[Download PDF] CAT 2004 Question Paper Paper with Solutions

Instructions

For the following questions answer them individually

Question 31

A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

Video Solution

Solution

The number of ways of selecting a colour for the first stripe is 4. The number of ways of selecting a colour for the second stripe is 3. Similarly, the number of ways of selecting colours for the third, fourth, fifth and sixth stripes are 3, 3, 3 and 3 respectively.
The total number of ways of selecting the colours is, therefore, 4*3*3*3*3*3 = 12*81.

Question 32

If $$\frac{a}{b+c}=\frac{b}{a+c} =\frac{c}{b+a} =r$$, then r cannot take any value except

Video Solution

Solution

a = r(b+c)

b = r(a+c)

c = r(a+b)

On adding all the equations,

a+b+c = 2r(a+b+c)

If r = 1/2, a+b+c = a+b+c (valid)

If r = -1, a+b+c = -2(a+b+c) => a+b+c = 0 => b+c = -a and a/(b+c) = a/(-a) = -1 (valid)

So, r can take the values 1/2 or -1

Question 33

Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

Video Solution

Solution

The speeds of Karan and Arjun are in the ratio 10:9. Let the speeds be 10s and 9s.
Time taken by Karan to cover 110 m = 110/10s = 11/s
Time taken by Arjun to cover 100 m = 100/9s = 11.11/s
Therefore, Karan reaches the finish line before Arjun. From the options, the only possible answer is d).

Question 34

In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts.

Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

Video Solution

Solution

Machine A takes 15 min to produce 1000 nuts with clean time. machine b takes 30 min to make 1500 nuts with clean time . So B is slower. So with B 900 nuts will be made in 180 mins but at last round cleaning time of 10 min no need to count hence 170 mins

Question 35

The total number of integers pairs (x, y) satisfying the equation x + y = xy is

Video Solution

Solution

xy = x + y

=> xy - x - y = 0

=> xy - x - y + 1 = 1

=> (x - 1) (y - 1) = 1

=> Both x - 1 and y - 1 have to be equal to 1 or -1.

So, values taken by (x,y) are (2,2) and (0,0).

=> 2 solutions

Instructions

Directions for the following four questions: Answer the questions on the basis of the information given below.

The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves the space blank. The scanner output read as follows:

In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2, and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example Nisha’s GPA is (6 + 2 + 4 + 6 + 0) / 5 = 3.6. Some additional facts are also known about the students’ grades. These are

(i) Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.

(ii) Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.

(iii) Tara received the same grade in exactly three courses.

Question 36

What grade did Preeti obtain in Statistics?

Video Solution

Solution

Let preeti obtain x and y in stastistics and operation respectively. Now we know that GPA = 3.2 .

So (x+y+2+2) = 16 .

So x+y = 12. for this only one value is possible x=y=6 .

So A grade .

Question 37

In operations, Tara could have received the same grade as

Video Solution

Solution

Since tara received the same grade in exactly 3 subjects , only one possibility is getting B in 3 subjects and F in other 2. So in operation her grade would be either B or F.Among options only manab has B in operations . hence option D.

Question 38

In Strategy, Gowri's grade point was higher than that obtained by

Video Solution

Solution

Knowing the GPA we can find gawris grade in strategy as

16 + x=19; x=3. So her grade was C.

Now considering hari's grade 12+x+y=14 ; so x+y=2.

So he must have got D or F in strategy. Hence in Strategy, Gowri's grade point was higher than that obtained by hari.

Question 39

What grade did Utkarsh obtain in Finance?

Video Solution

Solution

Considering utkarsh's grades we get , x+y = 6 . So possibilities of his missing grades are (4,2) or (6,0). Now according to given condition, his grades in marketing are same as faizal's in strategy and faizal got grade B in strategy . hence utkarsh got 4 in marketing and 2 in finance i.e. grade D . Hence option C.

Instructions

Directions for the following four questions: Answer the questions on the basis of the information given below.

The data points in the figure below represent monthly income and expenditure data of individual members of the Ahuja family, the Bose family, the Coomar family, and the Dubey family.

The X axis represents Expenditure and the Y axis represents the Income of the individual members.

For these questions, savings is defined as Savings = Income - Expenditure

Question 40

Which family has the lowest average income?

Video Solution

Solution

SInce the Y-axis gives the income, to find minimum average income see if any family has income in different months as below as possible in the graph.

From the graph we can see that coomar has lowest average income. Hence option C.

CAT Content

CAT 2004 Question Paper

A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

If $$\frac{a}{b+c}=\frac{b}{a+c} =\frac{c}{b+a} =r$$, then r cannot take any value except

Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

The total number of integers pairs (x, y) satisfying the equation x + y = xy is

What grade did Preeti obtain in Statistics?

In operations, Tara could have received the same grade as

In Strategy, Gowri's grade point was higher than that obtained by

What grade did Utkarsh obtain in Finance?

Which family has the lowest average income?

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CAT Content

CAT 2004 Question Paper

A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is

If $$\frac{a}{b+c}=\frac{b}{a+c} =\frac{c}{b+a} =r$$, then r cannot take any value except

Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

The total number of integers pairs (x, y) satisfying the equation x + y = xy is

What grade did Preeti obtain in Statistics?

In operations, Tara could have received the same grade as

In Strategy, Gowri's grade point was higher than that obtained by

What grade did Utkarsh obtain in Finance?

Which family has the lowest average income?

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