Official Quant thread for CAT 2013

MBA CAT 2024
29025
ABC is an isosceles triangle where AB=AC and BC=60. D is a point on BC such that the perpendicular distance from D to AB and AC is 16 and 32, respectively. What is the length of AB?
29026
@albiesriram said:
12 ko c aa raha hein
kaise? all the eqns in my prev post satisfy the condition in the question...
29027
@Tusharrr said:
how many integers satisfy the inequality∣ 10(x+1)/(x^2+2x+3) ∣≥1?Details : ∣a∣ this line sign is of absolute of a
When x ≥ -1

10(x + 1) ≥ x^2 + 2x + 3
=> x^2 - 8x - 7 ≤ 0
=> 4 - √23 ≤ x ≤ 4 + √23

When x
10(-x - 1) ≥ x^2 + 2x + 3
x^2 + 12x + 13 ≤ 0
-6 - √23 ≤ x ≤ -6 + √23

=> x = [-6 - √23, -6 + √23] U [4 - √23, 4 + √23]

So, 18 integers (-10 to -2 and 0 to 8)
29028
@albiesriram said:
OA for 9,10 is D n A11 &12
for 11 option B)
29029
@albiesriram said:
12 ko c aa raha hein
answer is d

http://math.stackexchange.com/questions/113637/puzzle-the-number-of-quadratic-equations-which-are-unchanged-by-squaring-their

edit: answer is c only, mistakes like these are costly
29030
@zuloo said:
it is clear that point x can't be on the same line as M for the above condition to be true.now let X be on the adjacent line at a distance x from the common point of intersection of lines including the one having M.now,sqrt(x^2+ (l/2)^2)> lwhich means x>sqrt(3)/2*ltherefore, for XM>l1- ((l+sqrt(3)/2*2l)/4l)(3-sqrt(3))/4i hope this helps.

Hi ,
I dint get the italicized portion. Can u plz explain with a diagram or in words only? Thanks

29031
@RDN said:

x2 +x + 1 = 0
ye imaginary root wala quadratic equation..
29032
@albiesriram said:
ye imaginary root wala quadratic equation..

my bad
29033

@psk.becks Q. Point X is randomly selected on the perimeter of a square of length L. M is the midpoint of side . whats the probability that XM> L
A. root 3 /3
B. (3 - (root)3)/3
C. (3 - (root)3)/4
D. (1+(root)3)/4
For this question i am attaching my solution , plz let me know where did i go wrong
29034

Is there an easy way to solve CAGR questions, particularly those ones with CAGR involved? I screw up such calculations. Any advice folks?

29035
There exists a 3-dimensional structure such that at height h the cross section is a square with side length 7sinh+7. If the height of the structure is 4pi, then the volume of the structure can be expressed as a*pi, where a is a positive integer. What is the value of a?
29036

29037

ravi6389

your solutuin is wrong because you assumed that same angles will subtend same lengths on the sides of square...
If you can visualise you will find that an angle (say 1 degree) will subtend larger length on the sides as compared to front....hence the probability for every angle from -30 to +30 will be different ... as the length of MX changes.....
had there been a circle instead of square then ur approach would be correct....since every angle subtends equal lengths on perimeter and hence equal probability...

29038
@psk.becks Thanks man..i am trying to visualize what you told
29039

ravi6389

try this
take a small angle dy.
let the length mx = X
so the length subtented = Xdy
as X changes so does the length subtended
29040
@albiesriram thanks yar
29041
@psk.becks yes you are correct but what i am doing also doesn't seem to be utterly wrong to me..coz i am getting the length of MX = L/sin(theta) so here only sin(theta) will be variable and accordingly X will vary..i have also kept the restriction for it to be applicable to two identical sides....
29042
Find the no of ways in which 10 different balls can be placed in 4 different boxes such that at max 2 boxes are empty.
29043

Find all pairs of positive integers (a,b) satisfying b^3=3a^2+3a+7


29044
@Buck.up said:
Find the no of ways in which 10 different balls can be placed in 4 different boxes such that at max 2 boxes are empty.
4^10 - 1.??