Instructions

For the following questions answer them individually

Question 81

In 4 years, the SI on a certain sum of money is $$\frac{7}{25}$$ of the principal. What is the annual rate of interest?

Video Solution

Solution

SI = $$\frac{PTR}{100}$$

Given SI = 7/25P when t=4

$$\frac{7}{25}P\ =\frac{4PR}{100}$$

=> R=7

Question 82

Thirty days are in September, April, June and November. Some months are of thirty one days. A month is chosen at random.
Then its probability of having exactly three days less than maximum of 31 is

Video Solution

Solution

Number of days in February = 28

Number of months having three days less than 31 i.e, 28 days = 1

$$\therefore\ $$Required probability = $$\frac{1}{12}$$

Hence, the correct answer is Option D

Question 83

Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of $$2^{nd}$$ escalator is 3:5 (steps). Find the total number of steps they both have taken
together.

Video Solution

Solution

First person: For every 2 steps he takes, the escalator moves by 3 steps at the same time.
Hence, 5 steps are covered at a time.
This is repeated 24 times(120/5).
Hence, first person takes = 24 *2 = 48 steps
Second person: For every 3 steps he takes, the escalator moves by 5 steps at the same time.
Hence, 8 steps are covered at a time.
This is repeated for 15 times(120/8)
Hence, second person takes = 3 * 15 = 45 steps
Total number of steps = 48 + 45 = 93

Question 84

The table below shows the temperatures in degrees Fahrenheit in a city over one week. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of
the following is the correct order of m, f, and a?

Video Solution

Solution

When arranged in ascending order, we get the noontime temperatures as:

66, 69, 70, 75, 77, 78 and 78.

m= 75.

f= 78 (occurs twice)

a= $$\ \frac{\ \left(66+69+70+75+77+78+78\right)}{7}=\ \ \frac{\ 513}{7}=73.29$$

So, a<m<f. -Option B

Question 85

Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower
bed runs a uniform path of such a width that the sides of the park are exactly double the
corresponding sides of the flower bed. The ratio of areas of the path to the flower bed is:

Video Solution

Solution

Lets assume the park is an equilateral triangle with side '2x' units, => the side of the flower bed = 'x' units

Area of park = $$\frac{\sqrt{\ 3}}{4}\cdot\left(2x\right)^2$$ =$$\frac{\sqrt{\ 3}}{4}\cdot4x^2$$

Area of flower bed = $$\frac{\sqrt{\ 3}}{4}\cdot x^2$$

Area of path = area of park - area of flower bed = $$\frac{\sqrt{\ 3}}{4}\cdot3x^2$$

Ratio of area of path to area of flower bed = $$\frac{\left(\frac{\sqrt{\ 3}}{4}\cdot3x^2\right)}{\frac{\sqrt{\ 3}}{4}x^2}$$ = 3:1

Question 86

Consider the following piecewise definition of the function f.

$$f(x) = \begin{cases}3 - x, if & x \leq 0\\x^2 + 2, if & x \geq 0\end{cases}$$

Evaluate f(-3).

Video Solution

Solution

f(x) = 3-x , if x$$\le\ $$0

$$\therefore\ $$ f(-3) = 3-(-3) = 6

Question 87

A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year- Ill, 150 Year-II, and 200 Year-I students who applied. Each Year-III’s name is placed in the lottery 3 times; each Year-II’s name, 2 times; and each Year-I’s name, 1 time. What is the probability that a Year-III’s name will be chosen?

Video Solution

Solution

By the given information,

Total number of Year III student's name= 3*100= 300

Total number of Year II student's name= 2*150= 300

Total number of Year I student's name= 1*200= 200.

Number of favourable outcomes= year III student's name= 300

Total Sample space= total number of names= 300+300+200= 800.

Therefore, required probability= $$\ \frac{\ 300}{800}=\ \ \frac{\ 3}{8}$$- Option D

Question 88

The average of nine numbers is M and the average of three of these is P. If the average of remaining numbers is N, then

Video Solution

Solution

This can be solved easily by using allegations

$$p=\frac{\left(p1q1+p2q2\right)}{q1+q2}$$

Here p = M , p1=P , p2=N

q1=3 , q2=6

$$\ \therefore\ M=\frac{\left(3P+6N\right)}{3+6}$$

On solving 3M = P+2N

Question 89

The intersection of two cubes cannot be

Video Solution

Solution

Cubes are a 3-D figure, and so, the intersection of two 3-D figure must be a 2-D figure.

So, Cube cannot be the intersection of two cubes.

Question 90

In a factory, each day the expected number of accidents is related to the number of overtime hour by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents. What is the expected number of accidents when no overtime hours are logged?

Video Solution

Solution

Let the number of overtime hours logged be x.

Let the number of accidents reported be A.

So, since the relationship between A and x is linear, we can write A= ax+c

Given, when x=1000, A=8.

So, 8= 1000a+ c--------------(1)

Again, when x= 400, A=5.

So, 5= 400a+ c ----------------(2)

Subtracting Eqn 2 from 1, we get,

600a= 3

=> a= 1/200.

Now putting this value of a in Eqn 1, we find

8= $$\ \frac{\ 1000}{200}+c$$

=>c= 8-5=3.

So, when x=0,

A= c= 3- option B

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SNAP 2007 Question Paper

In 4 years, the SI on a certain sum of money is $$\frac{7}{25}$$ of the principal. What is the annual rate of interest?

Thirty days are in September, April, June and November. Some months are of thirty one days. A month is chosen at random.
Then its probability of having exactly three days less than maximum of 31 is

Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of $$2^{nd}$$ escalator is 3:5 (steps). Find the total number of steps they both have taken
together.

Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower
bed runs a uniform path of such a width that the sides of the park are exactly double the
corresponding sides of the flower bed. The ratio of areas of the path to the flower bed is:

Consider the following piecewise definition of the function f.

$$f(x) = \begin{cases}3 - x, if & x \leq 0\\x^2 + 2, if & x \geq 0\end{cases}$$

Evaluate f(-3).

The average of nine numbers is M and the average of three of these is P. If the average of remaining numbers is N, then

The intersection of two cubes cannot be

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