CAT 1996 Question Paper

Total investment by B, C, D and E in year 1 = 24.11 Billion

Total investment by B, C, D and E in year 3 = 77.4 Billion

Increase = 77.4 - 24.11 = 53.29 Billion

% Increase = $$\frac{53.29}{24.11}*100$$ = 221%

Total investment of E = 57.8 Billion

Total investment of F = 93.2 Billion

Ratio = 57.8 : 93.2 = 19:31

Total contribution in year 2 = 6.7 + 7.5 + 12.5 + 5.6 +  17.4 + 25.3 = 75 billion

Contibution by D in year 2 = 5.6

% contribution by D = $$\frac{5.6}{75}*100$$ = 7.4%

Investment has increased for all the companies.

Investments of A, B and C = 6.7 + 7.5 + 12.5 = 26.7

Investments of A, B and C = 5.6 + 17.4 + 25.3 = 48.3

Difference = 21.6

% difference = $$\frac{21.6}{26.7}*100$$ = 80.8%

According to the divisible rule of 9, the sum of all digits should be divisible by 9.
i.e. 55+A+B = 9k
So sum can be either 63 or 72.
For 63, A+B should be 8.
In given options, option B has values of A and B whose sum is 8 and by putting them we are having a number which divisible by both 9 and 8.
Hence answer will be B.

After solving given equation, we will have inequality resolved to:

(x-1)(x-2)>0

Or we can say range of x will be as follows:

x<1;  x>2

Hence, option A has a set of values which don't lie in the possible range of x.

So the answer will be A.

Consider the following scenario:

One ration shop can be set up at C, so that it covers A,C and B. Another ration shop can be set up between E and D(such that distance of the shop from either of them is not greater than 2) so that it services both E and D.

So, two ration shops are required to be set up for them to be within 2 km of each city. Option a) is the correct answer.

Consider the following scenario:

So, if a ration shop is setup on the line joining A and E, just inside the 3 km radius circle, it will be within 3 km of each city.

Total number of cubes will be = $$\frac{12 \times 12 \times 12}{3 \times 3 \times 3}$$ = 64
Cubes with 3 sides painted = cubes at corner sides = 8
Cubes with 2 sides painted = cubes on lines = 24
Cubes with 1 sides painted = cubes on middle of surface = 24
So cubes with no side painted = 64 - (8+24+24) = 8