Instructions

Use the following information: Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer.
In case he decides to test, he has two options:
a) Use test I ;
b) Use test II.

Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer's end and penalty of Rs. 50 per defective widget has to be paid by Prakash.

Question 71

If there are 200 defective widgets in the lot, Prakash:

Video Solution

Solution

When there are 200 defective pieces:
Using test 1
Cost of testing= 2000
Cost of correcting 80% pieces = 4000
Cost of penalty on 20% pieces = 2000
Total = 8000

Using test 2
Cost of testing = 3000
Cost of correcting all pieces = 5000
Total = 8000

Using no test
Cost of penalty on all pieces= 10000

Hence he can use either 1st test or second test.

Instructions

Study the following graph and answer questions that follow. The x-axis denotes the years from 1983 to 1991

Question 72

The sum of food and fertilizer production has shown a constant value for how many years?

Video Solution

Solution

In order to find the number of years for which the sum is same, we need to determine the change in production of food and fertilizer. If there is no effective change, then the sum of their productions is same.

Change in 1984 => +1 - 1.5 = -0.5

Change in 1985 => 0

Change in 1986 => -1.5 + 1.5 = 0

Change in 1987 => 0

Change in 1988 => +1.5 - 1.5 = 0

Change in 1989 => -2.5 + 0 = -2.5

Change in 1990 => 0 + 1.5 = 1.5

Change in 1991 => 0

The change is 0 in 5 years. Hence, the answer is option D.

Question 73

If in 1988, the sum of the food and fertilizer production was 170 million tonnes, the value of food production must have been (approximately, in million tonnes) .

Video Solution

Solution

From the graph, in the year 1988, the ratio of food production to fertilizer production is 5:3.5 i.e 10:7
Let the food production be 10X and the fertilizer production be 7X

Hence, the total is 10X+7X = 17X which equals 170
So, X = 10 and the total food production equals 10*10 = 100

Question 74

From its apparent behaviour, the food production in year 1992 can be expected to .

Video Solution

Solution

Just by looking at the graphs of the previous year's it is difficult to guess how the food production in the year 1992 will be.
This is especially true as we don't have any information about the fertilizer production in the year 1992.

Hence, the correct answer is option (d)

Question 75

Going according to previous trends, one can say that the Fertilizer Production has shown an anomalous behavior in which year?

Video Solution

Solution

The fertilizer and food production has been inversely proportional over the years. ie when food production increased, fertilizer production fell and vice versa. But as we can see in 1988-89, when food production remained constant, the fertilizer production fell steeply and in 89-90 when food production increased steeply, the fertilizer production stayed constant. So, 1989 is the year of the anamoly.

Question 76

A scholar observed that if the production of fertilizers in 1989 had been the same as that in 1988, then the total fertilizer production for all the given years would have been 450 million tonnes. Using this information, and knowing that the food production has been plotted on the same scale, one may say that the food production in 1983 was (approximately, in million tonnes) .

Video Solution

Solution

Let each unit in the scale be equal to X

So, fertilizer production in 1983 is 2.5X
So, fertilizer production in 1984 is 3.5X
So, fertilizer production in 1985 is 3.5X
So, fertilizer production in 1986 is 2X
So, fertilizer production in 1987 is 2X
So, fertilizer production in 1988 is 3.5X
Assuming fertilizer production in 1989 is same as that of 1988 it equals 3.5X
So, fertilizer production in 1990 is X
So, fertilizer production in 1991 is X
Hence, the total is 22.5X
But this equals 450 million tonnes. Hence, X = 20 million tonnes

Therefore, food production in 1983 = 6.5X equals 130 million tonnes

Instructions

For the following questions answer them individually

Question 77

Choose the statement that expresses the idea most correctly.

Video Solution

Solution

The verb is/are refers to the noun "best part". As the phrase "best part" is singular, 'is' must be used here.

Hence, option A is correct.

Question 78

Choose the statement that expresses the idea most correctly.

Video Solution

Solution

The usage of the phrase "as well as" is preceded by a comma.

In a sentence where "as well as" is used, the verb must agree with the noun before the "as well as" phrase. Here, the verb was/were refers to the noun 'professor'. As professor is singular, the correct verb to be used here is 'was'.

Hence, option A is correct.

Question 79

Choose the statement that expresses the idea most correctly.

Video Solution

Solution

Option A is wrong because two independent clauses are not joined by a conjunction.

In option C, the sentence after colon is an independent clause. But, the sentence after colon must be a dependent clause. So, option C is incorrect.

The sentence in option D must have a comma after the completion of the dependent clause. Hence it is incorrect.

Option B is the correct answer.

Question 80

Choose the statement that expresses the idea most correctly.

Video Solution

Solution

If "one" is used to refer a person in the dependent clause, the same word must also be used in the independent clause. Options A, C and D violate this rule.

Option B is the correct answer.

CAT Content

CAT 1991 Question Paper

If there are 200 defective widgets in the lot, Prakash:

The sum of food and fertilizer production has shown a constant value for how many years?

If in 1988, the sum of the food and fertilizer production was 170 million tonnes, the value of food production must have been (approximately, in million tonnes) .

From its apparent behaviour, the food production in year 1992 can be expected to .

Going according to previous trends, one can say that the Fertilizer Production has shown an anomalous behavior in which year?

Choose the statement that expresses the idea most correctly.

Choose the statement that expresses the idea most correctly.

Choose the statement that expresses the idea most correctly.

Choose the statement that expresses the idea most correctly.

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CAT Content

CAT 1991 Question Paper

If there are 200 defective widgets in the lot, Prakash:

The sum of food and fertilizer production has shown a constant value for how many years?

If in 1988, the sum of the food and fertilizer production was 170 million tonnes, the value of food production must have been (approximately, in million tonnes) .

From its apparent behaviour, the food production in year 1992 can be expected to .

Going according to previous trends, one can say that the Fertilizer Production has shown an anomalous behavior in which year?

Choose the statement that expresses the idea most correctly.

Choose the statement that expresses the idea most correctly.

Choose the statement that expresses the idea most correctly.

Choose the statement that expresses the idea most correctly.

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