difficult problems

2.)

n --> 10-99
question --> n <80>80.
for x= 1, y= 6 i.e 16, x+y = 7 = prime, hence n<80> prime

for x =8, x is not prime and hence n is not prime.
for x =9, x is not prime and hence n is not prime.

hence x will be 7, 5, 3 ,2 or 1.
for all these cases n<80. Hence this condition is sufficient.

3.) 1,-3,2,5,-4,-6

variance = consecutive number product is negative.
1*-3=-ve
-3*2=-ve
5*-4=-ve
For all other cases it is positive

Hence variance = 3

4.) equilateral triangle divides circle in three equal parts.
hence arc ab = arc bc = arc ca
now arc abc = 24.
arc abc = arc ab + arc bc = 2 arc ab = 2 arc bc = 2 arc ca = 24
=> arc ab = arc bc = arc ca = 12
perimeter = pi * d = arc ab + arc bc + arc ca = 12+12+12 = 36
=> d = 36/pi = 11(approx)

anksanks wrote:1.)

districts = 11
to find minimum population in one, we assume other 10 to be maximum.
maximum = 10% more then minimum
let minimum in 1 = x.
then each of other ten will be x + 10% x = 1.1 x
now total = 132,000

hence minimum + ten maximum = 132000
x+10(1.1)x=132,000
=> x= 11,000

Can you try the geometry problem posted by "sudhir" in the same post. Any insight is appreciated.

Thanks.

anksanks wrote:3.) 1,-3,2,5,-4,-6

variance = consecutive number product is negative.
1*-3=-ve
-3*2=-ve
5*-4=-ve
For all other cases it is positive

Hence variance = 3

4.) equilateral triangle divides circle in three equal parts.
hence arc ab = arc bc = arc ca
now arc abc = 24.
arc abc = arc ab + arc bc = 2 arc ab = 2 arc bc = 2 arc ca = 24
=> arc ab = arc bc = arc ca = 12
perimeter = pi * d = arc ab + arc bc + arc ca = 12+12+12 = 36
=> d = 36/pi = 11(approx)

Thanks

sudhir3127 wrote:can u explain how u got 12 when the length of the arc is given as 24?

The Arc is A to B then B to C, a length of 24. This is 2/3 of the circle.

This implies 12 + 12 + 12

jslavi01 wrote:

sudhir3127 wrote:can u explain how u got 12 when the length of the arc is given as 24?

The Arc is A to B then B to C, a length of 24. This is 2/3 of the circle.

This implies 12 + 12 + 12

Well I think this problem can be solved in more than one way and can give different approximate solutions.

I think both the methods ( 1st method : 1/3*2 pi r and 2nd method: perimeter 12+12+12 = 2 pi r) are correct, unless someone can suggest otherwise.

But my understanding of chords and arcs has become more clear e.g. the ratio of sides of a triangle inscribed in the circle will be equal to to ratio of arc formed by the same chords.

Thanks everyone for their initiative. I hope this helps everyone.

He got 12 because the triangle is equilateral.

If the distance from AB = BC = CA are equal

The the arcs from AB = BC = CA are equal.

Since you want to find the diameter, it helped me by using

Circumference = PI*D = 2*PI*r

Circumference = PI* D = 36 (12 + 12 + 12)

PI can be estimated at little more than 3, which would give you a little less than 12 for your answer (C)