Correct Option
To determine the correct statement, we can assume a total number of candidates, for instance, 100.
- Number of men = 60% of 100 = 60.
- Men clearing the qualifying test = 70% of 60 = 42.
- Men successful in the final test = 80% of 42 = 33.6.
- Number of women = 40% of 100 = 40.
- Women clearing the qualifying test = 75% of 40 = 30.
- Women successful in the final test = 70% of 30 = 21.
Comparing the number of successful candidates: 33.6 men vs. 21 women. Since 33.6 > 21, more men cleared the examination than women. Thus, statement (3) is correct.
Incorrect Options
Let's evaluate the other options based on the calculated values:
- Option 1: Success rate is higher for women.
- Men's success rate = (Number of successful men / Total men) × 100 = (33.6 / 60) × 100 = 56%.
- Women's success rate = (Number of successful women / Total women) × 100 = (21 / 40) × 100 = 52.5%.
- Option 2: Overall success rate is below 50%.
- Total successful candidates = 33.6 (men) + 21 (women) = 54.6.
- Overall success rate = (Total successful candidates / Total candidates) × 100 = (54.6 / 100) × 100 = 54.6%.
- Option 4: Both (a) and (b) above are correct. As statements (1) and (2) are incorrect, this combined statement is also incorrect.