SNAP 2010 Question Paper

Let x be the average height of the class and n be the number of students in the class.
Consider statements I alone
xn - 56 = (x -1)(n -1)
⇒ x + n = 57        (1)
Hence, the value of x cannot be found. So, I alone is not sufficient.
Consider statement I alone:
xn - 42 = (x + 1)(n - 1)
⇒ x - n = 41           (2)
Hence, the value of x cannot be found. So, II alone is not sufficient.
Both the statements together are sufficient as the value of x can be found by solving (1) and (2)

Given that Ram > Shyam, Vikram > Jay.
Hence from this we can conclude that neither Ram nor Vikram is the shortest. And we have to find the shortest. And we have to find the shortest among them:
Consider statement alone:
We know that that Ram is not the shortest, either Shyam or Jay is the shortest.
Hence (I) alone is not sufficient.
Consider statement I alone Shyam > Vikram.
From the given information and the information in (II), we get Ram > Shyam > Vikram > Jay.
Hence, (II) alone is sufficient.

Let the total sales in July 2009 be Rs. x
Then, sales in September 2009 = Rs. 2x/3
Sales in November 2009 :
= 105% of Rs.$$\ \frac{\ 2x}{3}$$
= Rs. $$\ \ \frac{\ 105}{100}\ \times\ \ \ \frac{\ 2x}{3}$$
= Rs. $$\ \frac{\ 7x}{10}$$
Now, the percentage change in sales :
$$\frac{\left(\frac{\ 7x}{10}-x\ \right)\ }{x}\times\ 100=\ \frac{\ -3x\ \ }{10x}\times\ 100\ =-30\%$$

We have 
$$15x-\frac{2}{x}>1$$

Multiple by x on both sides considering x>0

⇒ $$15x^2-2>x$$
⇒$$15x^2-x-2>0$$
⇒$$15x^2-6x+5x-2>0$$
⇒ (3x+1)(5x-2)>0
we get x>2/5 or x<-1/3 but this is not considered as we have taken x>0

If x<0 the sign of inequality will reverse, and for it to be satisfied we will get the values of x between -1/3<x<0

Hence, the answer is Option D

Let the volume be V of 30% alcohol solution
Now amount of alcohol = 0.3V
Amount of alcohol in 40 liters solution = 24
Now total volume = V+40
Total amount of alcohol = (V+40)(0.5) = 0.5V +20
Now Equating amount of Alcohol :
we get 0.3V +24 = 0.5V +20
we get V = 20

Volume will be same 
Let length be h
we get :
$$66\ =\pi\ \times\ \frac{1}{20}\times\ \frac{1}{20}\times\ x$$
Cross multiplying
we get x=8400 cm or 84 metres

Total distance = 108+112 = 220m
Total time = 6 seconds 
Now we know that :
Relative speed = Distance / Time
so we get :
220/6 = v1+v2
110/3 =125/9 + v
we get v = $$\ \frac{\ 205}{9}$$m/s =$$=\ \frac{\ 205}{9}\times\ \ \frac{\ 18}{5}=$$ 82km/hr

We have R 
When multiplied by 8 we get 8R 
Now taking square we get $$64R^2$$
Dividing by 4 we get $$16R^2$$
Taking square root we get 4R

Let length be 3x, breadth be 2x, and height be x
Now we know that the area of four walls = 2h(l+b) = 2x(5x) = 10$$x^2$$
Now new length = 6x , new height = 0.5x and new breadth = x
So the area of four walls will now be: 2(0.5x)(7x)= 7$$x^2$$
Now therefore percentage change in area : $$\frac{7x^2-10x^2}{10x^2}\times\ 100\ =\ -30\%$$

Hence, the area decreases by 30%.

Exactly two consecutive months include both July-August and August-September. We cannot include July-September, as these months are not consecutive.
             

N - none of the three months

Number of people who read in July and August only = 7

Number of people who read in August and September only = 2

Therefore, the number of surveyed people who have read exactly for two consecutive months = 7+2 = 9

Answer is option B.