The micromanometer in a certain factory can measure the pressure
inside the gas chamber from 1 unit to 999999 units. Lately this instrument has
not been working properly. The problem with the instrument is that it always
skips the digit 5 and moves directly from digit 4 to 6. What is the actual
pressure inside the gas chamber if the micromanometer displays 003016?
(1)2201 (2)2202 (3)2600 (4)2960 (5)None
of these options
Solution follows here:
Solution:
This can be done by digitbydigit analysis using concepts of
Permutations and Combinations. But the best way out is using number theory as given
below:
Here we need to skip number ‘5’ while counting. This means,
we need to consider only 9 digits 0, 1, 2, 3, 4, 6, 7, 8, 9 of the base10
system. ∴The digits to be used in the ‘New system’ are 0, 1, 2, 3, 4, 6,
7, 8, 9. This implies the ‘New system’ is in someway similar to Base9 system,
which also considers nine single digit numbers (0 to 8). So, we compare the
Base10, Base9 and the ‘New system’ here:
Base10

Base9

Newsystem

Base10

Base9

Newsystem


0

0

0

9

10

10


1

1

1

10

11

11


2

2

2

11

12

12


3

3

3

12

13

13


4

4

4

13

14

14


5

5

6

14

15

16


6

6

7

15

16

17


7

7

8

16

17

18


8

8

9

17

18

19

Observe that the numbers 0, 1, 2, 3, 4 are same in Base9
system and the new system. Similarly, numbers 10, 11, 12, 13, 14 are same
respectively in Base9 and the new systems.
But numbers 5,6,7,8 in Base9 system are respectively equal
to 6,7,8,9 in the new system. Similarly, 15,16,17,18 in Base9 system are
respectively equal to 16,17,18,19 in the new system.
If we go by this logic, 3016 in the new system is equal to
3015 in Base9 system. Now we need to find (3015)_{9} equivalent in
Base10 system.
(3015)_{9 }= 5*9^{0} + 1*9^{1} + 0*9^{2}
+ 3*9^{3} = 5 + 9 + 3*729 = 2201
Answer (1)
No comments:
Post a Comment