10 x 27=270
p = prob(1st digit not 7)*prob(2nd digit not 7)*prob(3rd
digit not 7)
=(8/9)*(9/10)*(9/10)
=0.72
Sandhya had it right except that there are 900 numbers
between 100 and 999 inclusive (not 899).
1*2=2
2*2=4
2*4=8
8*4=32
Ans : 32
33
Out of 800 cheques 100 are for data processing.
Out of 16000 cheques = (100/800)*16,000 = 2000 cheques
All books can be arranged in 10! ways. A single pair of books can be taken as a unit and arranged among the 8 others in 9! ways. The pair of books can also be interchanged and therefore rearranged in 2! ways. Thus the probability of the pair always being together is (9!*2!)/10!
Ratio of diameters=1:2
Ratio of radius=1:2
Ratio of volumes=(4/3*3.14*r1^3)/(4/3*3.14*r2^3)
=r1^3/r2^3=1^3/2^3=1/8
Doug won the race
Explanation-
The ratio of steps covered by me, Doug, and Anne is = 6:7:8
Since Distance covered in Me 21 steps = Distance covered by Doug 24 steps = Distance covered by Anne 28 steps
LCM (21, 24, 28) = 168
For a distance of 168 units, the ratio of the distance covered in each step is;
= 8 : 7 : 6
Therefore the ratio of speeds is;
= 8×6: 7×7: 6×8
= 48 : 49 : 48
Here, the speed of the Doug is more than the speed of me and Anne
Hence, Doug won the race
Here is the solution to the given version of the puzzle (9 balls, one is heavier, need to identify oddball), where we label the balls A, B, …, I:
1. Weigh ABC versus DEF.
Scenario a: If these (1) balance, then we know the oddball is one of G, H, I.
2. Weigh G versus H.
Scenario a.i: If these (2) balance, the oddball is I.
Scenario a.ii: If these (2) do not balance, the heavier one is the oddball.
Scenario b: If these (1) do not balance, then the oddball is on the heavier side. For simplicity, assume the ABC side is heavier, so the oddball is one of A, B, C.
2. Weigh A versus B.
Scenario b.i: If these (2) balance, the oddball is C.
Scenario b.ii: If these (2) do not balance, the heavier one is the oddball.
answer is maximum of 2.
pages # figures
1000 1000 4
from 999 to 100 (999-99)*3 2700
from 99 to 10 (99-9)*2 180
from 9 to 1 (9-0)*1 9
total sum= 2893
c
42m
400