CAT 1996 Question Paper

Percentage of students more in marketing jobs than in finance jobs are 14%, 31%, 20%, 18% and 0% in 1992, 1993, 1994, 1995 and 1996 respectively.

=> Number of people = 14*800/100  +  31*650/100  +  20*1100/100  +  18*1200/100  = 112 + 202 + 220 + 216 = 750

Finance salary increase = 9810 - 5450 = 4360

% increase = $$\frac{4360}{5450}*100$$ = 80%

Total increase in 4 years = 8640 - 5290 = 3350

% increase = $$\frac{3350}{8640}$$ = 63.3%

Average per-year growth = 63.3/4 = 15.9%

As we do not know the average salary for students who did not pursue Finance, Marketing or Software jobs, we cannot find the average salary of all the students in 1993.

Hence, a unique value cannot be determined.

Number of students in 1994 passed out = 1100.

Number of students in 1994 from finance = 23% of 1100 = 23*11

Number of students in 1994 from software = 21% of 1100 = 21*11

Difference in salary = 12(23*11*7550-21*11*7050) = 3379200 = 33.8 lakhs

In either of the statements, a numerical value is not given.

With the given information, we can only find the radius in terms of N and T.

Hence, the radius cannot be determined using both the statements as well.

The proportions of liquid A in vessels 1, 2 and 3 are $$\frac{3}{8}$$, $$\frac{2}{5}$$ and $$\frac{4}{7}$$ respectively.

LCM of 8, 5 and 7 is 280 => Assume each container ha 280 litres.

=> Quantity of liquid A in vessels 1, 2 and 3 are 105, 112 and 160 respectively.

=> Total volume of A = 377 litres

Total volume of B = 840 - 377 = 463 litres

Hence, ratio can be found using both the statements and neither statement alone can be used to find the ratio.

For (a-b+c) > (a+b-c)
Considering first statement alone
if b<0, we can't say anything affirmative about inequality as information about c is unavailable.
Considering second statement alone, 
if c>0, we can't say anything about b.
Now if we consider both statement together 
i.e. b<0 and c>0, then term (-b+c) will be positive and additive to a whether term (b-c) will be negative and subtracting from a.
Hence (a-b+c) > (a+b-c).
And answer will be D.

$$(α^2 +β^2)$$ can be reduced to $$(α+β)^2 - 2(αβ)$$
Now as we can see, we need both values of (α+β) and (αβ) to solve the equation.
Hence answer will be D.

Considering first statement alone:
When loss is 25% on cost price, selling price will be $$\frac{3}{4}$$th of cost price but we can't get the absolute value of cost price.
Considering second statement alone:
As this statement can also be derived from 1st statement, but we need some other informations to get value of cost price
So answer will be A.