GRE Questions

---

Let us assume A is the faster and B is slower, A takes 10s to finish a lap of 50 m, B takes 17s(approx) to finish a lap of 50 m.
So at 11th sec A starts his 2nd lap by the time B will be in between so that is the first time they will meet each other, at 21st sec A starts his 3rd lap by the time B will be coming back to finish his 2nd lap. So that is the second time they meet in opposite. Then at 31st sec A will start his 4th lap by the time B would not even finish 2nd lap as he take 34(2*17) sec to finish 2 laps. So at 35th sec B will start his 3rd lap by the time A will be coming back to finish his 4th lap in the half way so they will meet 3rd time. At 41st sec A will start its fifth lap by the time B will be going to finish 3rd lap in same direction. At 50th second both will complete A's 5th lap and B's 3rd lap. So they will start next lap(A's 6th and B's 4th) from the same point in same direction. And A will finish the race after completing 300m(6*50) total distance and then they wont meet opposite to each other.

So totally they met 3 times in opposite direction.

All the above will stay where they are when they goes off. Basically anything that can swithch on or off will come under this.

Let S be the sample space.
Here n(S)= 23 = 8
Let E be the event of getting atmost two heads. Then,
n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}
Required probability = n(E)/n(S) = 6/8 = 3/4.

we know that speed = distance traveled/time taken
let the total distance traveled by the car is 2x km.
then time taken by it to cover first half is x/60 hour.
and for second half is x/40 hour.
Then average speed= total distance travelled / total time taken.

i.e. 2xx60+x40

=> 2x5x120

= 48 kmph.

We have 12 months.

In every month we get 28 or more days. 

So that implies we get 28 days in each and every month.

Here in 2nd column if you add the individual digits

 we get  3 + 7 + 0 =10 , 2 + 2 + 4 = 8 , 7 + 3 + 0 = 10

7   10   3  --> 7+3 =10

6   8     2  --> 6+2 =8

x   10   1  --> x+1 =10

Here we can observe that by adding 1st and 3rd column elements we get 2nd column elements

 --> x = 9

A Sandal.

It has sticking strips to make them fit for our feet. If you bind them only you can start walking or other wise it comes out.