# @vivek417

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###### CATNumber System
prateek7563 Says
A bag contains a total of 105 coins of rs1,50p,25p. find total no. of 1rs coins if there are rs50.5 in bag and it is known that number of 25p coins is 133.33% more than the number of 1rs coins.

U have...the following eqns

x+y+z = 105
x+0.5y+0.25z = 50.5
& z = (233.33/100) x

Solve these in terms of x & y..to get the values..thats all

Thanks
Vivek
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###### CATFact, Inference, Judgement For CAT 2008
1. Seventeen Century englandwas much like the Third World War today, in that a government office was a recognized route to wealth.
2. This parchment shows that the great fortune of that time derived more from what we would now call corruption than from commerce.
3. By the nineteenth ccentury,that had changed:technology had made it possible to create wealth faster than one could steal it.
4.The prototypical rich man of nineteenth century was not a courtier but an industrialist.

My take:-

1) J
2) I
3) J
4) J

Thanks
Vivek
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###### CATofficial quant thread for cat08
Q2) Find the complete range of values of x for which (x^2-7x+13)^x
x
=> ( - infinity , 4 ) ??

(x^2-7x+13)^x => (x^2-7x+13)^x
So x^2-7x+13 x^2-7x+12
(x-3)(x-4)
Hence 3

Thanks
Vivek
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###### CATofficial quant thread for cat08
hiiii plzzzzzz solve these problems
For how many integral values of M is M2( it is M square) +100M+1000 a perfect square ?
ans; 8

m^2 + 100m + 1000 = k^2
(m+50)^2 = k^2 +1500
(m+50-k)(m+50+k) = 1500

Now 1500 = 2^2*3^1*5^3...

So we have 3*2*4 = 24 factors

Now m+50+k should always be greater than 50
& m+50-k should always be less than 50

Use these criteria to filter out the values from 24 factors.....we will get the answer

Thanks
Vivek
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###### CATofficial quant thread for cat08

Q) If sin q and cos q are the roots of the equation ax^2+bx+c=0,then a,b,c are related as:
a) a^2+b^2+2ac=0
b) a^2-b^2+2ac=0
c) b^2+c^2-2ac=0
d) a^2-c^2+2ab=0

Here we have sin q + cos q = -b/a

& sin q * cos q = c/a

Now for the options....divide throughout by a^2....
like a^2-b^2+2ac=0

divide by a^2 then we have 1 - (b/a)^2 + 2*(c/a) = 0....now put the values & check.....thats it

Thanks
Vivek
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###### CATofficial quant thread for cat08
Q) Which pair of point slie on either side of the line 3x+2y-6=0?
a) (0,-7),(-7,-8]
b) (0,0),(2,3)
c) (1,1),(-1,-4)
d) (-1,1),(-2,-2)

Clearly only b satisfies the criteria. (0,0) gives negative result while (2,3) gives positive.

Thanks
Vivek
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###### CATofficial quant thread for cat08

2) Find the sum of all the four didgits number that can be formed with the didgits 3,2,3,4?

Here is my solution....

Sum of all numbers formed by n digits (a,b,c,d...n) = (n-1)! * (Sum of all digits) * 11...n times

So here we have 3! *(2+3+3+4) * 1111 = 79992

But since we have 2 3's...so total sum 79992/2 = 39996

Thanks
Vivek
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###### CATofficial quant thread for cat08

2. If the X-Y plane, what is the area of the region bounded between the two curves
f(x)=max(x-1,1-x)-1 and g(x)=min(x+2,-2-x)+3?

1. 2 sq units 2. 2.5sq units 3. 3 sq units 4.3.5 sq units
ans is 3.5
I am not getting the region....

I am getting answer as 3.5.

Lines are as follows:-

y=-x
y=-x+1
y= x-2
& y= x+5

So area = (7/2)*(2)^0.5 * (1/2)*(2)^0.5 = 7/2 =3.5

Thanks
Vivek
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###### CATofficial quant thread for cat08
hi bhai,
i am unable to visualise the figure...

Let the triangle be ABC & square be MNOP...

Here M lies on AB while P lies on BC.

Let side of square = x
So Sin 60 = x/BM

BM = 2x/root(3)

AMN is equilateral triangle...clearly visible

So AM = x

But BM + AM = 1
So 2x/root(3) + x = 1

Solve this to get the answer.

Thanks
Vivek
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