Model 1: How many such 6's are there in the following number sequence each of which is immediately preceded by 3 or 4 but not immediately followed by 8 or 9?
3 6 9 6 4 6 6 3 6 8 4 6 5 7 3 6 7 6 6 4 6 2 3 6 1 0
Solution:
Given number sequence is
3 6 9 6 4 6 6 3 6 8 4 6 5 7 3 6 7 6 6 4 6 2 3 6 1 0
A number which comes after a given number is said to follow it while the one which precedes the given number goes before it.
Thus, the numbers satisfying the given conditions may be marked(with red colour) as follows:
3 6 9 6 4 6 6 3 6 8 4 6 5 7 3 6 7 6 6 4 6 2 3 6 1 0
Therefore, there are five such 6's.
Model 2: How many pairs of successive numbers have a difference of 3 each? If the series:
7 4 1 2 2 8 4 1 2 1 8 5 5 2 2 1 7 1 4 2 1 4 2 6 3.
Solution:
Given series is:
7 4 1 2 2 8 4 1 2 1 8 5 5 2 2 1 7 1 2 1 4 2 6 3.
Here,
7 - 4 = 3
4 - 1 = 3
8 - 5 = 3
5 - 2 = 3
4 - 1 = 3
6 - 3 = 3
So, the pairs of successive numbers having a difference of 3 can be shown below:
7 4 1 2 2 8 4 1 2 1 8 5 5 2 2 1 7 1 2 1 4 2 6 3
Therefore, there are six such pairs.
Model 3: Jasmine is ninth from the right end in a row of 60 girls. Find the position of Jasmine from the left end?
Solution:
Given that:
Total number of girls = 50
From right end in a row Jasmine is in ninth position.
Therefore, number of girls towards the left of Jasmine = 60 - 9
= 51
So, Jasmine is 52nd from left end.
Model 4: Edward remembers that his brother's birthday is after fifteenth but before eighteenth of February whereas his sister Rebecca remembers that her brother's birthday is after sixteenth but below nineteenth of February. On which day in February is Edward's brother's birthday?
Solution:
Given that:
Edward remembers that his brother's birthday is after fifteenth.
His sister Rebecca remembers that her brother's birthday is after sixteenth.
According to Edward, the brother's birthday is on one of the days among 16th and 17th February.
According to Rebecca, the brother's birthday is on one of the days among 17th and 18th February.
Therefore, Edward's brother's birthday is on the day which is same in both comparisions.
So, it is on 17th February.
Model 5: If the seventh day of a month is three days sooner than Friday, what day will it be on the nineteenth day of the month.
Solution:
Given that
seventh day of a month is three days sooner than Friday.
So, the seventh day of the month is three days earlier than Friday, which is Tuesday.
Therefore, the fourteenth day is also Tuesday.
Hence, nineteenth day is Sunday.