HEC USAT-GS (General Science) quantitative reasoning Averages MCQs with Answers

HEC USAT-GS (General Science) quantitative reasoning: Averages MCQs — sample questions

Question 1
Q1. If the sum of three consecutive odd natural numbers is 57, then the first number is:
- A) 17
- B) 18
- C) 27
- D) 19
Answer: 17
Explanation: Three consecutive odd numbers: n + (n+2) + (n+4) = 3n + 6 = 57 → n = 17.
Question 2
Q2. 2^5 means
- A) 2 x 5
- B) 2 + 5
- C) 2 x 2 x 2 x 2 x 2
- D) 2 ÷ 5
Answer: 2 x 2 x 2 x 2 x 2
Explanation: An exponent means repeated multiplication: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
Question 3
Q3. The sum of 5 successive odd numbers is 1075. What is the largest of these numbers?
- A) 215
- B) 223
- C) 219
- D) 217
Answer: 219
Explanation: Five consecutive odd numbers: n−4, n−2, n, n+2, n+4; sum = 5n = 1075 → n = 215; largest = 219.
Question 4
Q4. If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to___________?
- A) 55/601
- B) 601/55
- C) 11/120
- D) 120/11
Answer: 11/120
Explanation: Numbers with sum 55, HCF 5, LCM 120 are 15 and 40; sum of reciprocals = 1/15+1/40 = 11/120.
Question 5
Q5. The difference between two numbers is 18. If 4 times the second number is 18 less than three times the first number, what is the sum of these two numbers?
- A) 324
- B) 54
- C) 90
- D) 36
Answer: 90
Explanation: From x − y = 18 and 4y = 3x − 18, solving gives y = 36 and x = 54, so their sum is 90.
Question 6
Q6. The mean of five numbers is 18. If one number is excluded, their mean becomes 16. What is the excluded number?
- 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
Question 7
Q7. If the mean of 7 terms is 40, what is the sum of those terms?
- A) 280
- B) 400
- C) 320
- D) 140
Answer: 280
Explanation: Sum = mean × number of terms = 40 × 7 = 280.
Question 8
Q8. The sum of four consecutive even numbers is 292. What would be the smallest number?
- A) 74
- B) 76
- C) 70
- D) 68
Answer: 70
Explanation: Let the four consecutive even numbers be n, n+2, n+4, n+6; their sum = 4n + 12 = 292, giving n = 70.
Question 9
Q9. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is :___________?
- A) 20
- B) 30
- C) 40
- D) None of these
Answer: 20
Explanation: The correct value is 20. Apply the formula or arithmetic step shown in the question and
Question 10
Q10. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is________?
- A) 75
- B) 81
- C) 85
- D) 89
Answer: 85
Explanation: 551 = 19 × 29 and 1073 = 29 × 37, so the common middle number is 29. The three co-prime numbers are 19, 29, and 37; their sum = 85.
Question 11
Q11. The sum of five consecutive even numbers is 440. What is the sum of a different set of five consecutive integers whose second-smallest number is 121 less than double the smallest number of the first set?
- A) 240
- B) 248
- C) 228
- D) None of these
Answer: 240
Explanation: The correct value is 240. Apply the formula or arithmetic step shown in the question and
Question 12
Q12. The sum of three consecutive even natural numbers is 78. What is the largest of those numbers?
- A) 22
- B) 24
- C) 26
- D) 28
Answer: 28
Explanation: Let the three consecutive even numbers be n, n+2, n+4. Their sum 3n+6 = 78 gives n = 24, so the largest is 28.
Question 13
Q13. If the sum of two numbers is 33 and their difference is 15, the smaller number is :__________?
- A) 9
- B) 12
- C) 15
- D) 18
Answer: 9
Explanation: Two simultaneous equations x+y=33 and x−y=15 give the smaller number y = (33−15)/2 = 9.
Question 14
Q14. The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
- A) 248
- B) 240
- C) 228
- D) 236
Answer: 240
Explanation: Set x has middle value 440/5 = 88, so least = 84; second least of new set = 2×84 − 121 = 47, making the least 46; sum of five consecutive integers from 46 = 240.
Question 15
Q15. The sum of the squares of two positive integers is 100 and the difference of their squares is 28. What is the sum of the numbers?
- 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
Question 16
Q16. The sum of two numbers is 25 and their difference is 13. Find their product :
- A) 104
- B) 114
- C) 315
- D) 325
Answer: 114
Explanation: x+y = 25 and x−y = 13 give x = 19, y = 6; product = 19×6 = 114.
Question 17
Q17. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
- A) 40
- B) 400
- C) 5040
- D) 2520
Answer: 5040
Explanation: LOGARITHMS has 10 distinct letters; the number of 4-letter arrangements = P(10,4) = 10×9×8×7 = 5040.
Question 18
Q18. The sum of the square of the three consecutive even natural numbers is 1460. Find the numbers?
- A) 18, 20, 22
- B) 20, 22, 24
- C) 22, 24, 26
- D) 24, 26, 28
Answer: 20, 22, 24
Explanation: Let the three consecutive even numbers be n, n+2, n+4; n² + (n+2)² + (n+4)² = 1460 gives n = 20; the numbers are 20, 22, 24.
Question 19
Q19. What is the square of the standard deviation called?
- A) Variance
- B) Dispersion
- C) Range
- D) Mean
Answer: Variance
Explanation: Variance is defined as the average of the squared deviations from the mean, which equals the square of the standard deviation.
Question 20
Q20. The arithmetic mean between 4 and 6 is:
- A) 5
- B) 6
- C) 8
- D) 10
Answer: 5
Explanation: Arithmetic mean = (4+6)/2 = 5. 5 is correct because it matches what the question requires. Show the calculation clearly when solving similar quantitative items.