Detailed solution
x^2 > |x|
x > 0 then x^2 > x
x(x-1) > 0
x 1
but for positive x x>1 ......... equ 1
x -x
x(x+1) > 0
x 0
but for negative x x
From 1 and 2
x^2 > 1
v^2-vw = 0
v(v-w) =0
either v =0 or v-w =0 or both
but v and w are different integers so v = 0 Suff
v is not 2 nothing else can be said about v. Insuff
Let D be total distance between station A and B
Speed of train leaving A Va = D/4
Speed of train leaving B Vb = D/3.5
By 7 am. train A would have covered half the distance so remaining distance = D/2
Relative speed of train A wrt B = Va - (-Vb) = Va + Vb = D/4 + D/3.5
using relative distance = relative speed * time
D/2 = (D/4 + D/3.5) * t
t = 14/15 hour = 56 minutes
Hope this helps
Lets speed be P km/h and Q kmph respectively
Using relative distance = relative velocity * time
relative distance = 120 km
(P +Q) * 1 = 120 ................ (i)
(P - Q ) * 6 = 120 ................ (ii)
solving i and ii P = 70, Q = 50
Alternate way
number of codes when second digit is zero + number of codes when second digit is one
= 8 * 1 * 9 (second and third digits can not be 0 at same time) + 8*1*10
= 72 + 80
= 152
Total number of codes with constraint (second and third digits cannot be 0 at the same time) = 8*2*10 = 160
Number of codes where second and third digits are zero = 8*1*1 = 8
Required codes = 160 - 8 = 152