Question

For at least how many of the given indices is the weightage of the bottom 50% of the companies that constitute the index less than 30%?

• A. 2
• B. 4
• C. 6
• D. Cannot be determined
• A. 3.0%
• B. 2.4%
• C. 2.0%
• D. Cannot be determined
• A. 2
• B. 4
• C. 6
• D. 7

Answer 1

The Correct Option is B

To determine for how many indices the weightage of the bottom 50% of the companies is less than 30%, we start by understanding that the top 20% and bottom 20% weightages are given. By elimination, the remaining middle 60% of companies will have a cumulative weightage of:

Weightage of middle 60% = 100% - Weightage of top 20% - Weightage of bottom 20% 

Therefore, weightage of bottom 50% of companies = Weightage of middle 60% + Weightage of bottom 20%. We need this to be less than 30% for the bottom 50%.

Let's calculate for each index:

Index	Weightage of top 20%	Weightage of bottom 20%	Weightage of middle 60%	Bottom 50%
SENSEX	43%	5.5%	51.5%	5.5% + 25.75% = 31.25%
NIKKEI	41.6%	7.2%	51.2%	7.2% + 25.6% = 32.8%
KOPSI	39.8%	3.8%	56.4%	3.8% + 28.2% = 32%
DOW JONES	44.1%	2.7%	53.2%	2.7% + 26.6% = 29.3%
NIFTY	46.4%	5.1%	48.5%	5.1% + 24.25% = 29.35%
NASDAQ	39.4%	3.5%	57.1%	3.5% + 28.55% = 32.05%
FTSE 100	43.4%	2.8%	53.8%	2.8% + 26.9% = 29.7%
HANG SENG	47.1%	3.1%	49.8%	3.1% + 24.9% = 28%
DAX	38.6%	5.9%	55.5%	5.9% + 27.75% = 33.65%
STRAITS TIMES	39.5%	6.3%	54.2%	6.3% + 27.1% = 33.4%
KLSE	37.6%	7.2%	55.2%	7.2% + 27.6% = 34.8%
S & P 500	42.6%	4.1%	53.3%	4.1% + 26.65% = 30.75%

Hence, for the indices where weightage is <30% (highlighted in calculation): DOW JONES, NIFTY, FTSE 100, HANG SENG. Therefore, 4 indices satisfy the condition.

Answer 2

The objective is to determine the minimum weightage of a company among the top 10 companies in the SENSEX.

Given that the SENSEX consists of 30 companies, 20% of these companies would account for the top 6 companies (20% of 30 = 6). Therefore, the weightage of these top 6 companies comprises 43% of the SENSEX.

Since the question asks for the minimum weightage among the top 10 companies, we will include 4 additional companies to complete the top 10 companies. We need to distribute the remaining (top) weightage of these 4 companies.

Considering that the bottom 20% of the companies holds a 5.5% weightage, and these account for the bottom 6 companies, the remaining weightage for the middle tier companies is calculated as follows:

Total weightage of all companies is 100%. If the bottom 20% accounts for 5.5%, then the remaining weightage for the top 80% equals 94.5%.

Out of this 94.5%, the top 6 companies account for 43% as mentioned. This leaves 94.5% - 43% = 51.5% for the remaining 80% of companies not in the bottom or top tiers.

The 24 companies that are neither in the top 20% nor in the bottom 20% have a total weightage of 51.5%. This approximates to a 2.15% weightage for each of these middle-tier companies (51.5% divided by 24).

As a result, the minimum weightage for a company among the top 10 companies would be slightly above any of the individual middle-tier companies' average weightage.

The smallest choice that could be logically given to a company among the top 10 in consideration of the average and distribution would be 2.4%.

The correct answer is: 2.4%

Answer 3

To determine for how many indices the weightage of the top 40% of the companies is definitely more than 60%, we need to examine if the accumulated weightage of the top 20% plus another 20% will exceed 60%. 

Given the weightage of the top 20% for each index from the table:

Index	Weightage of top 20%
SENSEX	43%
NIKKEI	41.6%
KOPSI	39.8%
DOW JONES	44.1%
NIFTY	46.4%
NASDAQ	39.4%
FTSE 100	43.4%
HANG SENG	47.1%
DAX	38.6%
STRAITS TIMES	39.5%
KLSE	37.6%
S & P 500	42.6%

To ensure the top 40% exceeds 60%, the weightage of the top 20% must be at least 40%, ensuring that adding another 20% brings it comfortably over 60%.

We identify these indices where weightage of top 20% ≥ 40%:

• NIKKEI - 41.6%
• SENSEX - 43%
• DOW JONES - 44.1%
• NIFTY - 46.4%
• FTSE 100 - 43.4%
• HANG SENG - 47.1%
• S & P 500 - 42.6%

There are 7 indices where the top 20% weightage is above 40%.