Official Quant thread for CAT 2013

@mani0303 said:
It's 150_/2
think again .


In a semicircle with centre O and diameter AB, a parallelogram PQOA is formed where P and Q lie on the circumference of the semicircle. Find the ratio of the area of the semicircle to the area of the parallelogram PQOA.
@amresh_maverick said:
think again .In a semicircle with centre O and diameter AB, a parallelogram PQOA is formed where P and Q lie on the circumference of the semicircle. Find the ratio of the area of the semicircle to the area of the parallelogram PQOA.
pi:_/3 ?
There are 10 identical blocks of cuboid of dimension 2 inches — 3 inches — 5 inches. The blocks are kept one on top of the other in a random fashion to form a structure. How many structures with unique heights can be created using these blocks? (Neglect instability of the structure) NOTE: Two of the flat faces of each cube are parallel to the ground.
@amresh_maverick said:
think again .In a semicircle with centre O and diameter AB, a parallelogram PQOA is formed where P and Q lie on the circumference of the semicircle. Find the ratio of the area of the semicircle to the area of the parallelogram PQOA.
OA :pie /_/3


Volume of a cylinder is only 60% as compared to a cone, while height of the cylinder is 1 cm more than that of the cone. What is the height of the cone so that radii as well as the heights of both the solids have values (in cm) as integers?

a 5 cm
b 4 cm
c 9 cm
d 25 cm
e 7 cm


PS: pata nahi P aise kyun dikh raha hai, it is 3.14
@jaspunit said:
@psk.becks could you plz expalin that?
the p'gram PQOA is a rhombus of each side =r, and the smaller diagonal = r
angle POA = 60 degrees
area = r*r*sin60 ..
@Logrhythm said:
he buys 120 instead of 100 --> 20% profithe sells 108 instead of 120 and gives 25 disc on 120...so he sells 108 at 90here he incurs a loss of 1800/108 = 16.66so overall profit/loss = 20-16.66-(20*16.66/100) = 0.008% profit seems like i made a functional mistake somewhere....what is the OA??
No profit no loss
@amresh_maverick said:
There are 10 identical blocks of cuboid of dimension 2 inches — 3 inches — 5 inches. The blocks are kept one on top of the other in a random fashion to form a structure. How many structures with unique heights can be created using these blocks? (Neglect instability of the structure) NOTE: Two of the flat faces of each cube are parallel to the ground.
30 ??
@amresh_maverick said:
There are 10 identical blocks of cuboid of dimension 2 inches — 3 inches — 5 inches. The blocks are kept one on top of the other in a random fashion to form a structure. How many structures with unique heights can be created using these blocks? (Neglect instability of the structure) NOTE: Two of the flat faces of each cube are parallel to the ground.
30 values of height? 20-50 excluding 49?

regards
scrabbler

@amresh_maverick said:
OA ie /_/3Volume of a cylinder is only 60% as compared to a cone, while height of the cylinder is 1 cm more than that of the cone. What is the height of the cone so that radii as well as the heights of both the solids have values (in cm) as integers?
4 hi hona chahiye .. or i'm missing something important here :neutral:


@amresh_maverick said:
ratio :6/5 AB
bhai approach post kar

@amresh_maverick said:
OA ie /_/3Volume of a cylinder is only 60% as compared to a cone, while height of the cylinder is 1 cm more than that of the cone. What is the height of the cone so that radii as well as the heights of both the solids have values (in cm) as integers? a 5 cm b 4 cm c 9 cm d 25 cm e 7 cm PS: pata nahi P aise kyun dikh raha hai, it is 3.14
@cynara said:
4 hi hona chahiye .. or i'm missing something important here
OA : 4


@raopradeep said:
bhai approach post kar
@amresh_maverick said:
There are 10 identical blocks of cuboid of dimension 2 inches — 3 inches — 5 inches. The blocks are kept one on top of the other in a random fashion to form a structure. How many structures with unique heights can be created using these blocks? (Neglect instability of the structure) NOTE: Two of the flat faces of each cube are parallel to the ground.
min height = 20
every height from 20 to 30 possible by substituting 2 with 3...
next we can have an increase by substituting 3 2's with 3 5's and 2 2's with with 2 3's so as to get .. we can do this till 48... as 48 = 9*5 + 3 .. but 49 cannot be expressed hence 30 numbers...

@scrabbler said:
30 values of height? 20-50 excluding 49?regardsscrabbler
can this be looked the other way as: number of solutions of the equation: 2x+3y+5z=10?
@raopradeep said:
bhai approach post kar
@amresh_maverick said:
OA ie /_/3Volume of a cylinder is only 60% as compared to a cone, while height of the cylinder is 1 cm more than that of the cone. What is the height of the cone so that radii as well as the heights of both the solids have values (in cm) as integers? a 5 cm b 4 cm c 9 cm d 25 cm e 7 cm PS: pata nahi P aise kyun dikh raha hai, it is 3.14
1/3*pi*r1^2*h = 5/3*pi*r2^2*(h+1)
h/h+1 = 5r2^2/r1^2 satisfying for h = 4, r2 = 2 , r1 = 5....so height of the cone = 4?
SOLVE ...

Consider a pyramid with square base, whose side length is l, and height is 10 cm . Find the total surface area of the pyramid if the volume of the pyramid is 1000 cm^3.

Team BV--Pratik Gauri
@bodhi_vriksha said:
SOLVE ...Consider a pyramid with square base, whose side length is l, and height is 10 cm . Find the total surface area of the pyramid if the volume of the pyramid is 1000 cm^3.Team BV--Pratik Gauri
600??
@heylady said:
600??
Post your approach ..
I am waiting for other people to try as well :)

Team BV--Pratik Gauri
@bodhi_vriksha said:
Post your approach .. I am waiting for other people to try as well Team BV--Pratik Gauri
VOlume=1/3 * L^2 * H
L=10 sqrt 3
Lateral height^2= Height^2+ (Base)/(2)^2
Lateral Height= Sqrt 75
Now Surface area= Area of base+4 * area of triangular faces
Area of base= area of square=300

Area of triangular faces= 4* 1/2* sq root 300 * sq root 75
Area of triangular faces= 300
TSA= 300+300= 600
@heylady good .. :)
Now try this one
A circle C is such that it touches two sides of an equilateral triangle as well as the circumcircle of the given triangle. what is the ratio of areas of incircle :circle C: circumcircle.

Team BV--Pratik Gauri