Official Quant thread for CAT 2013

MBA CAT 2024
16103
@ishu1991 said:
Solve the eq.(x^4)-2(x^3)+4(x^2)+6x-21=0,if two of its roots are equal in magnitude and opposite in sign.
roots be ---- a, -a, b, c
b+c = 2
-a2 + ab + ac + (-ab) + ac +bc = 4
bc - a2 = 4
a2bc = 21

solving -- a2( 4 + a2) = 21
=>a2 = 3 => a = root 3
bc = 4 + 3 = 7
solving dis with b + c = 2
b = 1+isqrt(6)
c = 1-isqrt(6)

16104
@hatemonger said:
@mailtoankit Ge sir... wnt it be 56??
solution post karo..
16105
@mailtoankit I am not sure about 56 0r 55 is liye to apse pucha ap solution bata do to doubt ho jayega mera ..
16106
@mailtoankit ya ya sir got it thanks...
16107
@bs0409 said:
Is it 5/2???Has to be done by assuming the altitudes of the three triangles
how ?? plz elaborate it !!!
16108
how many distinct rectangles of perimeter not more than 258 cm can have both length and breadth as positive integers when expressed in cms ??
16109
@techgeek2050

16110
@swapnil4ever2u said:
how ?? plz elaborate it !!!
Let Height of Triangle ADE be h1, Height of Triangle,MDE be h2 and Height of Triangle BMC be h3

Now from similarity of ADE and ABC DE/BC =h1/h1+h2+h3
And from similarity of MDE and MBC DE/BC = h2/h3

h1/h1+h2+h3 = h2/h3

h1+h2+h3/h3 =h1/h2

Also;

Area of ADE/Area of MDE= 1/2*h1*x / 1/2*h2*x
=h1/h2=7/3

therefore h1+h2+h3/h3 = 7/3

3h1+3h2+3h3 = 7h3

3h1+3h2 =4h3

3h1/h2 + 3 = 4h3/h2

3 * 7/3 +3 = 4h3/h2
10 =4h3/h2

h2/h3 =2/5
16111
@mailtoankit said:
55?x + y + z = 90x - y/2 - z/4 = 5 -----> x = 5 + y/2 + z/4...putting this value in first eqn5 + y/2 + z/4 + y + z =906y = 350 - 5zy = 350 - 5z/6for y to be max z will be minfor z = 4y = 350 - 5(4)/6 = 55@hatemonger
if i eliminate z from the 2 equations, i get
5x - y = 110
y = 5x - 110

isn't there any way to proceed after this ?
16112

The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volume of cone to cube.

#please provide the explanation.
16113
@somnathbhatta said:
The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volume of cone to cube.#please provide the explanation.
is the OA (pi/12)?
16114
@somnathbhatta said:
The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volume of cone to cube.#please provide the explanation.

laregest cone that can be frmed from the cube of side 7 cm is when side of cube is diameter of cone and side of cube is height of cone
so for cone radius is 7/2 and height is 7 cm volume is 1/3*22/7*7/2*7/2*7
volume of cube is 7*7*7
so ratio is 11:42

16115
@ishu1991 said:
laregest cone that can be frmed from the cube of side 7 cm is when side of cube is diameter of cone and side of cube is height of cone so for cone radius is 7/2 and height is 7 cm volume is 1/3*22/7*7/2*7/2*7volume of cube is 7*7*7 so ratio is 11:42
the OA is correct.
please explain why the height=side of cube ?
16116

@somnathbhatta said:
the OA is correct. please explain why the height=side of cube ?

think yourself when u put ur standing cone in to cube ur height will be same as standing side of cube
16117
@somnathbhatta said:
The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volume of cone to cube.#please provide the explanation.
11:42?

radius of cone = 7/2
height of cone = side of cube = 7

1/3*pi*(7/2)^2*7/(7)^3 = 11/42
16118
@somnathbhatta said:
The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volume of cone to cube.
#please provide the explanation.
radius of cone=7/2 cm
height of cone=7 cm
ANS=(1/3)*pi*(7/2)*(7/2)*7 : 7*7*7
=pi/12
16119
At a party some couples were invited.Out of them only 23 couples were having one child per couple with them.When I observed it I found 13 men were without any children and 20 women were also without any children.It is known that only couples are allowed to attend the party.Total number of couples at the party were
a.28
b.30
c.33
d cbd
16120
@bs0409 said:
At a party some couples were invited.Out of them only 23 couples were having one child per couple with them.When I observed it I found 13 men were without any children and 20 women were also without any children.It is known that only couples are allowed to attend the party.Total number of couples at the party werea.28b.30c.33d cbd
Is it 28??
23 children mean 23 couples
but 13 men and 20 women do not hv children...this means 28-20=8 women have children and 28-13=15 men have children..
hence 15+8=23 couples have children (23)...
16121
@Logrhythm said:
Is it 28??
23 children mean 23 couples
but 13 men and 20 women do not hv children...this means 28-20=8 women have children and 28-13=15 men have children..
hence 15+8=23 couples have children (23)...
Where are u using the fact that only couples are allowed to attend the party???
16122
@bs0409 said:
Where are u using the fact that only couples are allowed to attend the party???
then the question has incosistent data, how does 13 men and 20 women make sense? it can only be back tracked using options....pl let me knw if the answer is wrong or you have a different explanation..