SNAP 2008

The total number of moviegoers in a city = Number of people who watch less than 1 movie per week + Number of people who watch one or more movie per week

For city A, the percentage of viewers who watch less than one movie a week = 60, hence the percentage of viewers who view one or more movies per week = 100-60 = 40

=> 40% of the total number of viewers in A = 2400    => The total number of viewers = $$\ \frac{\ 2400\times\ 100}{40}$$ = 6000

=> The number of viewers who watch less than one movie a week = $$6000\times\ \frac{\ 60}{100}$$ =3600

Similarly, we can tabulate the data for the rest of the cities:

Both A and D have second lowest number of movie watchers. B is the answer.

The total number of moviegoers in a city = Number of people who watch less than 1 movie per week + Number of people who watch one or more movie per week

For city A, the percentage of viewers who watch less than one movie a week = 60, hence the percentage of viewers who view one or more movies per week = 100-60 = 40

=> 40% of the total number of viewers in A = 2400    => The total number of viewers = $$\ \frac{\ 2400\times\ 100}{40}$$ = 6000

=> The number of viewers who watch less than one movie a week = $$6000\times\ \frac{\ 60}{100}$$ =3600

Similarly, we can tabulate the data for the rest of the cities:

The total number of all moviegoers in the five cities who watch less than one movie per week = 3600+750+13600+3300+24000 = 45250

Here, $$\ \frac{\ n\left(n-1\right)}{2}$$(not inclusive) term to $$\ \frac{\ n\left(n+1\right)}{2}$$(inclusive) term is the nth place alphabet.   (1st place alphabet is a, 2nd place alphabet is b, and so on.) 

=> $$\ \frac{\ n\left(n-1\right)}{2}$$ < 288 < $$\ \frac{\ n\left(n+1\right)}{2}$$

=> n(n-1) < 576 < n(n+1)

n = 24 

At 24th place, x is the alphabet.

We have, p$$^2$$ + 5 < 5p + 14

=> p$$^2$$ - 5p - 9 < 0

=> p< $$\ \frac{\ 5\ +\ \sqrt{\ 61}}{2}$$ or p> $$\ \frac{\ 5\ -\ \sqrt{\ 61}}{2}$$ 

=> p<6.4 or p>-1.4

Hence, p ≤ 6, p > −1 will satisfy the inequalities

The sweetness of glucose = 0.74, the sweetness of lactose = 0.16 The sweetness of Maltose = 0.32

Using alligation, the ratio = $$\ \dfrac{\ 0.32-0.16}{0.74-0.32}$$ = $$\ \dfrac{\ 16}{42}$$ = 8:21

Assuming the sides of the cube = a, then surface painted blue = 6a$$^2$$

Now after cutting into half the blue surface = 3a$$^2$$ for each solid and a new colourless surface with area a$$^2$$ is generated.

Hence the total surface area  = 3a$$^2$$ + a$$^2$$ = 4a$$^2$$

% surface area not painted blue = $$\ \dfrac{\ a^2}{4a^2}\times\ 100$$ = 25

The number of different journey tickets that are required by the authorities = The number of selecting 2 stations $$\times\ $$ 2   (For every pair stations say A and B, there are two tickets required A to B and B to A)

= $$\\^{10}C_2$$ * 2 = 45*2=90

The probability of throwing a 6 = $$\ \frac{\ \ 1}{\ 6}$$

The probability of not throwing a 6 = $$\ \frac{\ \ 5}{\ 6}$$

The probability that A wins = $$\ \frac{\ \ 1}{\ 6}+\ \frac{\ 5}{\ 6}\times\ \ \frac{\ 5}{6}\times\ \ \frac{\ 1}{6}+\ \frac{\ 5}{6}\ \times\ \ \frac{\ 5}{6}\times\ \ \frac{\ 5}{6}\times\ \ \frac{\ 5}{6}\times\ \frac{\ 1}{6}\ +\ ...............$$

= $$\ \frac{\ 1}{6}\left(1+\left(\ \frac{\ 5}{6}\right)^2+\left(\ \frac{\ 5}{6}\right)^4.........\right)$$

= $$\ \ \frac{\ 1}{6}\left(\ \dfrac{\ 1}{\ 1-\ \frac{\ 25}{36}}\right)$$ = $$\ \frac{\ 6}{11}$$

The expected return of A  = 11*$$\ \frac{\ 6}{11}$$ = 6

Hence the expected return of B = 11-6=5

A says that, for an investment of Rs. 75, the return will be 5% on Rs. 10, with a 30% tax. 

So, Total return= $$\ \frac{\ 5}{100\ }\cdot10$$.

After tax deduction, Final Return= $$\ \frac{\ 5}{100\ }\cdot10\cdot\ \frac{\ 70}{100}$$ = 0.35

Percentage return= $$\ \frac{\ 0.35}{75}\cdot100$$= $$\ \frac{\ 35}{75}$$= 0.467%

B says that, for an investment of Rs. 90, the return will be 4% on Rs. 10, tax free.

So, Total return= $$\ \frac{\ 4}{100}\cdot10$$ =0.4

Percentage return for B= $$\ \frac{\ 0.4}{90}\cdot100$$= $$\ \frac{\ 40}{90}$$= 0.444%

Since, Percentage return in case A is greater than that in case B. Therefore, Option B is correct.

Total number of chips = 11+9+13+7=40

Total number of chips in each stack = 40/4 = 10

Total number of white chips = 9, 

The maximum number of white chips in a stack will be obtained when 1 white chip given to each of 3 stacks and 6 white chips to 1 stack.

Hence, 6 is the answer.