Official Quant thread for CAT 2013

@sumit99 said:
Mr praveen has to build a wall 1000 meters long in 50 days. he employs 56 men but at the end of 27 days finds only 448 meters are built. How many more men must be employed so that the work may be finished in time?
-> [448/(56*27)] *23x =552

X=81
-> 81-56=25
@YouMadFellow said:
56 men built 448 meters in 27 days => 1 man builds 8 meters in 27 days=> 1 man builds (8/27) meters in 1 dayNow, remaining = 1000 - 448 = 552So, 552/[(8/27)*23] = Total men required after that = 81 So, extra men required = 81 - 56 = 25 ?
552/[(8/27)*23] i do not get this step??
@Aman.Malhotra said:
-> [448/(56*27)] *23x =552X=81-> 81-56=25
cud u explain it 4m the basics or step by step?
@sumit99 said:
Mr praveen has to build a wall 1000 meters long in 50 days. he employs 56 men but at the end of 27 days finds only 448 meters are built. How many more men must be employed so that the work may be finished in time?
56*x*27 = 448
=> x = 448/1512

23*(56 + x)*448/1512 = 552

=> x = 25
@sumit99 said:
cud u explain it 4m the basics or step by step?
If 448 units can be made by (56*27) ManDays than how many man X is requred to make rest 552 [1000-448] units.

[448/(56*27)] *23x =552

X=81
81-56[already men available ]=25
required



Find the area of right angle triangle whose inradius is 4 and circumradiusis 10?
Explain with Detail
@jain4444 said:
56*x*27 = 448 => x = 448/1512 23*(56 + x)*448/1512 = 552 => x = 25
hw this underlined equ comes ??? what is the formula u used here??
@Aman.Malhotra said:
If 448 units can be made by (56*27) ManDays than how many man X is requred to make rest 552 [1000-448] units.[448/(56*27)] *23x =552X=8181-56[already men available ]=25 requiredFind the area of right angle triangle whose inradius is 4 and circumradiusis 10?Explain with Detail
[448/(56*27)] *23x hw u wrote this part?????
A train weighs 1800 tons. The train resistance is constant at 12 pounds per ton. If 700 horsepower are available to pull this train up a 2% grade, what will be its speed in miles per hour?
There are three three pairs of real numbers (x1,y1), (x2,y2), and (x3,y3) that satisfies both x³ - 3xy² = 2005 and y³ - 3x²y = 2004.
Compute:
(1 - x1/y1)(1 - x2/y2)(1 - x3/y3).
@Aman.Malhotra said:

Find the area of right angle triangle whose inradius is 4 and circumradiusis 10?Explain with Detail
There is a direct formula for this, but still:

ABC with right angle at B. (D,E,F are the points where incircle meets the sides AB, BC, CA)

Area of triangle = (1/2)*(r)*( AB + BC + CA)

BE = BD = r, AD = y, AF = y, FC = 2R - y, CE = 2R - y,
AB = r + y, BC = 2R + r - y , CA = 2R

Area = (1/2)*(r)*(r + y + r - y + 2R + 2R) = r*(r + 2R)
=> Area = (4)*(4 + 20) = 96 ?
if x and y are real numbers, then solve the equation x√(y-1)+y√(x-1) ­=xy.
@jain4444 said:
There are three three pairs of real numbers (x1,y1), (x2,y2), and (x3,y3) that satisfies both x³ - 3xy² = 2005 and y³ - 3x²y = 2004.Compute:(1 - x1/y1)(1 - x2/y2)(1 - x3/y3).
Subtracting, we get (x-y)^3 = 1 => (x - y) = 1

=> 1 - (x/y) = -1/y

Converting one of the equations to equation in y
=> y^3 - 3(1 + y)^2 * y = 2004
=> y^3 - 3( y^2 + 2y + 1)*y = 2004

2y^3 + 6y^2 + 3y + 2004 = 0
-> y1*y2*y3 = -2004/2 = -1002

So, (-1/y1)*(-1/y2)*(-1/y3) = 1/1002 ?

@jain4444 said:
if x and y are real numbers, then solve the equation x√(y-1)+y√(x-1) ­=xy.
@jain4444 bhai options batado upar walo ke..

take y-1=t^2
x-1=k^2 and proceed,get.
t/y+k/x = 1
x,y = 2,2 satisfy ?
@jain4444 said:
S is the set of nonnegative integers. It can be divided in 2012 distinct subsets ,each containing equal number of elements and the elements of each subsets add up to the same Number. What is the minimum possible integer which is the largest element in S?
is it 4025 ? options ?
@sumit99 said:
Mr praveen has to build a wall 1000 meters long in 50 days. he employs 56 men but at the end of 27 days finds only 448 meters are built. How many more men must be employed so that the work may be finished in time?
x= 56.27.552 / 448.23
81-56=25 more men needed
@YouMadFellow said:
Subtracting, we get (x-y)^3 = 1 => (x - y) = 1=> 1 - (x/y) = -1/yConverting one of the equations to equation in y=> y^3 - 3(1 + y)^2 * y = 2004=> y^3 - 3( y^2 + 2y + 1)*y = 20042y^3 + 6y^2 + 3y + 2004 = 0-> y1*y2*y3 = -2004/2 = -1002So, (-1/y1)*(-1/y2)*(-1/y3) = 1/1002 ?
@sujamait said:
@jain4444 bhai options batado upar walo ke..take y-1=t^2x-1=k^2 and proceed,get.t/y+k/x = 1x,y = 2,2 satisfy ?


perfect
@sujamait said:
is it 4025 ? options ?

solution given by chill sir

its 4023

0 + 4023 = 1 + 4022 = 2 + 4021........ = 2012 + 2011


A 3x3 square is partitioned into 9 unit squares. Each unit square is painted either white or black with each color being equally likely, chosen independently at random. The square is then rotated 90 degrees clockwise about its center, and every white square in a position formally occupied by a black square is painted black. The colors of the other squares are left unchanged. What is the probability that the grid is now entirely black?
@jain4444 said:
perfect solution given by chill sir its 4023 0 + 4023 = 1 + 4022 = 2 + 4021........ = 2012 + 2011A 3x3 square is partitioned into 9 unit squares. Each unit square is painted either white or black with each color being equally likely, chosen independently at random. The square is then rotated 90 degrees clockwise about its center, and every white square in a position formally occupied by a black square is painted black. The colors of the other squares are left unchanged. What is the probability that the grid is now entirely black?
kuch jayada hee fundu Q hein,Oye boy Charlie
total cases = 2^9 = 512
favourable cases,here..
I - F
1 - 7
2 - 4
3 - 1
4 - 8
5 - 5
6 - 2
7 - 9
8 - 6
9 - 3
I are replaced by F
now,to be all backi ..
1.if any on F side is white then it respective partner on I side has to be black
2.if it is black then I side also has to be black
5 -5 has to be black only..
So,when 1 white on F side... 8C1
when 2 white on F side ..8C2
likewise...8C8
so,
P=8c1 + ..8c8 / 512 = 2^8-1 / 512 ?
...........................
@sumit99 said:
Mr praveen has to build a wall 1000 meters long in 50 days. he employs 56 men but at the end of 27 days finds only 448 meters are built. How many more men must be employed so that the work may be finished in time?
work done by 1 man in 1 day =448/56*27 = 8/27 m
now
552m of wall is to be built in 23 days
so
23*[8/27]*[56+x]=552
x= 25
@sujamait ...kaise ho bhai...tayyari kasi chal rahi hain XAT ki
@jain4444 said:

A 3x3 square is partitioned into 9 unit squares. Each unit square is painted either white or black with each color being equally likely, chosen independently at random. The square is then rotated 90 degrees clockwise about its center, and every white square in a position formally occupied by a black square is painted black. The colors of the other squares are left unchanged. What is the probability that the grid is now entirely black?
49/512? :neutral:
@sujamait sir k answer dekh k lag raha h ki I did a complete disaster :/
@vijay_chandola said:
49/512? @sujamait sir k answer dekh k lag raha h ki I did a complete disaster :/
aisa kuch nhn hai @vijay_chandola share logic...galat ho sakta hai mera bhi...