Arithmetic- Averages And Weighted Averages

Question 1

Average of 12, 15, 18, 22, and 28?

Answer 1

19 (Sum=95, 95/5=19)

Question 2

The average of 4 numbers is 15. Three are 12, 14, and 18. What is the 4th?

Answer 2

16 (Total sum must be 60. 60 - 44 = 16)

Question 3

Test scores: 78, 85, 92. Need an 88 average over 4 tests. Score needed?

Answer 3

97 (Total needed: 352. 352 - 255 = 97)

Question 4

HW (20%): 100, Midterm (30%): 80, Final (50%): 90. Overall grade?

Answer 4

89 (20 + 24 + 45 = 89)

Question 5

Group A (10 ppl, avg 25), Group B (20 ppl, avg 40). Combined average?

Answer 5

35 ( [250 + 800] / 30 = 1050 / 30 = 35)

Question 6

Average of 5 consecutive integers if the middle number is 24?

Answer 6

24 (In any odd-numbered set of consecutive integers, the middle number is the average)

Question 7

Average of 6 numbers is 30. One removed, average of 5 is 25. Number removed?

Answer 7

55 (Original sum 180, new sum 125. 180 - 125 = 55)

Question 8

Average of 10 numbers is 50. Every number increased by 7. New average?

Answer 8

57 (Average increases by the same amount as the individual terms)

Question 9

40 mph for 3 hours and 60 mph for 2 hours. Average speed?

Answer 9

48 mph (Total distance 240 / Total time 5)

Question 10

Round trip: 200 mph there, 300 mph back. Average speed?

Answer 10

240 mph (2xy / [x+y] -> 120000 / 500 = 240)

Question 11

Average of the first seven multiples of 4?

Answer 11

16 (4, 8, 12, 16, 20, 24, 28. Middle is 16)

Question 12

Mix 5 lbs nuts ($4/lb) with 10 lbs nuts ($7/lb). Cost per pound?

Answer 12

$6/lb ([20 + 70] / 15 = 90 / 15 = 6)

Question 13

Average of 14, 0, 18, and 24?

Answer 13

14 (56 / 4 = 14)

Question 14

Average of x, 2x, and 6 is 10. Value of x?

Answer 14

8 (3x + 6 = 30 -> 3x = 24 -> x = 8)

Question 15

Average height of 5 players is 72”. New 78” player joins. New average?

Answer 15

73” (Original sum 360 + 78 = 438. 438 / 6 = 73)

Question 16

40 items at $10 each, 60 items at $15 each. Average price?

Answer 16

$13 ( [400 + 900] / 100 = 1300 / 100 = 13)

Question 17

Average of all integers from 10 to 50?

Answer 17

30 ( [First + Last] / 2 -> 60 / 2 = 30)

Question 18

If the average of 12 numbers is 12.5, what is the sum?

Answer 18

150 (12 * 12.5 = 150)

Question 19

Average of -8, -4, 0, 4, and 8?

Answer 19

0 (Sum is 0)

Question 20

5 students scored 100, 10 scored 90, 5 scored 80. Class average?

Answer 20

90 ( [500 + 900 + 400] / 20 = 1800 / 20 = 90)

Question 21

Average of the first five prime numbers (2, 3, 5, 7, 11)?

Answer 21

5.6 (28 / 5 = 5.6)

Question 22

Average of 8 numbers is 12. First 5 avg 10. Avg of last 3?

Answer 22

15.33 (Total 96 - First five sum 50 = 46. 46 / 3 = 15.33)

Question 23

20L of 10% salt mixed with 30L of 20% salt. Final %?

Answer 23

16% ( [2L salt + 6L salt] / 50L total = 8/50 = 16%)

Question 24

Ratio of two numbers is 3:5. Average is 16. What are the numbers?

Answer 24

12 and 20 (3x + 5x = 32 -> 8x = 32 -> x = 4)

Question 25

Average of four consecutive even integers if the sum is 52?

Answer 25

13 (Sum 52 / 4 = 13. The numbers are 10, 12, 14, 16)

Question 26

4 employees earn $40k, 1 manager earns $90k. Average salary?

Answer 26

$50k ( [160k + 90k] / 5 = 250k / 5 = 50k)

Question 27

Avg on 5 tests is 84. First four: 80, 90, 82, 88. 5th score?

Answer 27

80 (Total needed 420. Current sum 340. 420 - 340 = 80)

Question 28

Mon attendance 40, Tue 50, Wed 30. 5-day avg is 45. Avg of Thu/Fri?

Answer 28

52.5 (Total needed 225. Mon-Wed sum 120. 225 - 120 = 105. 105 / 2 = 52.5)

Question 29

Average of 1/2, 1/4, and 1/8?

Answer 29

7/24 ( [4/8 + 2/8 + 1/8] / 3 = 7/8 / 3 = 7/24)

Question 30

Average price of 3 items is $15. One item price increases by $6. New avg?

Answer 30

$17 (Total sum increases by $6, average increases by 6/3 = $2)

Question 31

4 ppl avg 150 lbs. Replace 120 lb person with 160 lb person. New avg?

Answer 31

160 lbs (Net gain +40 lbs. 40 / 4 = +10 lbs avg increase. 150 + 10 = 160)

Question 32

Avg of a, b, c is 15. Avg of a and b is 12. Value of c?

Answer 32

21 (Total 45 - [a+b] sum 24 = 21)

Question 33

Average of 1^2, 2^2, and 3^2?

Answer 33

4.66 ( [1 + 4 + 9] / 3 = 14 / 3 = 4.66)

Question 34

1/4 of class scored 80, 3/4 scored 92. Class average?

Answer 34

89 (20 + 69 = 89)

Question 35

Runner averages 8 mph for 45 minutes. Miles run?

Answer 35

6 miles (8 mph * 0.75 hours = 6)

Question 36

Average of 10 numbers is A. If A is added to the set, new average?

Answer 36

A (Adding the average to a set doesn't change the average)

Question 37

10 quarters ($2.50) and 15 dimes ($1.50). Average coin value?

Answer 37

16 cents ( $4.00 / 25 coins = 0.16)

Question 38

Average of the first 100 positive integers?

Answer 38

50.5 ( [1 + 100] / 2 = 50.5)

Question 39

Class X (20 ppl, avg 80), Class Y (30 ppl, avg 70). Combined avg?

Answer 39

74 ( [1600 + 2100] / 50 = 3700 / 50 = 74)

Question 40

Average of n numbers is k. Each number multiplied by m. New average?

Answer 40

km (The average is scaled by the same factor m)