CAT 2000 Question Paper

Since in 94 total production was 50% more than 89 , so total production = 150. Also we know that total production in given 4 sectors in 94  = 76.8. Hence other than the 4 sectors total production is 150 - 76.8 = 73.2 . Hence  the percentage increase in production between 1989 and 1994 in sectors other than the four listed above is: (73.2-40) / 40 is approx 87.5% . Hence option B. 

For 40 units total fixed costs would be 1200 + 800 = 2000 and variable cost = 3700 . So total cost = 5700 (approx). Hence approximate average unit cost for July = 5700 / 40 = 142.5 . Hence option C is the correct answer. 

We know that  MC is the rate of change in total cost for unit change in quantity produced. SO for 40 units total cost = 2000+3700 = 5700 and for 50 units  = 2000 + 5000 = 7000. So for additional 10 units change in total costs is 1300 . So for 1 unit we have MC = 130.

As the graph is an increasing function, MC will always increase for increase in number of units.

Total sales = 150 * 40 = 6000. Total costs = 2000 + 3650(approx).= 5600 to 5700 .Hence , profit = 6000 - 5600 = 400 (approx). Hence option C.

As adding a shift dramatically increases the costs, we need to consider the two regions, 0<x<=30 and 30<x<=60, separately.

Region 1: As variable cost is less than equal to 100, and sales price is 150, profit would be max when production is maximum possible i.e. at 30 units.

Hence, at 30 units, total cost = 800 + 2400 = 3200. Sales = 30 * 150 = 4500. Profit = 4500-3200 = 1300

Region 2: As variable cost is less than equal to 100, and sales price is 150, profit would be max when production is maximum possible i.e. at 60 units

Hence, at 60 units, total cost = 800 + 1200 + 6500 = 8500. Sales = 150*60 = 9000. Hence, Profit = 9000 - 8500 = 500

Hence, profit is maximum at 30 units.

When we take some value and check for the variation , we find that actual variation is opposite to that of option C.

Upto a certain level, AC is greater than MC and then AC is less than MC.

For producing 31 units, the average cost is 1200 + 800 + 2400 = Rs. 4400.
Average cost = 4400/31 = Rs.142 (Approx).

Let us calculate the marginal cost at this point. 
As the number of units increases from 31 to 40, the variable cost increases from Rs.2400 to Rs.3700.
Marginal cost = (3700-2400)/10 = 1300/10 = Rs.130.

MC < AC for 31 units.

Let us calculate MC and AC for 60 units. 

Average cost = (2000 + 6800)/60 = 8800/60 = Rs.146.66
As the number of units increases from 50 to 60, the variable cost increases from Rs.5000 to Rs.6800.
Marginal cost = Rs.1800/10 = Rs.180

MC > AC for 60 units. 
As we can see, the trend is the inverse of what is mentioned in option C. Since none of the options capture the trend precisely, option D is the right answer.

Let’s comprehend the given information first. The ratio of the number of children from classes one to five to all children aged 6 to 10 is very high, often greater than 1. This is the premise. The author says that it is not a valid report as the data is based on official enrolment data compiled from school records and therefore is exaggerated. This is the conclusion.

Here, the assumption is that the enrolment data in school records is often not correct. In order to strengthen the argument, we need to bolster the assumption.

Now, let’s check each option to determine the option that strengthens the assumption.

The first option is the definition of gross enrolment ratio. This statement gives the reason for the high gross enrolment ratios. Hence it is strengthening the premise and weakening the conclusion. Therefore, option A is wrong.

The passage does not talk about the attendance of the students and also attendance is not related to the gross enrolment ratio. Option B does not strengthen the argument. Hence, option B is wrong.

Option C says that 22 percent of the children who do not belong to the age group 6-10 and who have not started going to school but have enrolled in class one are included in the numerator of the ratio. This explains why the ratio is high. Also, the ratio is clearly exaggerated as the students have not started going to school yet. Therefore, option C is the answer as it explains why the ratios are exaggerated.

The decline in the number of children in the age group 6 - 10 has nothing to do with the gross enrolment ratio. Hence, option D is wrong.

Therefore, the answer is option C.

It is given that 90 percent of a club’s performance can be explained by wage bills. If a player’s salary is based on only on their abilities then the clubs that paid more amounts must finish higher. This relation will not hold true if there is pay discrimination. The conclusion of the passage is that certain clubs seem to have achieved less than they could have, by not recruiting black players.

Here, the assumption is that certain clubs paid more than many other clubs but did not finish at a position they could have had.

Now, let’s check each option and verify whether it strengthens Szymanski’s conclusions.

Option A is not relevant here because it does not address our assumption in any way. Hence, option A is wrong.

The clubs that the author is talking about could have chosen a few black players, paid the black players lower wages and achieved as much as they did now. So, if it is a fact that clubs hired white players at relatively high wages and did not show proportionately good performance, then we can conclude that these clubs achieved less than they could have had. Hence, option B is correct.

According to option C, the towns have a history of discrimination against blacks. But, the clubs might or might not show the discrimination. Hence, the underperformance of these clubs cannot strengthen Szymanski’s conclusions. Therefore, option C is wrong.

Option D is a fact which can be deduced from the information given in the passage. Hence, it doesn’t strengthen the conclusion.

Therefore, option B is the correct answer.

The reason for the minister to advance his new recommendation is most likely because of an incident or incidents which might have occurred in the prisons due to snapping of tensions among the prisoners. This reason is best captured in option d), which says that disturbances have been reported in 58 prisons.