NAB Investigation Officer (BS-17) Mathematics Averages — Set 3

1. Question 1

   Q1. The sum of the squares of two numbers is 97, and the square of their difference is 25. The product of the two numbers is:

   • A) 36
   • B) 63
   • C) 45
   • D) 54

   Answer: 36

   Explanation: Expanding (x − y)² = x² − 2xy + y² = 25, and substituting x² + y² = 97 gives 97 − 2xy = 25, so the product xy = 36.

2. Question 2

   Q2. The sum of two numbers is 45. 4 times the first number is 9 less than 5 times the second. What are the two numbers?

   • A) 24 and 21
   • B) 22 and 23
   • C) 25 and 20
   • D) 26 and 21

   Answer: 24 and 21

   Explanation: Setting up x + y = 45 and 4x = 5y − 9, substituting x = 45 − y gives y = 21 and x = 24.

3. Question 3

   Q3. What is the sum of the first 5 composite numbers?

   • A) 25
   • B) 33
   • C) 37
   • D) 43

   Answer: 37

   Explanation: The first five composite numbers are 4, 6, 8, 9, 10; their sum is 4+6+8+9+10 = 37.

4. Question 4

   Q4. The mean of five numbers is 18. If one number is excluded, then their mean is 16. The excluded number is ____.

   • A) 24
   • B) 26
   • C) 28
   • D) None of these

   Answer: 26

   Explanation: The correct value is 26. Apply the formula or arithmetic step shown in the question and

5. Question 5

   Q5. The sum of the squares of two positive integers is 100 and their difference of their square is 28. The sum of the numbers is?

   • A) 10
   • B) 12
   • C) 14
   • D) None of these

   Answer: 14

   Explanation: The correct value is 14. Apply the formula or arithmetic step shown in the question and

6. Question 6

   Q6. The sum of two numbers 10 is and their product is 20. What is the sum of their reciprocals:

   • A) on Jan 10
   • B) on Jan 02
   • C) on 1
   • D) on 2

   Answer: on Jan 02

   Explanation: Sum of reciprocals = (x+y)/(xy) = 10/20 = 1/2. Show the calculation clearly when solving similar quantitative items.

7. Question 7

   Q7. Find the sum of two consecutive even numbers, the difference of whose squares is 84?

   • A) 42
   • B) 44
   • C) 46
   • D) None of these

   Answer: 42

   Explanation: The correct value is 42. Apply the formula or arithmetic step shown in the question and

8. Question 8

   Q8. What is meant by a linear equation?

   • A) First degree
   • B) Second degree
   • C) Third degree
   • D) None of these

   Answer: First degree

   Explanation: The correct value is First degree. Apply the formula or arithmetic step shown in the question and

9. Question 9

   Q9. The sum of two numbers is 25 and their difference is 13. What is their product?

   • A) 100
   • B) 114
   • C) 126
   • D) 138

   Answer: 114

   Explanation: Let the numbers be a and b; a+b=25 and a−b=13 give a=19 and b=6; product = 19×6 = 114.

10. Question 10

    Q10. The square of the standard deviation is called:

    • A) Variance
    • B) Dispersion
    • C) Range
    • D) Mean

    Answer: Variance

    Explanation: By definition in statistics, variance is the average of the squared differences from the mean, which equals the square of the standard deviation.

11. Question 11

    Q11. The median of 3, 7, 5, 9, and 1 is:

    • A) 3
    • B) 5
    • C) 7
    • D) 9

    Answer: 5

    Explanation: Arranging in order: 1, 3, 5, 7, 9; the middle (3rd) value is 5.

12. Question 12

    Q12. In a class with scores 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, what is the median score?

    • A) 65
    • B) 67.5
    • C) 68
    • D) 70

    Answer: 67.5

    Explanation: With 10 values arranged in order, the median is the average of the 5th and 6th values: (65 + 70)/2 = 67.5.

13. Question 13

    Q13. Find the mean of: 4, 8, 12, 16, 20.

    • A) 10
    • B) 14
    • C) 16
    • D) 12

    Answer: 12

    Explanation: Mean = (4+8+12+16+20) ÷ 5 = 60 ÷ 5 = 12. Show the calculation clearly when solving similar quantitative items.

14. Question 14

    Q14. Find the median of: 3, 5, 7, 9, 11.

    • A) 5
    • B) 9
    • C) 7
    • D) 11

    Answer: 7

    Explanation: With five values in ascending order, the median is the third (middle) value, which is 7.

15. Question 15

    Q15. The mean of 5 numbers is 18. What is their sum?

    • A) 18
    • B) 90
    • C) 23
    • D) 72

    Answer: 90

    Explanation: Sum = mean × count = 18 × 5 = 90. Show the calculation clearly when solving similar quantitative items.

16. Question 16

    Q16. The mean of 4 numbers is 15. Three of the numbers are 12, 18, and 14. Find the fourth number.

    • A) 14
    • B) 16
    • C) 20
    • D) 15

    Answer: 16

    Explanation: Total sum = 4 × 15 = 60; fourth number = 60 − 12 − 18 − 14 = 16.

17. Question 17

    Q17. Find the median of: 4, 7, 2, 9, 5 (after arranging in order).

    • A) 5
    • B) 7
    • C) 4
    • D) 9

    Answer: 5

    Explanation: Arranging in ascending order: 2, 4, 5, 7, 9; with five values the median is the middle value, which is 5.

18. Question 18

    Q18. What is the sum of the first 10 natural numbers?

    • A) 45
    • B) 50
    • C) 55
    • D) 60

    Answer: 55

    Explanation: Sum of first n natural numbers = n(n+1)/2; for n=10, this gives 10×11/2 = 55.

19. Question 19

    Q19. Standard deviation measures which of the following?

    • A) Central tendency
    • B) Spread of data around the mean
    • C) Sum of all values
    • D) The most frequent value

    Answer: Spread of data around the mean

    Explanation: Standard deviation quantifies the dispersion or spread of data values around the arithmetic mean.

20. Question 20

    Q20. Find the mean of: 10, 12, 15, 18, 20

    • A) 15
    • B) 13
    • C) 14
    • D) 16

    Answer: 15

    Explanation: Mean = (10+12+15+18+20)/5 = 75/5 = 15. 15 is correct because it matches what the question requires. Show the calculation clearly when solving similar quantitative items.