Numerical Applications Test 6

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Numerical Applications Test 6

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Weekly Quiz Competition

Question 1
1 / -0

The arithmetic mean of $$12$$ and $$20$$ is :

A
$$12$$

B
$$14$$

C
$$16$$

D
$$18$$

Solution

The arithmetic mean of two numbers is their average.

So, the AM of $$12$$ and $$20$$ is $$ \dfrac { 12+ 20 }{ 2 }= 16$$
Question 2
1 / -0

$$A$$ is 3 times more efficient than $$B$$. Hence, he takes 60 days less in painting a room. In how many days, work will be completed, if $$A$$ and $$B$$ both work together ?

A
30 days

B
45 days

C
$$22\displaystyle\frac{1}{2}$$ days

D
$$17\displaystyle\frac{1}{2}$$ days

Solution

Let $$A$$ takes $$'n'$$ days to paint the room.
So $$B$$ will take $$3n$$ days to paint the room.
$$\Rightarrow 3n - n = 60$$
or $$n = 30$$
$$\Rightarrow A = 30, B = 90$$
$$A$$ & $$B$$ will do $$\displaystyle\dfrac{1}{30} + \displaystyle\dfrac{1}{90} = \displaystyle\dfrac{4}{90} = \displaystyle\dfrac{2}{45}$$ work in a day.
So they will complete the work in $$\displaystyle\dfrac{45}{2} = 22\displaystyle\dfrac{1}{2}$$ days.
Question 3
1 / -0

Mean of $$14, 17, 11, 13, 26, 21, 31$$, and $$19 $$

A
18

B
19

C
17

D
None of these

Solution

Sum of number $$\displaystyle =152$$
Required mean $$\displaystyle =152/8=19$$
Question 4
1 / -0

Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence.
1. Page 2. Pagan 3. Palisade 4. Pageant 5. Palate

A
$$1,4,2,3,5$$

B
$$2,4,1,3,5$$

C
$$2,1,4,5,3$$

D
$$1,4,2,5,3$$

Solution

Words 1,2 and 4 have first 3 letter as "pag" and words "3 and 5 have first 3 letters as "pal". So words starting with "pal" will come later than words starting with "pag" as in Alphabet set the letter "g" comes after letter "a".

The fourth letter of word 5 is "a" and of word 3 is "i" hence word 3 will be the last in order.
So choice A and B are incorrect and the answer will be either C or D.

Simply arranging the 4th letter of words 1,2 and 4 will give the correct sequence choice as C.
Question 5
1 / -0

The weights of 9 apples are 50,60,65,62,67,70,64,45,48 grams Their mean weight is

A
$$60.5\ gram$$

B
$$60\ gram$$

C
$$59\ gram$$

D
$$62\ gram$$

Solution

Mean =$$\dfrac{Total\ weight\ of\ 9\ apples}{Total\ no\ of\ apple}$$
$$\Rightarrow \dfrac{50+60+65+62+67+70+64+45+48}{9}$$
$$\Rightarrow \dfrac{531}{9}=59$$
Question 6
1 / -0

How many times in a day the two hands of a clock coincide?

A
11

B
12

C
22

D
24

Solution

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. Thus the minute hand and the hour hand coincide 22 times in a day.
Option C is correct.
Question 7
1 / -0

If a regular square pyramid has a base of side $$8 cm$$ and height of $$30 cm$$, then its volume is

A
$$120 cm^3.$$

B
$$240 cm^3.$$

C
$$640 cm^3.$$

D
$$900 cm^3.$$

Solution

Given that:
Side $$a=8\ cm$$, Height $$h=30\ cm$$
As we know that
Volume of regular square pyramid
$$\Rightarrow a^2\dfrac{h}{3}$$
$$\Rightarrow 8^2\dfrac{30}{3}$$
$$\Rightarrow 64\times 10$$
$$\Rightarrow 640\ cm^3$$
This is the required solution.
Question 8
1 / -0

The mean of the factors of 24 is;

A
$$\displaystyle \frac{12}{5}$$

B
$$\displaystyle \frac{9}{5}$$

C
$$\displaystyle \frac{15}{2}$$

D
$$\displaystyle \frac{17}{5}$$

Solution

The factor of 24 are 1,2,3,4,6,8,12,24
$$\therefore A.M=\dfrac{\sum x}{n}$$
$$\Rightarrow \dfrac{1+2+3+4+6+8+12+24}{8}$$
$$\Rightarrow \dfrac{60}{8}=\dfrac{15}{2}$$
Question 9
1 / -0

The arithmetic mean of 5, 6, 8, 9, 12, 13, 17 is

A
$$20$$

B
$$15$$

C
$$10$$

D
$$25$$

Solution

Arithmetic mean $$=\dfrac {\text{Sum of Terms}}{\text{No. of Terms}}=\dfrac {5+6+8+9+12+13+17}{7}$$

Arithmetic mean $$=\dfrac {70}{7} = 10$$
Question 10
1 / -0

The mean of first 8 natural numbers is

A
$$4.5$$

B
$$5$$

C
$$4$$

D
$$5.5$$

Solution

$$\textbf{Step 1: Finding the sum of observations and number of observations}$$

$$\text{The first 8 natural numbers are }1,\;2,\;3,\;4,\;5,\;6,\;7,\;8$$

$$\text{Sum of observations}=1+2+3+4+5+6+7+8=36$$

$$\text{Number of observations}=8$$

$$\textbf{Step 2: Finding the mean}$$

$$\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}$$

$$\text{Mean}=\dfrac{36}{8}=4.5$$

$$\textbf{Thus, the mean of the first 8 natural numbers is 4.5}$$

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Re-Attempt Weekly Quiz Competition

Numerical Applications Test 6

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Numerical Applications Test 6

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SHARING IS CARING

Question 1

$$12$$

$$14$$

$$16$$

$$18$$

Solution

Question 2

30 days

45 days

$$22\displaystyle\frac{1}{2}$$ days

$$17\displaystyle\frac{1}{2}$$ days

Solution

Question 3

18

19

17

None of these

Solution

Question 4

$$1,4,2,3,5$$

$$2,4,1,3,5$$

$$2,1,4,5,3$$

$$1,4,2,5,3$$

Solution

Question 5

$$60.5\ gram$$

$$60\ gram$$

$$59\ gram$$

$$62\ gram$$

Solution

Question 6

11

12

22

24

Solution

Question 7

$$120 cm^3.$$

$$240 cm^3.$$

$$640 cm^3.$$

$$900 cm^3.$$

Solution

Question 8

$$\displaystyle \frac{12}{5}$$

$$\displaystyle \frac{9}{5}$$

$$\displaystyle \frac{15}{2}$$

$$\displaystyle \frac{17}{5}$$

Solution

Question 9

$$20$$

$$15$$

$$10$$

$$25$$

Solution

Question 10

$$4.5$$

$$5$$

$$4$$

$$5.5$$

Solution

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