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Basic numeracy & statistics MCQ with Answers

20 questionswith explanationsfor RAS, Patwari, VDO and other Rajasthan exams

Questions

Q1

What is the average of 12, 15, 18, 21 and 24?

  1. (1)16
  2. (2)18
  3. (3)19
  4. (4)20

Answer: (2) 18

Explanation

Sum = 90, count = 5, average = 18.

Q2

What is the arithmetic mean of 4, 8, 12, 16 and 20?

  1. (1)12
  2. (2)10
  3. (3)14
  4. (4)15

Answer: (1) 12

Explanation

Mean = (4 + 8 + 12 + 16 + 20) ÷ 5 = 60 ÷ 5 = 12.

Q3

What is the mode of the data: 2, 3, 4, 3, 5, 3, 4?

  1. (1)4
  2. (2)2
  3. (3)3
  4. (4)5

Answer: (3) 3

Explanation

3 occurs most often (3 times), so the mode is 3.

Q4

What is 20% of 250?

  1. (1)25
  2. (2)40
  3. (3)60
  4. (4)50

Answer: (4) 50

Explanation

20% of 250 = 250 × 20/100 = 50.

Q5

What is the simple interest on ₹5,000 at 8% per annum for 3 years?

  1. (1)₹1,200
  2. (2)₹1,000
  3. (3)₹1,500
  4. (4)₹400

Answer: (1) ₹1,200

Explanation

SI = P × R × T / 100 = 5000 × 8 × 3 / 100 = ₹1,200.

Q6

What is the median of 7, 3, 9, 5, 11, 1?

  1. (1)5
  2. (2)7
  3. (3)6
  4. (4)9

Answer: (3) 6

Explanation

Arranged: 1, 3, 5, 7, 9, 11. Median = (5 + 7) ÷ 2 = 6.

Q7

If the price of sugar rises by 25%, by what percentage must a family reduce its consumption so that its expenditure on sugar remains unchanged?

  1. (1)25%
  2. (2)20%
  3. (3)15%
  4. (4)30%

Answer: (2) 20%

Explanation

Reduction = 25/(100 + 25) × 100 = 20%.

Q8

₹1,200 is divided between A and B in the ratio 3 : 5. What is B's share?

  1. (1)₹750
  2. (2)₹450
  3. (3)₹720
  4. (4)₹800

Answer: (1) ₹750

Explanation

B's share = 1200 × 5/8 = ₹750.

Q9

The average of 5 numbers is 20. If one number is removed, the average of the remaining numbers becomes 18. What is the removed number?

  1. (1)20
  2. (2)28
  3. (3)22
  4. (4)30

Answer: (2) 28

Explanation

Removed number = 5 × 20 − 4 × 18 = 100 − 72 = 28.

Q10

What is the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually?

  1. (1)₹2,000
  2. (2)₹2,200
  3. (3)₹2,100
  4. (4)₹1,100

Answer: (3) ₹2,100

Explanation

Amount = 10000 × (1.1)² = ₹12,100; CI = 12,100 − 10,000 = ₹2,100.

Q11

Two successive discounts of 20% and 10% are equivalent to a single discount of:

  1. (1)30%
  2. (2)25%
  3. (3)32%
  4. (4)28%

Answer: (4) 28%

Explanation

Single discount = 20 + 10 − (20 × 10)/100 = 28%.

Q12

In a moderately skewed distribution, the mean is 30 and the median is 32. Using the empirical relation, what is the mode?

  1. (1)34
  2. (2)36
  3. (3)31
  4. (4)38

Answer: (2) 36

Explanation

Mode = 3 × Median − 2 × Mean = 96 − 60 = 36.

Q13

The present ages of A and B are in the ratio 4 : 5. After 5 years, the ratio will be 5 : 6. What is A's present age?

  1. (1)25 years
  2. (2)16 years
  3. (3)24 years
  4. (4)20 years

Answer: (4) 20 years

Explanation

(4x + 5)/(5x + 5) = 5/6 ⇒ 24x + 30 = 25x + 25 ⇒ x = 5; A = 4 × 5 = 20 years.

Q14

What is the median of the data: 12, 7, 15, 9, 20, 11, 18?

  1. (1)13
  2. (2)12
  3. (3)15
  4. (4)11

Answer: (2) 12

Explanation

Arranged in order: 7, 9, 11, 12, 15, 18, 20; the 4th (middle) value is 12.

Q15

What is the range of the data: 34, 18, 52, 27, 41, 19?

  1. (1)25
  2. (2)70
  3. (3)33
  4. (4)34

Answer: (4) 34

Explanation

Range = largest − smallest = 52 − 18 = 34.

Q16

Class A has 30 students with average marks 60, and class B has 20 students with average marks 70. What is the average marks of all 50 students taken together?

  1. (1)62
  2. (2)65
  3. (3)64
  4. (4)66

Answer: (3) 64

Explanation

Weighted average = (30 × 60 + 20 × 70)/50 = 3200/50 = 64.

Q17

The mean of 10 observations is 25. It was later found that one observation, 34, was wrongly copied as 43. What is the correct mean?

  1. (1)25.9
  2. (2)23.2
  3. (3)23
  4. (4)24.1

Answer: (4) 24.1

Explanation

Correct sum = 250 − 43 + 34 = 241; correct mean = 241/10 = 24.1.

Q18

What is the standard deviation (population) of the data: 2, 4, 4, 4, 5, 5, 7, 9?

  1. (1)2.14
  2. (2)2
  3. (3)32
  4. (4)4

Answer: (2) 2

Explanation

Mean = 40/8 = 5; sum of squared deviations = 32; variance = 32/8 = 4; SD = √4 = 2.

Q19

Two fair dice are thrown together. What is the probability that the sum of the numbers obtained is 7?

  1. (1)5/36
  2. (2)1/6
  3. (3)7/36
  4. (4)1/12

Answer: (2) 1/6

Explanation

Favourable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 out of 36, so P = 6/36 = 1/6.

Q20

One card is drawn at random from a well-shuffled pack of 52 playing cards. What is the probability that it is either a king or a heart?

  1. (1)17/52
  2. (2)1/4
  3. (3)4/13
  4. (4)1/52

Answer: (3) 4/13

Explanation

P = 4/52 + 13/52 − 1/52 (king of hearts counted twice) = 16/52 = 4/13.