u have to do that 2 times as we can start the origin from two ends...

regarding the foot of the perpendicular question .. the following would be helpful..

length of the foot of perpendicular from( x1,y1) to (ax+b+c=0)

is |ax1+by1+c|/rt(a^2+b^2)

wen the point is origin length=|c|/rt(a^2+b^2)
2089
@mbajamesbond said:
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?A) 503 B) 640 C) 724 D) 758 E) 1013
e??
2090
@mbajamesbond said:
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?A) 503 B) 640 C) 724 D) 758 E) 1013
10c2+10c3..10c10-(8c1+8c2..8c8)
2091
@mbajamesbond said:
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?A) 503 B) 640 C) 724 D) 758 E) 1013
Case 1 : John goes

Number of groups = 2^8 = 256

Case 2: John doesn't go

Number of groups = 2^9 - 9C0 - 9C1 = 502

Total groups = 758 ?
2092
@mbajamesbond said:
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?A) 503 B) 640 C) 724 D) 758 E) 1013
john doesn't goes to match - 9c2+9c3+..+9c9=2^9-1-9
john goes - 8c0+8c1+8c2+..+8c8=2^8

so 502+256=758
2093
@mbajamesbond said:
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?A) 503 B) 640 C) 724 D) 758 E) 1013
when 2=10C2 -1
when 3=10C3 - 8C1
when 4=10C4 - 8C2
when 5=10C5 - 8C3
.
.
.
.
when 9 = 10C9 - 8C7
2094
@mbajamesbond said:
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go. How many different groups of at least two boys are therethat can go to see the match?A) 503 B) 640 C) 724 D) 758 E) 1013
2 cases -

john & piet are selected

then , 8c1 + 8c2 + .....8c8 => 2^8-1 => 255

john & piet not selected

then, 8c2 + 8c3 +..........8c8 => 2^8-9 => 247

thus, 503 ?
2095
Find the least possible value of a+b,where a,b are +ve integers such that 11 divides a+13b and 13 divides a+11b.
2096
@mbajamesbond said:
when 2=10C2 -1when 3=10C3 - 8C1when 4=10C4 - 8C2when 5=10C5 - 8C3....when 9 = 10C9 - 8C7
explain karna yar
2097
@mbajamesbond bhai 5 ?? b=6 aur a=-1
2098
@Brooklyn said:
explain karna yar
There are 10 boys in a class. On Saturday an important match will be played in the city.The boys that will go to watch the game will go as one group. If John will go to watch,then Piet will certainly also go.

Now the min no. os students has to be 2 with the exception of john and piet.

So 1 group can be choosen by

when 2=10C2 -1

Similary when the 3rd friend joins in

when 3=10C3 - 8C1

And so on until the last student

when 4=10C4 - 8C2
when 5=10C5 - 8C3

How many different groups of at least two boys are therethat can go to see the match?



when 9 = 10C9 - 8C7
2099
@sauravd2001 said:
@mbajamesbond bhai 5 ?? b=6 aur a=-1
which question?
2100
@mbajamesbond least possible value wale ka