Numerical Applications Test 38

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Numerical Applications Test 38

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Weekly Quiz Competition

Question 1
1 / -0

Computer K can perform $$x$$ calculations in $$y$$ seconds and computer L can perform $$r$$ calculations in $$s$$ minutes. Find the number of calculations they can perform in $$t$$ minutes by working together simultaneously.

A
$$t\left (\dfrac {x}{60y} + \dfrac {r}{s}\right )$$

B
$$t\left (\dfrac {60x}{y} + \dfrac {r}{s}\right )$$

C
$$t\left (\dfrac {x}{y} + \dfrac {r}{s}\right )$$

D
$$t\left (\dfrac {x}{y} + \dfrac {60r}{s}\right )$$

E
$$60t\left (\dfrac {x}{y} + \dfrac {r}{s}\right )$$

Solution

Given, computer $$K$$ can perform $$x$$ calculations in $$y$$ seconds and computer $$L$$ can perform $$r$$ calculations in s minutes.
Then computer $$K$$ can do one calculation $$=$$ $$\dfrac{60x}{y}$$ minutes
And computer $$L$$ can do one calculation $$=$$ $$\dfrac{r}{s}$$ minutes
Then both computer calculation in $$t$$ minutes $$=$$ $$\left ( \dfrac{60x}{y}+\dfrac{r}{s} \right )t$$
Question 2
1 / -0

The monthly fees for single rooms at $$5$$ colleges are $$370$$, $$310$$, $$380$$, $$340$$, and $$310$$, respectively. What is the mean of these monthly fees?

A
$$310$$

B
$$340$$

C
$$342$$

D
$$350$$

E
$$380$$

Solution

The mean is same like average. Add all and then divide by the number of colleges.
Average $$=$$ $$\dfrac {(370+310+380+340+310)}{5}=\dfrac {1710}{5}=342$$
Therefore the mean of these monthly fees is $$342$$.
Hence, option $$C$$ is correct.
Question 3
1 / -0

What is the average(arithmetic mean) of all the multiples of ten from $$10$$ to $$190$$ inclusive?

A
$$90$$

B
$$95$$

C
$$100$$

D
$$105$$

E
$$110$$

Solution
Question 4
1 / -0

A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

A
Rs. $$7.98$$

B
Rs. $$8$$

C
Rs. $$8.50$$

D
Rs. $$9$$

Solution

Total quantity of petrol consumed in 3 years = $$\begin{pmatrix}\dfrac{400}{7.50}+\dfrac{4000}{8}+\dfrac{4000}{8.50}\end{pmatrix}$$ litres
= $$4000 \begin{pmatrix}\dfrac{2}{15}+\dfrac{1}{8}\dfrac{2}{17}\end{pmatrix}$$ litres
= $$\begin{pmatrix}\dfrac{76700}{51}\end{pmatrix}$$ litres
Total amount spent = Rs. (3 x 4000) = Rs. 12000.
$$\therefore$$ Average cost = Rs. $$\begin{pmatrix}\dfrac{12000\times 51}{76700}\end{pmatrix}$$ = Rs. $$\dfrac{6120}{767}$$ = Rs. $$7.98$$
Question 5
1 / -0

A square pyramid is inscribed in a cube of total surface area of $$24$$ square cm such that the base of the pyramid is the same as the base of the cube. What is the volume of the pyramid?

A
$$\dfrac 13$$

B
$$\dfrac 83$$

C
$$6$$

D
$$4$$

E
$$8$$

Solution

Given that total surface area of cube is $$24$$ and cube has $$6$$ faces. so the area of each face is $$\dfrac {24}6 = 4$$
therefore the length of side of each face and the height of cube is $$2$$
So the volume of pyramid is $$\dfrac {lwh}3 = 2 \times 2 \times \dfrac 23 = \dfrac 83$$
Question 6
1 / -0

January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

A
Monday

B
Tuesday

C
Wednesday

D
Sunday

Solution

The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Question 7
1 / -0

The amount of time taken to paint a wall is inversely proportional to the number of painters working on the job. If it takes 3 painters 5 days to complete such a job, how many days longer will it take if there are only 2 painters working?

A
$$2.5$$

B
$$2$$

C
$$2.4$$

D
None

Solution
Question 8
1 / -0

Let $$\boxed { n }$$ be defined as $$\frac{(n+2)!}{(n-1)!}$$, what is the value of $$\frac{\boxed{7}}{\boxed {3}}$$ ?

A
4.4

B
8.4

C
12.4

D
16.4

E
20.4

Solution

Given, box $$n$$ is equal to $$\dfrac{(n+2)!}{(n-1)!}=(n+2)(n+1)n$$
We get box $$7$$ is equal to $$9 \times 8 \times 7 =504$$
We get box $$3$$ is equal to $$5 \times 4 \times 3 = 60$$
Therefore, If we divide those two, we get $$\dfrac{504}{60} = 8.4$$.
Question 9
1 / -0

If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?

A
3

B
15

C
17

D
35

E
42
Question 10
1 / -0

What is the average of four tenths and five thousandths?

A
$$25002$$

B
$$2502$$

C
$$0.225$$

D
$$0.2025$$

E
$$0.02025$$

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Numerical Applications Test 38

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Numerical Applications Test 38

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Question 1

$$t\left (\dfrac {x}{60y} + \dfrac {r}{s}\right )$$

$$t\left (\dfrac {60x}{y} + \dfrac {r}{s}\right )$$

$$t\left (\dfrac {x}{y} + \dfrac {r}{s}\right )$$

$$t\left (\dfrac {x}{y} + \dfrac {60r}{s}\right )$$

$$60t\left (\dfrac {x}{y} + \dfrac {r}{s}\right )$$

Solution

Question 2

$$310$$

$$340$$

$$342$$

$$350$$

$$380$$

Solution

Question 3

$$90$$

$$95$$

$$100$$

$$105$$

$$110$$

Solution

Question 4

Rs. $$7.98$$

Rs. $$8$$

Rs. $$8.50$$

Rs. $$9$$

Solution

Question 5

$$\dfrac 13$$

$$\dfrac 83$$

$$6$$

$$4$$

$$8$$

Solution

Question 6

Monday

Tuesday

Wednesday

Sunday

Solution

Question 7

$$2.5$$

$$2$$

$$2.4$$

None

Solution

Question 8

4.4

8.4

12.4

16.4

20.4

Solution

Question 9

3

15

17

35

42

Question 10

$$25002$$

$$2502$$

$$0.225$$

$$0.2025$$

$$0.02025$$

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