Mix Test - 3

From the given graph the data can be depicted as:

Percentage of unemployed people in the countries as per the data is given below,

A = 30, B = 40, C = 20, D = 60, E = 10, F = 25

∴ Highest percentage of unemployed people are in country D.

Hence, the correct option is (C).

Let total population of the country be x.

Percentage of unemployed people in Country C = 20%

⇒ Number of people unemployed in country C = $\frac{\mathrm{x}}{5}$

Percentage of unemployed people in Country F = 25%

⇒ Number of people unemployed in country F = $\frac{\mathrm{x}}{4}$

∴ Required percentage = $\frac{{\displaystyle \frac{\mathrm{x}}{5}}}{\frac{\mathrm{x}}{4}}\times 100=80\%$

Hence, the correct option is (B).

Given:

Percentage of unemployment in country A = 30%

Percentage of unemployment in country B = 40%

Percentage of unemployment in country C = 20%

Percentage of unemployment in country D = 60%

Percentage of unemployment in country E = 10%

Percentage of unemployment in country F = 25%

Formula:

Average = $\frac{\mathrm{Sum} \mathrm{of} \mathrm{all} \mathrm{the} \mathrm{observations}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{observations}}$

Calculation:

Sum of all observations = 30% + 40% + 20% + 60% + 10% + 25% = 185%

Number of observations = $\frac{185\%}{6}=30.833\%$

As we can see that country A, C, E and F has lower unemployment percentage than average unemployment percentage.

∴ The country which have the low unemployment percentage compared to the average unemployment are A, C, E, F.

Hence, the correct option is (B).

Given:

Percentage of unemployed people in Country A = 30%

Percentage of unemployed people in Country D = 60%

Let the population of each country be x.

Number of people unemployed in country A = $\frac{3\mathrm{x}}{10}$

Number of people unemployed in country D = $\frac{3\mathrm{x}}{5}$

∴ Required ratio = $\frac{3\mathrm{x}}{10}:\frac{3\mathrm{x}}{5}=1:2$

Hence, the correct option is (D).

Given:

Percentage of unemployed people in country B = 40

Percentage of unemployed people in country C = 20

Calculation:

Required difference = 40 – 20 = 20%

Hence, the correct option is (A).

Given:

Number = 1683

Formula:

If N = x^a × y^b (where x and y are prime numbers), then,

Number of factors = (a + 1) × (b + 1)

Calculation:

Factors of 1683 = 3² × 11¹ × 17¹

∴ Number of factors = (2 + 1) × (1 + 1) × (1 + 1) = 12

Hence, the correct option is (A).

According to the question,

\(\frac{x}{y}=\frac{5}{6}\)

\(\Rightarrow 6 x-5 y=0\) .....(i)

\(\frac{x-8}{y-8}=\frac{4}{5}\)

\(\Rightarrow 5 x-40=4 y-32\)

\(\Rightarrow 5 x-4 y=8\) .....(ii)

From equation (i)

\(6 x-5 y=0\)

\(\Rightarrow x=\frac{5 y}{6}\)

Substituting in ...(ii)

\(5 x-4 y=8\)

\(\Rightarrow 5\left(\frac{5 y}{6}\right)-4 y=8\)

\(\Rightarrow \frac{y}{6}=8\)

\(\Rightarrow y=48\)

Therefore,

\(x=\frac{5 y}{6} \)

\(\Rightarrow x=\frac{5 \times 48}{6}\)

\(\Rightarrow x=40\)

So, the numbers are 40, 48.

Hence, the correct option is (C).

Given:

Articles = 40

The profit is 25%

Calculation:

40CP = x × SP

$\Rightarrow \frac{\mathrm{CP}}{\mathrm{SP}}=\frac{\mathrm{x}}{40}$      ---(i)

As the profit% is 25%

$\frac{\mathrm{CP}}{\mathrm{SP}}=\frac{100}{125}=\frac{4}{5}$      ---(ii)

Equating (i) and (ii), we'll get

$\frac{\mathrm{x}}{40}=\frac{4}{5}$

$\mathrm{x}=\frac{4}{5}\times 40=32$

∴ The value of x is 32.

Hence, the correct option is (B).

Given:

Marked Price of article = Rs. 800

Selling Price of article = Rs. 512

Formula:

Selling Price = Marked Price × $\frac{100-\mathrm{Discount}\%}{100}$

Let the discount percent be x.

$\Rightarrow 512=800\times {\left(\frac{100-\mathrm{x}}{100}\right)}^2$

$\Rightarrow \frac{64}{100}={\left(\frac{100-\mathrm{x}}{100}\right)}^2$

⇒ x = 20%

∴ The required answer is 20%.

Hence, the correct option is (B).

Given:

C.P. of 5 bottles = Rs.300

S.P. of 5 bottles = Rs. 740

∴ Profit earned by selling 5 bottles = Rs. 440

Rs. 440 is earned by selling 5 bottles.

$\Rightarrow \frac{5\times 7040}{440}=80$

∴ By selling 80 bottles, there will be a profit of Rs 7040.

Hence, the correct option is (B).

768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2⁸ × 3

⇒ 768 × 3 = 2⁸ × 3² = (2⁴ × 3)² (multiplication by 3 to make perfect square)

∴ 768 must be multiplied by 3 to get a perfect square.

Hence, the correct option is (D).

Concept:

The least number which is exactly divisible by each of the given numbers is called the least common multiple of those numbers.

The least number which is exactly divisible by each one of the given number is called their LCM.

The four digit number is = 9999

Calculation:

24 = 2 × 2 × 2 × 3

30 = 2 × 3 × 5

36 = 2 × 2 × 3 × 3

LCM of 24, 30 and 36 is = 2 × 2 × 2 × 3 × 3 × 5 = 360

When we divide 9999 by 360 we get quotient 27 and remainder 279.

Largest four digit number which is divisible by each of 24, 30 and 36 is = 9999 - 279 = 9720

Hence, the correct option is (A).

The number = 540

Factorization = 2 × 270

= 2 × 3 × 90 

= 2 × 3 × 2 × 45

= 2 × 3 × 2 × 3 × 15

=  2 × 3 × 2 × 3 × 3 × 5

= 22 × 33 × 51

Number of even factors of N = (p + 1) × (q + 1) × r

Here, p = 3, q = 1 and r = 2

Number of even factors of 540 = (3 + 1)(1 + 1)(2) = 16

∴ The number of even factors of 540 is 16.

Hence, the correct option is (C).

Given:

A : B = 5 : 3

B : C = 11 : 10

C : D = 5 : 6

Calculations:

We can write these ration in fractions as

$\frac{\mathrm{A}}{\mathrm{B}}=\frac{5}{3}$      ----(1)

$\frac{\mathrm{B}}{\mathrm{C}}=\frac{11}{10}$      ----(2)

$\frac{\mathrm{C}}{\mathrm{D}}=\frac{5}{6}$      ----(3)

Multiplying numerator and denominator of equation (3) by 6 we get,

$\Rightarrow \frac{\mathrm{C}}{\mathrm{D}}=\frac{30}{36}$

Multiplying numerator and denominator of equation (2) by 3 we get,

$\Rightarrow \frac{\mathrm{B}}{\mathrm{C}}=\frac{33}{30}$

Multiplying numerator and denominator of equation (1) by 11 we get,

$\Rightarrow \frac{\mathrm{A}}{\mathrm{B}}=\frac{55}{33}$

So, we can write it in the form

A : B : C : D = 55 : 33 : 30 : 36

∴ The ratio of A : B : C : D is 55 : 33 : 30 : 36.

Hence, the correct option is (B).

Let 'S' be the sample space.

Total number of balls in the box = 6 black + 8 white = 14 balls

n(S) = 14

Let E be the event of drawing a white ball from the box, n(E) = 8

∴ Probability that the ball drawn from the box is white = $=\frac{\mathrm{n}\left(\mathrm{S}\right)}{\mathrm{n}\left(\mathrm{E}\right)}=\frac{8}{14}=\frac{4}{7}$

Hence, the correct option is (D).