Question

Determine the number of times 3 is present in the given series where it is followed by a prime number but not preceded by a number which is a multiple of 2 ?
3 5 4 8 4 3 7 0 9 8 3 9 4 3 7 7 5 3 1 2 0 7 3 2

• A. 3
• B. 2
• C. 0
• D. 6
• E. 4

Hint:

In series-scanning questions, number each position, list every occurrence of the target digit, then check all conditions methodically. Prime numbers up to 10: 2, 3, 5, 7.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Scan the series for each occurrence of 3, check: (i) is the next number prime? (ii) is the previous number NOT a multiple of 2 (i.e., not even)?

Step 2: Detailed Explanation:
Series: 3(1) 5 4 8 4 3(6) 7 0 9 8 3(11) 9 4 3(14) 7 7 5 3(19) 1 2 0 7 3(24) 2.
Check each `3':
Position 1: prev=none (start), next=5 (prime $\checkmark$). No preceding number, so not preceded by even $\checkmark$. Count.
Position 6: prev=4 (even $\times$), next=7 (prime). Fails (preceded by even).
Position 11: prev=8 (even $\times$), next=9 (not prime, $9=3\times3$). Fails both.
Position 14: prev=4 (even $\times$), next=7 (prime). Fails (preceded by even).
Position 19: prev=5 (odd $\checkmark$), next=1 (not prime $\times$). Fails (next not prime).
Position 24: prev=7 (odd $\checkmark$), next=2 (prime $\checkmark$). Count.
Total = 2.

Step 3: Final Answer:
The count is 2.