Q1
2008/2 = 1004
1004/2 = 502
502/2 = 251
=> 2008 = 2*2*2*251
Now let's search for the divisor of 251. Try 251 / {2;3;5;7;11;13}
We stopped at 13 because 251 < 16² and we know that it won't be divided by 14,15,16.
So we found none divisor => 251 is a prime number.
The last result 2008 = 2*2*2*251
=> his 8 divisors is
2
2*2
2*2*2
2*2*2*251
1
251
251*2
251*2*2
Q2
There are 2 ways to do it, one is to convert all to base 10, add then convert back to base 8, one is to convert all to base 8 then add
I'd do the 2nd, since i know how to add numbers in base 8. If you don't do 1st method
132(4) = 1*16 + 3*4 + 2 = 2*8 + 14 = 3*8 + 6 = 36(8)
1011(2) = 1*8 + 0*4 + 1*2 + 1 = 1*8 + 3 = 13(8)
=> 66(8) + 36(8) + 13(8) = 137(8)
Q3
M = 5*X + 2
N = 5*Y + 4
M+N = 5*(X+Y) + 6 = 5*(X+Y) + 5+1 = 5*(X+Y+1) + 1
=> 1
Q4
each boy has many sisters as brothers
=> even number of sister&brother
=> nb of children: X = 1 + A + A
A = number of girl
A+1 = number of boy
the possible couples (boy,girl) are: (1,0),(2,1),(3,2),(4,3),...,(A+1,A)
twice brother as sister
=> A+1 = 2(A-1)
=> A=3
the couple is (4,3) (a girl has 4 brothers and 2 sisters and a boy has sister=brother)
Nb children = 7
Q5
Easiest clue: the boy in white shirt... => 1 boy is white shirt, other boy is black (different color) otherwise there won't be solution
Need a table to resolve this problem. (there is no method)
(a)3 whites 2 blacks
(b)2 couples possible (white,black) or (black,white). Let's randomly choose the 1st and go on
(c)(white,white) or (black,black). It must be white,white since one of the guy from (b) chose black, it cant be 3 blacks
(d)same gender, let's say male,male. But if carry is male and wear black shirt, pita must be male and wear white shirt
But if Pita wear white, we got 4 whites so not work. Try girl,girl (make sure you draw a table to see what i'm talking about)
(e)Let's say miken boy, jamie girl. The rest (Bary) is boy (since we had 3 girls in table). Now we fill the table. Pita don't have color yet, since we had 3 whites so he could only be black
Miken and Bary are both boy and both white shirt. That's not what we expected so we had to modify Miken (we dont have much choice for Bary)
So let's target Miken
=> return to case (b) => miken black shirt, carry white
(c) still works since white,white is the only choice
(d) pita caryy same gender => let's say male,male
(e)jamie miken different gender => we got 2 male already so (d) must be girl,girl
Jamie is white shirt, miken black shirt so let's say jamie boy, miken girl
Fill the rest of the table, Bary white boy, Jamie white boy too so not work
It must be Jamie girl, miken boy. Fill the rest, Bary white boy
Everything works well now, 2 boys are Miken and Bary. Bary is white so he is the answer.

Q6
Not sure what you mean by radii, radius?
(PI*1²)/(Pi*4²)=1/16
Q7
35
(well just learn how to count)
Q8
After 4 years you mean?
X=salary
year1:X*1.1
year2:X*1.1*1.1
..
year4:X*1.1*1.1*1.1*1.1=X*1.4641
=>46.41%
Q9
X*0.8*1.25=X
no gain
Q10
1day=24*60*60=86400s
1day=20*40=800 winks
=>1 wink = 86400/800=108s
Q11
the left side pattern is 1+2+4+6+8+...= 1+2*(1+2+3+...)
the right side pattern is 1+4+6+8+...= 1+2*(2+3+4+...)
1+2*(1+2+3+...) <= 289 <= 1+2*(2+3+4+...)
2*(1+2+3+...) <= 288 <= 2*(2+3+4+...)
1+2+3+... <= 144 <= 2+3+4+...
(1+X)*X/2 <= 144 <= (2+X+1)*X/2
(1+X)*X <= 288 <= (3+X)*X
Simply resolve inequation (1+X)*X <= 28 and 288 <= (3+X)*X. You do it. The answer is X=16
The row we search is X+1= 17th row
Q12
When place on bookshelf, A front cover is on the right side, back cover of Z is on the left side.
backA frontA - backB frontB - ... - backY frontY - backZ frontZ
Not sure if I inderstand correctly english. He eats frontA and backZ
=> 1/4 + (from backB to frontY is 2*24=48) + 1/4 = 48.5 inches
Q13
10² + 24² = 26²
quare rectangle => Farking easy
area=10*24/2=120
rectangle long = 120/3=40
=>perimeter=3*2+40*2=86
Q14
don't understand the question
(1/2)/(2/3)=3/4=0.75?
Q15
X - 1/4X - 11/18(X-1/4X) - 3 = 1/24X
X=12 (do it yourself)
Q16
this is a probability question, i forgot the formula, so ask someone else
Q17
1+2+3+4+...+X = (1+X)*X/2 = 66
(1+X)*X*132
X=11
(for 2 people, 1 shake. 3 people 1+2 shake... => 12 people in party)
Q18
not understand
Q19
total score=30*4=120
his score= n*4-m
ratio= (4n-m)/120