Question

Study the following number sequence and answer the given question.
$5$,$1$,$4$,$7$,$3$,$9$,$8$,$5$,$7$,$2$,$6$,$3$,$1$,$5$,$8$,$6$,$3$,$8$,$5$,$2$,$2$,$4$,$3$,$4$,$9$,$6$
How many even numbers are there in the sequence which are immediately preceded by an odd number but immediately followed by an even number?
(A) $1$
(B) $2$
(C) $3$
(D) $4$

Answer 1

Hint: We know that an even number is a number which is a multiple of $2$ and if the number is not multiple of $2$ then it is an odd number. while attempting this question firstly underline even numbers then check whether the number preceding the underlined even number is odd or not if it is odd then check the number next to underlined even number whether it is even or not. Then, count the even number which is immediately preceded by an odd number but immediately followed by an even number.

Complete step-by-step solution:
The given sequence of the number is $5$,$1$,$4$,$7$,$3$,$9$,$8$,$5$,$7$,$2$,$6$,$3$,$1$,$5$,$8$,$6$,$3$,$8$,$5$,$2$,$2$,$4$,$3$,$4$,$9$,$6$.
Firstly, underline the even number
\[5,1,\underline 4 ,7,3,9,\underline 8 ,5,7,\underline 2 ,\underline 6 ,3,1,5,\underline 8 ,\underline 6 ,3,\underline 8 ,5,\underline 2 ,\underline 2 ,\underline 4 ,3,\underline 4 ,9,\underline 6 \].
Now, check the number immediately preceding the underlined number whether it is odd or even number and then the number immediately following the underlined number.
Those combinations in which the underlined number is immediately preceded by an odd number and immediately followed by an even number is given below.
$7,2,6$
$5,8,6$
$5,2,2$
Thus, we get three even numbers which are immediately preceded by an odd number but immediately followed by an even number.

Hence, option (C) is correct.

Note: If it is asked how many even numbers which are immediately preceded by a prime number. then similarly we underline the even number then check whether the preceding number is prime or not.