1.) (E) 159
sum of numbers till n = n(n+1)/2 , sum of even numbers will be almost half of this i.e. n(n+1)/4 .
so if S = 79.80, then n= 159.
2.) (E) 5.60
3.) (C) 3 , with 2 we will have exactly 50%, so for more than 50% should be 3.
4.) AB + CD = AAA
adding 2 2 digit numbers is giving a 3 digit number. So hunderds digit of the 3 digit number has to be 1
so it becomes 1B + CD = 111
B cannot be 1, CD cannot be 99 (they are distinct)
so CD can take any value from 98 to 92.
So (E) Cannot be determined
5.) (A) 12 ( and A's comes to 18)
6.) (A) 2/27
7.) (A) 1.4
eqn of circle = x^2 + y^2 = 1, center = (0,0) radius = 1
min dist of line from circle = dist of line from the center - radius
Make the distance of the line from the circle to be 0 and we see that it becomes a tangent to the circle.
Now we know if we draw a line from the center to the point where the tangent touches the circle the line and the tangent are perpendicular to each other.
So we need to find the equation of this line first.
We can take the line back where it was now
Since the lines are perpendicular m1 x m2 = -1
m of line = 3/4
so slope of the new line = -4/3
Since the line passes through the origin (center of circle) its eqn => y=-4/3x
now we need to get the point of intersection of our two lines, which comes out to be (36/25,-48/25)
now get the distance of this point from the origin and subtract the radius from it.
Comes to 1.4 (may have made calculation errors )
So A.
8.) (B) 25 (values will be like 45,45,45,45,70)
9.) (A) 25% , to be divisible by 8 the number needs to have 3 2s in it. Only a multiple of 4 can provide that. Number of numbers divisible by 4 = 96/4 = 24. So P(8) = 24/96 = 25% .
10.) A + 25 , each of the new 5 consecutive numbers are going to be 5 more than the prev 5 consecutive numbers.
great work Bunuel