Official Quant thread for CAT 2013

MBA CAT 2024
11461
@gautam22 said:
yes sir if we draw a tangent at C(construction) parallel to AB
to draw tangent at C, draw perpendicular bisectors of both line, they will intersect at center, join center and C, now draw a line perpendicular to this line, that would be the tangent at C

i doubt this is what u wanted
11462
@gautam22 said:
can we draw a tangent parallel to AB in d attached figure,then d line joining the mid point of AB , centre of circle and point C all lie on d same straight line........can we do that....PFA the figure@chillfactor sir @krum sir
This will be possible only if C lies on the perpendicular bisector of AB.
11463

A grocer uses a weighing balance in which one pan is 0.5 kg and other 0.75kg. He puts a certain quantity of food grains in 0.5kg pan and finds the weight as a two digit no. however as the customer insists he puts 0.75 kg pan. now indicated weight is 9.5 kg more than the weight which is obtained by reversing the digits of previous weight. which of the following cannot be the actual weight of food grains

43.25
36.25
41.5
more than one of the above


11464
@Cat.Aspirant123

Join C and F..D and C.. & also A and E..

Now, Angle AEF=180-70 = 110 [Coz ADFE is a cyclic quadrilateral, & Angle FDA and Angle AEF are opposite]..

Again, Angle CAF = Angle EFA[Pair of alternate angles, coz AC is parallel to EF]...(i)

Now, In Triangle CDA, Angle CDA=90..Therefore, Angle CDF=90-70=20..

Now, Angle CDA=Angle CAF[Since CF is the common line and angle subtended by it on the arc are equal]..

Thus, Angle CAF=20..and, Angle EFA=20 degrees..(From Eqn i)

11465
@sparklingaubade said:
Sixteen students took part in a math competition where every problemwas a multiple choice question with four choices. After the contest, it is found that any twostudents had at most one answer in common. Determine the maximum number of questions.
I think 81 will be the maximum
1 answer common to all, so rest 5 will be different for all
=> 5*16 + 1 = 81 questions (at most)

EDIT:- This is incorrect, I don't know how but some how I mixed up two different questions
11466
@chillfactor said:
I think 81 will be the maximum1 answer common to all, so rest 5 will be different for all=> 5*16 + 1 = 81 questions (at most)
sirji thoda ache se explain kardo..thoda understand nhn ho paya..ty..
11467
x and y are natural numbers such that they satisfy the equation x + y + 31 = 2xy. Find the maximum possible integral power of 6 in (xy)!.[n! is the product of the first €˜n €™ natural numbers.]..
11468
@badwal.aman said:
x and y are natural numbers such that they satisfy the equation x + y + 31 = 2xy. Find the maximum possible integral power of 6 in (xy)!.[n! is the product of the first €˜n €™ natural numbers.]..
14?
11469
@maddy2807 expalin kar do..
11470
@badwal.aman said:
@maddy2807 expalin kar do..
given equation is
x+y+31= 2xy

Modify this equation, to
(2x-1)(2y-1)= 63

63 can be factored in two ways.
CASE I: 9*7
2x-1=9
=> x=5
2y-1=7
=> y=4
so xy= 20

CASE II: 63*1
2x-1=63
=>x=32
2y-1=1
=> y=1
xy= 32

Hence form CASE II we have 32 as the value of xy which is maximum
now to find the maximum power of 6 that can divide 32! is equivalent to maximum power of 3 which can divide 32!
Hence, 14.
11471
@gautam22 said:
sir ye (xy)!.....x*y hai ya 10x+y?
x*y hai
11472
@sparklingaubade said:
Find the set of all positive integers n with the property that the set fn; n +1; n + 2; n + 3; n + 4; n + 5g can be partitioned into two sets such that theproduct of the numbers in one set equals the product of the numbers in theother set.
3 cases possible

Case->1 3k,3k,3k+2,3k+2,3k+1

Case->2 3k ,3k,3k+1,3k+1,3k+2

Case ->3 3k+1,3k+1,3k+2,3k+2,3k

For Case 1 and case 3 ,3k+1 and 3k+2 is possible but for Case 2 no such case is possible
11473
@badwal.aman said:
x and y are natural numbers such that they satisfy the equation x + y + 31 = 2xy. Find the maximum possible integral power of 6 in (xy)!.[n! is the product of the first €˜n €™ natural numbers.]..
2xy-x-y-31=0

4xy-2x-2y-62=0

(2x-1)*(2y-1)=63

(2x-1)*(2y-1)=1*63,3*21,7*9

(x,y)=(1,32)

32!
Power of 3 in 32 is 10+3+1=14
11474

A man swims from A to B and back in 4.5 hours . A block of wood when allowed to go with stream from A to B takes 6 hours . What is the ratio of speed of man in still water to that of the stream to the stream ? OA is 3:1 can anyone explain the how the solution is arrived at ?

11475
@dream_IIMA said:
A grocer uses a weighing balance in which one pan is 0.5 kg and other 0.75kg. He puts a certain quantity of food grains in 0.5kg pan and finds the weight as a two digit no. however as the customer insists he puts 0.75 kg pan. now indicated weight is 9.5 kg more than the weight which is obtained by reversing the digits of previous weight. which of the following cannot be the actual weight of food grains43.2536.2541.5more than one of the above
for 43.25
1st weight = 43.25-.25 = 43
2nd weight = 43.25+.25 = 43.5

34+9.5=43.5 , so condition satisfied

for 36.25
1st weight = 36.25-.25 = 36
2nd weight = 36.25+.25 = 36.5
condition not satisfied

similarly for 41.5, condition won't be satisfied

so , more than one of the above ?
11476
@sparklingaubade said:
Twelve knights sit around a round table. Every knight hates the twoknights sitting next to him, but none of the other nine knights. A task groupof fve knights is to be sent to save a princess in trouble. No two knights who hate each other can be included in the group. In how many ways canthe group be selected?x_x_x_x_x_ a+b+c+d+e = 2=15but it is wrong, can anybody explain why I am getting wrong??
12* 9c4 = 1512 ?? (considering a group of 5)
11477
@rags-at-work said:
A man swims from A to B and back in 4.5 hours . A block of wood when allowed to go with stream from A to B takes 6 hours . What is the ratio of speed of man in still water to that of the stream to the stream ? OA is 3:1 can anyone explain the how the solution is arrived at ?
let distance - D
speed of man - m
speed of stream - s

D/(m+s)+D/(m-s)=4.5
D/s=6

==> 6s/(m+s)+6s/(m-s)=4.5
==> 12ms/(m^2-s^2)=4.5
==> 12m/s=4.5m^2/s^2-4.5

take m/s as x
==> 3x^2-8x-3=0
==> x=3

so m:s=3:1
11478
@rags-at-work said:
A man swims from A to B and back in 4.5 hours . A block of wood when allowed to go with stream from A to B takes 6 hours . What is the ratio of speed of man in still water to that of the stream to the stream ? OA is 3:1 can anyone explain the how the solution is arrived at ?
Let the distance of A to B is L.
Speed of man X
Speed of Stream Y
and the ratio between X and Y be k
Now by given conditions
L/(x+y) + L/(x-y)= 4.5.....Eq 1
L/y = 6......Eq 2.
From eq 1 .. 2xL/(x^2-y^2)= 4.5
and frm eq 2....L/y= 6
divide both the equations you shall get a quadritic equation ...substiute X=YK in the quadritic
u shall get 3k^2 - 8k - 3= 0
1 value of k shall be 3 or the ratio 3:1 ...
11479
@rags-at-work said:
A man swims from A to B and back in 4.5 hours . A block of wood when allowed to go with stream from A to B takes 6 hours . What is the ratio of speed of man in still water to that of the stream to the stream ? OA is 3:1 can anyone explain the how the solution is arrived at ?
d= dist from A to B
u= speed of man
x= speed of stream

d/(u+x)+d/(u-x)=4.5
d/x=6
d=6x

so...6x/(u+x)+6x/(u-x)=4.5
put u=3...x=1
these values will satisfy the above eqn
11480
@rags-at-work said:
A man swims from A to B and back in 4.5 hours . A block of wood when allowed to go with stream from A to B takes 6 hours . What is the ratio of speed of man in still water to that of the stream to the stream ? OA is 3:1 can anyone explain the how the solution is arrived at ?
x/(u-v)+x/(u-v)=4.5

x/v=6

12uv/(u^2-v^2)=4.5

4.5u^2-4.5v^2-12uv=0
9u^2-9v^2-24uv=0
(9u+3v)*(u-3v)=0
u=3v