Level 1
Averages MCQs set 2 for Join Pak Navy: Initial Academic Test Mathematics — 20 solved questions.
Q1. The sum of the squares of three numbers is 138, and the sum of their products, taken two at a time, is 15. What is the sum of the three numbers?
Answer: √168
Explanation: The correct value is √168. Apply the formula or arithmetic step shown in the question and
Q2. The sum of the squares of two numbers is 97, and the square of their difference is 25. What is the product of the two numbers?
Answer: 36
Explanation: Given a²+b²=97 and (a−b)²=25: expanding gives a²−2ab+b²=25, so 97−2ab=25, thus ab=36. Show the calculation clearly when solving similar quantitative items.
Q3. If the sum of two numbers is 30 and their difference is 8, what is their product'?
Answer: 209
Explanation: The correct value is 209. Apply the formula or arithmetic step shown in the question and
Q4. The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is___________?
Answer: 51.4 approx.
Explanation: Setting up: 0.20×80 + 0.25×31 + 0.55×x = 52. So 16+7.75+0.55x = 52, giving x ≈ 51.4.
Q5. 2 numbers differ by 5. If their product is 336, then the sum of the 2 numbers is:
Answer: 37
Explanation: Numbers differ by 5 and have product 336: solving x(x+5)=336 gives x=16 and x+5=21. Sum = 37.
Q6. The sum of two numbers is 10 and their product is 20. What is the sum of their reciprocals?
Answer: 01-Feb
Explanation: Sum of reciprocals = (1/a + 1/b) = (a+b)/(ab) = 10/20 = 1/2.
Q7. The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is___________?
Answer: 36.5
Explanation: Corrected sum = 50 × 36 − 23 + 48 = 1825; corrected mean = 1825 ÷ 50 = 36.5.
Q8. The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 kg and of girls is 40 kg. How many boys are in the class?
Answer: 60
Explanation: The correct value is 60. Apply the formula or arithmetic step shown in the question and
Q9. The sum of two numbers is 2490. If 6.5 % of one number is equal to 8.5 % of the other then the numbers are:_________?
Answer: 1411, 1079
Explanation: 6.5x = 8.5y gives x/y = 17/13. With x+y=2490: x = 2490×17/30 = 1411, y = 1079.
Q10. The ____ is equal to the sum of all the values in the data divided by the number of values in the data.
Answer: Mean
Explanation: The arithmetic mean (or average) is calculated by dividing the sum of all values by the count of values in the dataset.
Q11. The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is__________?
Answer: 4
Explanation: 528 = 33×16. Co-prime pairs summing to 16: (1,15), (3,13), (5,11), (7,9) - giving 4 pairs.
Q12. If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is___________?
Answer: 40
Explanation: Adding a constant to every number increases the mean by the same constant; new mean = 35 + 5 = 40.
Q13. What is the sum of the first five prime numbers?
Answer: 28
Explanation: The first five prime numbers are 2, 3, 5, 7, and 11; their sum = 28.
Q14. The sum of two numbers is 67 and their difference is 3. What are the numbers?
Answer: 32 and 35
Explanation: With sum 67 and difference 3, the two numbers are (67+3)/2 = 35 and (67−3)/2 = 32.
Q15. The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is__________?
Answer: None of these
Explanation: The correct value is None of these. Apply the formula or arithmetic step shown in the question and
Q16. The sum of two numbers is 45. Four times the first number is 9 less than five times the second. What are the two numbers?
Answer: 24 and 21
Explanation: From x + y = 45 and 4x = 5y − 9, substituting x = 45 − y gives 4(45 − y) = 5y − 9, which solves to y = 21 and x = 24.
Q17. In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
Answer: 12
Explanation: Let the series be n, n+2, n+4, n+6, n+8, n+10; the 2nd and 6th terms sum to 2n+12 = 24, giving n = 6, so the 4th term = 12.
Q18. The sum of two numbers is 45. One number is two-thirds of the other. What is the smaller number?
Answer: 18
Explanation: Let the larger number be x and the smaller be (2/3)x; their sum x + (2/3)x = (5/3)x = 45 gives x = 27, so the smaller number = 18.
Q19. The sum of two numbers is 138, and their difference is 68. What is the smallest number?
Answer: 35
Explanation: Adding the two equations: 2x = 206 gives x = 103; subtracting gives y = 35, which is the smaller number.
Q20. 2''⁵ means:
Answer: 2 x 2 x 2 x 2 x 2
Explanation: Exponentiation (raising to a power) means repeated multiplication, so 2⁵ = 2×2×2×2×2.