Numerical Ability Test

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Numerical Ability Test - 25

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Weekly Quiz Competition

Question 1
5 / -1

The difference between the mean of the first eight composite natural numbers and the mean of the first eight prime numbers, is:

A
1/4

B
3/20

C
1/5

D
1/8

Solution

Concept:

Composite Numbers = They are those numbers that have more than two factors. For example, 6 (1 × 2 × 3) is a composite number since it has three factors.

Prime Numbers = They are natural numbers greater than 1 and are not a product of two smaller natural numbers. A prime number has exactly two factors, that is, 1 and the number itself.

Formula used:

Mean/ Average = Sum of all observations/ Total no of all observations

Calculation:

First eight composite natural numbers = 4, 6, 8, 9, 10, 12, 14, 15

First eight prime numbers = 2, 3, 5, 7, 11, 13, 17, 19

Mean of the first 8 composite numbers = (4 + 6 + 8 + 9 + 10 + 12 + 14 + 15) ÷ 8

⇒ 78 ÷ 8

Mean of the first 8 prime numbers = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19) ÷ 8 = 77 ÷ 8

∴ The required difference = 78 ÷ 8 - 77 ÷ 8 = 1/8
Question 2
5 / -1

3 numbers whose average is 112, the first number is 1/6th the sum of the other two numbers. What is the first number?

A
45

B
30

C
15

D
48

Solution

∵ Average of three numbers is 112

This means sum of 3 numbers is = 112 × 3 = 336

Let the first number be X

Then X = (1/6) × (Sum of other two numbers) = (1/6) × (336 - X)

⇒ X + X/6 = 336/6

⇒ X = 336/7 = 48

∴ First number = 48
Question 3
5 / -1

There are 15 students in a class. Their average weight is 40 kg. When one student leaves the class, the average weight is 39.5 kg. What is the weight of the student who left the class (where kg means kilogram)?

A
47 kg

B
42 kg

C
52 kg

D
48 kg

Solution

Given:

There are 15 students in a class.

Their average weight is 40 kg.

When one student leaves the class, the average weight is 39.5 kg.

Calculation:

The total weight of 15 students is 15 × 40 = 600 kg

The total weight of 14 students is 14 × 39.5 = 553 kg

The weight of new students is 600 - 553 = 47 kg

∴ The correct option is 1
Question 4
5 / -1

A park had an average of 30 children playing on weekdays and an average of 60 children playing on weekends. Find the average number of children playing per day in the park for the month of June beginning with a Saturday.

A
45

B
60

C
40

D
30

Solution

Given:

Average of 30 children playing on weekdays

Average of 60 children playing on weekends

Concept used:

Calculation of overall average.

Solution:

Total number of children playing on weekdays in June = 30 × 20 = 600 (as June has 20 weekdays)

Total number of children playing on weekends in June = 60 × 10 = 600 (as June has 10 weekends)

Total number of children playing in June = 600 + 600 = 1200

Average number of children playing per day = Total number of children / Total days = 1200 / 30 = 40

Therefore, the average number of children playing per day in the park for June is 40.

Mistake Points

This question is from the official paper of SSC.

In most of the world, the workdays are from Monday to Friday and the weekend is from Saturday to Sunday.

So we have to consider Saturday and Sunday as weekends.

In June beginning with a Saturday, 10 weekends and 20 weekdays present.
Question 5
5 / -1

A truck owner buys petrol at Rs. 6.50, Rs. 7 and Rs. 7.50 per litre for three successive years. What approximately will be the average cost per litre of petrol if he spends Rs. 3200 each year?

A
6.1

B
6.23

C
6.97

D
7.12

Solution

⇒ Amount spend yearly on petrol = Rs. 3200

⇒ Total amount of petrol consumed = (3200/6.50) + (3200/7) + (3200/7.50) = 1376.11 litres

⇒ Total amount spent in 3 years on petrol = 3200 × 3 = Rs. 9600

⇒ Average cost per litre of petrol = Total amount spent in 3 years on petrol/ Total amount of petrol consumed

⇒ Average cost per liter of petrol = 9600/1376.11 = 6.97

∴ Average cost per liter of petrol is Rs. 6.97
Question 6
5 / -1

Find the average of 1³ + 2³ + 3³ + 4³ .....+ 20³.

A
2202

B
2200

C
2205

D
2204

Solution

Given:

Number of terms = 20

Formula used:

Average = [n(n + 1)/2]² × (1/no. of terms)

Where n is number of term.

Calculation:

Average = [(20 × 21)/2]² × 1/20

⇒ Average = (10 × 10 × 21 × 21)/20 = 2205

∴ The answer will be 2205.
Question 7
5 / -1

The average of the first four numbers is three times the fifth number. If the average of all the five numbers is 85.8, then the fifth number is;

A
39

B
34

C
33

D
29

Solution

Let the fifth number be x, then

Average of first four number is = 3x

According to the question

4 × 3x + x = 85.8 × 5

⇒ 12x + x = 429

⇒ 13x = 429

⇒ x = 429/13

∴ x = 33
Question 8
5 / -1

The average age of Ram and Shyam is 28 years. If Rahim replaces Ram, then the average age will become 26 years. If Rahim replaces Shyam, then the average age will become 30 years. What are the respective ages of Ram, Shyam and Rahim?

A
32 years, 24 years and 28 years

B
34 years, 40 years and 30 years

C
48 years, 40 years and 26 years

D
38 years, 44 years and 36 years

Solution

Calculation:

Ram + Shyam = 28 × 2 = 56

Rahim + Shyam = 26 × 2 = 52

Rahim + Ram = 30 × 2 = 60

Hence, Ram + Shyam + Rahim = (56 + 60 + 52)/2 = 84

Age of Ram = 84 - 52 = 32 years

Age of Shyam = 84 - 60 = 24 years

Age of Rahim = 84 - 56 = 28 years

∴ Option 1 is the correct answer.
Question 9
5 / -1

Including Anni 12 persons, had gone to restaurants in which, every 11 persons spends 64 rupees on food 12^th person spends 66 more rupees than average of all 12 persons then find the total expense on food.

A
840

B
890

C
900

D
920

Solution

Given:

12 persons had gone to restaurants.

11 out of 12 spend 64 rupees on food each.

12th person spends Rs. 66 rupees more than the average of all persons

Formula used:

Total weight = Average weight × Number of boxes

Calculation:

Let the average expenditure be X

As 11 persons each spend 64 rupees and the 12^th spends X + 66

⇒ (11× 64 + X + 66) / 12 = X

⇒ 11 × 64 + X + 66 = 12X

⇒ 11X = 11 × 64 + 66, X = 64 + 6, X = 70

∴ Total expanse is 12 × 70 = 840
Question 10
5 / -1

A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.

A
30

B
37

C
39

D
40

Solution

GIVEN:

Batsman score in 17th inning = 87 and his average increases by 3

CALCULATION:

Batsman score in 17th inning = 87 and his average increases by 3

⇒ Let the average after 17th inning = x

⇒ Average after 16th inning = (x - 3)

⇒ 16 × (x - 3) + 87 = 17x

⇒ x = 87 - 48

⇒ x = 39

∴ His Average after the 17th inning will be 39

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Re-Attempt Weekly Quiz Competition

Numerical Ability Test - 25

Result

Numerical Ability Test - 25

Score

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SHARING IS CARING

Question 1

1/4

3/20

1/5

1/8

Solution

Question 2

45

30

15

48

Solution

Question 3

47 kg

42 kg

52 kg

48 kg

Solution

Question 4

45

60

40

30

Solution

Question 5

6.1

6.23

6.97

7.12

Solution

Question 6

2202

2200

2205

2204

Solution

Question 7

39

34

33

29

Solution

Question 8

32 years, 24 years and 28 years

34 years, 40 years and 30 years

48 years, 40 years and 26 years

38 years, 44 years and 36 years

Solution

Question 9

840

890

900

920

Solution

Question 10

30

37

39

40

Solution

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