Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice

The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?

  1. 30 years

  2. 24 years

  3. 26 years

  4. 22 years

  5. 36 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the sum of ages of the 8 men be S. The new sum is S - 20 - 24 + W1 + W2 = S + 16 (since average increases by 2, total increases by 8 * 2 = 16). Thus, W1 + W2 = 16 + 44 = 60. The average age of the two women is 60 / 2 = 30.

Multiple choice

Within the set X, which encompasses 15 positive integers, only 14 are specified: 59, 62, 55, 58, 63, 54, 57, 60, 51, 50, 52, 66, 68, and 49. If the average of the complete set of 15 integers is 58, what is the value of the missing integer in the data set?

  1. 68

  2. 66

  3. 64

  4. 62

  5. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of 15 integers with an average of 58 is 15 * 58 = 870. The sum of the 14 given integers is 59+62+55+58+63+54+57+60+51+50+52+66+68+49 = 804. The missing integer is 870 - 804 = 66.

Multiple choice

During a school trip, a group consisting of 12 students, their coach, and a chaperone discussed their ages while enjoying their outing. They found that the average age of the entire group, which includes the coach and the chaperone, is 17 years. Among the students, the first eight have an average age of 16 years, while the remaining four students have an average age of 14 years. Additionally, the chaperone is six years younger than the coach. What is the age of the coach?

  1. 20 years

  2. 24 years

  3. 30 years

  4. 32 years

  5. 36 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age = 14 people * 17 = 238. Students' total = 8*16 + 4*14 = 128 + 56 = 184. Coach + Chaperone = 238 - 184 = 54. Let Coach be C, Chaperone is C-6. C + C - 6 = 54, 2C = 60, C = 30.

Multiple choice

In a classroom, five students, Alex, Sarah, David, Emma, and Lily, have different numbers of pencils. Alex possesses the fewest pencils, with only 5, while Sarah boasts the highest count of 20. Ensuring that no two students share the same number of pencils, what might be the average number of pencils each student possesses?

  1. 9

  2. 13

  3. 16

  4. 17

  5. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The five numbers are distinct integers between 5 and 20 inclusive. The average must be greater than the minimum (5) and less than the maximum (20). While any set of 5 distinct numbers between 5 and 20 is possible, 13 is a reasonable average for a set like {5, 8, 13, 19, 20} or similar.

Multiple choice

In a university, there are two classes, Class X and Class Y. Class X has 20 students, and Class Y has 30 students. The average score of students in Class X is 75, while the average score of students in Class Y is 70. Quantity A The average score of all the students in both classes combined Quantity B 72.5

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The weighted average is ((20 * 75) + (30 * 70)) / (20 + 30) = (1500 + 2100) / 50 = 3600 / 50 = 72. Quantity A is 72, which is less than Quantity B (72.5).