CAT 2007 Question Paper

From the information given in the question, D has a better rank than E and B has a better rank than C. Also, C = 4 or 5.
From statement A, A = 5 => C = 4. But we do not know if D or B is number 1.
From statement B, B = 3 or 4. Again, we cannot determine the number 1 rank precisely.
By using both the statements together, we know C = 4, A = 5, B = 3 and D has a better rank than E.
So, D = 1 and E = 2. Therefore, the question can be answered by using both the statements together.
Hence, option D.

Let the total number of employees be 100k.
Number of males = 30k. Number of females = 70k.
Number of female engineers = 7k.
From statement A, number of male engineers = 25k - 7k = 18k.
From statement B, number of male engineers = (6/5)*7k.
Therefore, percentage of male engineers can be calculated.
So, the question can be answered by either statement alone.

From statement A, we know that the club scored four goals in the second half but we do not know the number of goals scored by the opposition. So, we cannot answer the question.
From statement B, we know that the opposition scored 4 goals in the match but we do not know the number of goals scored by Mahindra and Mahindra club. So, we cannot answer the question.
Using both the statements, we know that the opposition scored 4 goals in the match and Mahindra and Mahindra scored 4 goals in the second half. But, we do not know if the score was 3-0 or 4-1 at the end of first half. If it was 4-1, then Mahindra and Mahindra would win the match after the second half. But if the score was 3-0 at the end of first half, the match would end in a draw after the second half.
Therefore, the question cannot be answered even by using both the statements together.

Fixed costs in 2006 are consumables, rent of building, rates and taxes, repair and maintenance expenses and selling and marketing expenses. We can see this from the trend followed in the years 2002-2006.

Fixed costs in 2006 = 1400 + 1200 + 400 + 800 + 5800 = 9600

We can see that that material , labour and operation costs depend on no. of units.

If we take units = x .

Total cost of these 3 materials is 50x +20x+30x = 100x and remaining fixed cost taking same as in 2006 we get , 9600+100x , but here x = 1400.

We have total cost per unir (9600+100*1400)/1400 = 107(approx).

Hence option B. 

Fixed costs in 2006 are consumables, rent of building, rates and taxes, repair and maintenance expenses and selling and marketing expenses. We can see this from the trend followed in the years 2002-2006.

Fixed costs in 2006 = 1400 + 1200 + 400 + 800 + 5800 = 9600 => fixed costs in 2007 are same.

We can see that that material , labour and operation costs depend on no. of units.

If we take units = x .

Total cost of these 3 materials is 50x +20x+30x = 100x and remaining fixed cost taking same as in 2006 we get , 9600+100x.

As the selling price is 125, we have 100x + 9600 < 125*x.

Solving this we get x = 384.

Hence option  C. 

Fixed costs in 2006 are consumables, rent of building, rates and taxes, repair and maintenance expenses and selling and marketing expenses. We can see this from the trend followed in the years 2002-2006.

Fixed costs in 2006 = 1400 + 1200 + 400 + 800 + 5800 = 9600 => fixed costs in 2007 are same.

We can see that that material , labour and operation costs depend on no. of units.

If we take units = x .

Total cost of these 3 materials is 50x +20x+30x = 100x and remaining fixed cost taking same as in 2006 we get , 9600+100x.

Selling price is reduced by 5% => SP = 125 * 0.95 = Rs 118.75

Profit = 118.75x - 100x - 9600 = 18.75x - 9600

Profit will be maximum when x is maximum

=> 2000 units.

Fixed costs in 2006 are consumables, rent of building, rates and taxes, repair and maintenance expenses and selling and marketing expenses. We can see this from the trend followed in the years 2002-2006.

Fixed costs in 2006 = 1400 + 1200 + 400 + 800 + 5800 = 9600 => fixed costs in 2007 are same.

We can see that that material , labour and operation costs depend on no. of units.

If we take units = x .

Total cost of these 3 materials is 50x +20x+30x = 100x and remaining fixed cost taking same as in 2006 we get , 9600+100x.

Selling price = 125 - 5 = Rs 120.

Profit = 120x - 100x - 9600 = 20x - 9600

When x = 1700 => Profit = 20*1700 - 9600 = 34000 - 9600 = Rs 24400.

According to given condition No of male students in 11,12 and in total are 44 , 48 and 380.

So No of males in secondary are 380-44-48=288.

288 students => 45% of total secondary students.

There are 640 secondary section students, 80 11th class students and 80 12th class students.

If the fraction of vegetarians in 12th class is x, then

80x + 80*0.5 + 640*0.55 = 0.53*800

=> x + 0.5 + 4.4 = 5.3 => x = 0.4

=> There are 32 vegetarian students in class 12.

25% of class 12 i.e 8 are males.

So there are 24 vegetarian female students.

No. of non-veg males = 40 and veg females=24. Required answer 40 - 24 = 16.

There are 640 secondary section students, 80 11th class students and 80 12th class students.

If the fraction of vegetarians in 12th class is x, then

80x + 80*0.5 + 640*0.55 = 0.53*800

=> x + 0.5 + 4.4 = 5.3 => x = 0.4

=> 40% are vegetarians in class 12.