Instructions

Answer the questions based on the following information. A series $$S_{1}$$ of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series $$S_{2}$$, the nth term is defined as the difference between the (n+1)th term and the nth term of series $$S_{1}$$, $$S_{2}$$ is an arithmetic progression with a common difference of 30.

Question 41

First term of $$S_{1}$$ is

Video Solution

Solution

Assume the first series as a,b,a/2,c,a+20
and second series as x1,x2,x3,x4
x1=b-a, x2= a/2-b, x3=c-a/2, and x4=a+20-c
x2-x1=30 => 3a-4b=60
and x4-x3=30 => 3a-4c=20
and x4-x2=60 => a-2c+2b=80
Solving we get, a=100, b=60, and c=70
S1= 100,60,50,70,120

S2 = -40, -10, 20, 50

Question 42

Fourth term of $$S_{2}$$

Video Solution

Solution

Assume the first series as a,b,a/2,c,a+20
and second series as x1,x2,x3,x4
x1=b-a, x2= a/2-b, x3=c-a/2, and x4=a+20-c
x2-x1=30 => 3a-4b=60
and x4-x3=30 => 3a-4c=20
and x4-x2=60 => a-2c+2b=80
Solving we get, a=100, b=60, and c=70
S1= 100,60,50,70,120
S2 = -40, -10, 20, 50

Question 43

What is the difference between fourth terms of $$S_{1}$$ and $$S_{2}$$ ?

Video Solution

Solution

Assume the first series as a,b,a/2,c,a+20
and second series as x1,x2,x3,x4
x1=b-a, x2= a/2-b, x3=c-a/2, and x4=a+20-c
x2-x1=30 => 3a-4b=60
and x4-x3=30 => 3a-4c=20
and x4-x2=60 => a-2c+2b=80
Solving we get, a=100, b=60, and c=70
S1= 100,60,50,70,120

S2 = -40, -10, 20, 50

Difference = 20

Question 44

What is the average value of the terms of series $$S_{1}$$?

Video Solution

Solution

Assume the first series as a,b,a/2,c,a+20
and second series as x1,x2,x3,x4
x1=b-a, x2= a/2-b, x3=c-a/2, and x4=a+20-c
x2-x1=30 => 3a-4b=60
and x4-x3=30 => 3a-4c=20
and x4-x2=60 => a-2c+2b=80
Solving we get, a=100, b=60, and c=70
S1= 100,60,50,70,120

S2 = -40, -10, 20, 50

Avg. = $$(100+60+50+70 +120) \div 5 = 80$$

Question 45

What is the sum of series $$S_{2}$$?

Video Solution

Solution

Assume the first series as a,b,a/2,c,a+20
and second series as x1,x2,x3,x4
x1=b-a, x2= a/2-b, x3=c-a/2, and x4=a+20-c
x2-x1=30 => 3a-4b=60
and x4-x3=30 => 3a-4c=20
and x4-x2=60 => a-2c+2b=80
Solving we get, a=100, b=60, and c=70
S1= 100,60,50,70,120

S2 = -40, -10, 20, 50
Sum = 20

Instructions

Answer the questions based on the following information.

Question 46

The average revenue collected in the given 7 years is approximately

Video Solution

Solution

Average will be = $$(120 + 130 + 145 + 165 + 185 + 200 + 220) \div 7 = 166$$ (nearly)

Question 47

The expenditure for the 7 years together form what per cent of the revenues during the same period?

Video Solution

Solution

Total expenditure = 102 + 110 + 115 + 125 + 135 + 140 + 150 = 877
Total revenue = 120 + 130 + 145 + 165 + 185 + 200 + 220 = 1165
%expenditure to revenue = $$\frac{877}{1165} \times 100$$ = 75 (nearly)

Question 48

Which year showed the greatest percentage increase in profit as compared to the previous year?

Video Solution

Solution

percentage increase in profit in year 1990 = 25%
in 1991 = 20%
in 1992 = 33.33%
in 1993 = 25%
in 1994 = 20%
in 1995 = 16.66%

So highest %increase is in year 1992.

Question 49

In which year was the growth in expenditure maximum as compared to the previous year?

Video Solution

Solution

%increase in expenditure in year 1990 = above 7 but lower than 8
in year 1991 = near to 4
in year 1992 = above 8
in year 1993 = 8%
in year 1994 = lower than 4
in year 1995 = above 7 but lower than 8
Hence highest percentage increase is in year 1992

Question 50

If the profit in 1996 shows the annual rate of growth as it had shown in 1995 over the previous year, then what approximately will be the profit in 1996?

Video Solution

Solution

%increase in profit in year 1995 = 16.66%
With this increment, profit in year 1996 = 70(1+$$(16.66 \div 100)$$) = 82 (nearly)

CAT Content

CAT 1996 Question Paper

First term of $$S_{1}$$ is

Fourth term of $$S_{2}$$

What is the difference between fourth terms of $$S_{1}$$ and $$S_{2}$$ ?

What is the average value of the terms of series $$S_{1}$$?

What is the sum of series $$S_{2}$$?

The average revenue collected in the given 7 years is approximately

The expenditure for the 7 years together form what per cent of the revenues during the same period?

Which year showed the greatest percentage increase in profit as compared to the previous year?

In which year was the growth in expenditure maximum as compared to the previous year?

If the profit in 1996 shows the annual rate of growth as it had shown in 1995 over the previous year, then what approximately will be the profit in 1996?

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CAT Content

CAT 1996 Question Paper

First term of $$S_{1}$$ is

Fourth term of $$S_{2}$$

What is the difference between fourth terms of $$S_{1}$$ and $$S_{2}$$ ?

What is the average value of the terms of series $$S_{1}$$?

What is the sum of series $$S_{2}$$?

The average revenue collected in the given 7 years is approximately

The expenditure for the 7 years together form what per cent of the revenues during the same period?

Which year showed the greatest percentage increase in profit as compared to the previous year?

In which year was the growth in expenditure maximum as compared to the previous year?

If the profit in 1996 shows the annual rate of growth as it had shown in 1995 over the previous year, then what approximately will be the profit in 1996?

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