Q #1

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Directions: Read the following information to answer the question.

A customer buys an Internet connection from VSNL. The connection cost Rs.2,500 for a total of 200 hours of usage or a validity period of one year, whichever expires first. The customer can connect to the Internet only by dialing a local number and will be billed at Rs.2 per local call of 3 minutes while he accesses the internet.

If Satyam provides a connection and charges Rs. 15 per hour of actual Internet usage, then what is the minimum usage level for the VSNL connection so that it is economically viable for the customer?

If Satyam provides a connection and charges Rs. 15 per hour of actual Internet usage, then what is the minimum usage level for the VSNL connection so that it is economically viable for the customer?

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Minimum usage level required = x

2500/x < 15

2500 < 15x

x> 2500/15 ⇒ x > 166.67 hours

Q #2

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Directions: Read the following information to answer the question.

A watch dealer incurs an expense of Rs.150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100.

If he is able to sell only 1200 out of the 1500 watches he has made in the season, then in the season he has made a profit of:

If he is able to sell only 1200 out of the 1500 watches he has made in the season, then in the season he has made a profit of:

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On each of the 1200 watches that he sells in the season, he makes a profit of Rs. 100(i.e. Rs. 250 - Rs. 150). On each of the 300 (i.e. 1500 - 1200) watches that are not sold, he incurs a loss of Rs. 150, which is the manufacturing cost. His additional expense is Rs. 30,000 (given). Thus his net profit in the season is Rs. (1,20,000 - 45,000 - 30,000) = Rs. 45,000.

Q #3

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Directions: Read the following information to answer the question.

For a balanced diet Khiladi Akshay Kumar needs to take pulse between 1/2 kg and 1 kg for every 3 kg of rice. Let there be an unequal percent rise in the prices of rice and pulse. Assuming that Akshay doesn't take unbalanced diet and keeps his total amount of consumption of rice and pulse same as earlier, the maximum percent rise in the consumption of rice Akshay can make will be about

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Since maximum rise is there

we need to assume that initially Akshay took 1 kg of pulse for every 3 kg of rice

and after price rise he takes 1/2 kg of pulse for every 3 kg of rice

now initially he eats x kg rice and x/3 kg pulse

Let akshay consumes y kg of rice after price rise so total consumption = y+y/6

x+x/3=y+y/6

y=8x/7

this will lead to 14% rise if the prices rise by equal percentage.

Q #4

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Directions: Read the following information to answer the question.

Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?

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(a + b + c + d)2 = (4m + 1)2

Thus, a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd) = 16m2 + 8m + 1

a2 + b2 + c2 + d2 will have the minimum value if (ab + ac + ad + bc + bd + cd) is the maximum.

This is possible if a = b = c = d = (m + 0.25) …….since a + b + c + d = 4m + 1

In that case 2(ab + ac + ad + bc + bd + cd) = 12(m + 0.25)2 = 12m2 + 6m + 0.75 Thus, the minimum value of a2 + b2 + c2 + d2 = (16m2 + 8m + 1) – 2(ab + ac + ad + bc + bd + cd)

= (16m2 + 8m + 1) – (12m2 + 6m + 0.75)

= 4m2 + 2m + 0.25

Since it is an integer, the actual minimum value = 4m2 + 2m + 1