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

A group of men and women go to a restaurant. There are more men than women. If each person pays the bill based on what they ate, the average amount paid by a man is Rs. 1,300 and by a woman is Rs. 1,000. If instead the total bill is split equally among all the people, which of the following could be the amount each person pays?

  1. Rs. 1,320

  2. Rs. 1,100

  3. Rs. 1,160

  4. Rs. 1,135
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be number of men and W be number of women. M > W. Average = (1300M + 1000W) / (M+W). Since M > W, the average must be closer to 1300 than 1000. The range is 1000 < Avg < 1300. Specifically, if M=2, W=1, Avg = 3600/3 = 1200. If M=3, W=2, Avg = 5900/5 = 1180. 1160 is a possible value.

Multiple choice

The average weight of 50 sugar cubes is 5 grams. If the weight of the carry bag is included, then the average weight increases by 0.05 g. What is the weight of the bag?

  1. 6.55 g

  2. 7.33 g

  3. 7.44 g

  4. 7.55 g

  5. 8.55 g
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total weight of 50 cubes is 50 * 5 = 250g. With the bag, there are 51 items (or the bag is added to the total weight). The new average is 5.05g. Total weight = 51 * 5.05 = 257.55g. The bag weight is 257.55 - 250 = 7.55g.

Multiple choice

A person covers 50% of the journey at 28 km/h, 25% at 42 km/h, and the remainder at 14 km/h. What is his average speed?

  1. 24 km/h

  2. 21 km/h

  3. 28 km/h

  4. 30 km/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total distance be 400 km. 50% (200 km) at 28 km/h takes 200/28 = 50/7 hours. 25% (100 km) at 42 km/h takes 100/42 = 50/21 hours. 25% (100 km) at 14 km/h takes 100/14 = 50/7 hours. Total time = 50/7 + 50/21 + 50/7 = (150+50+150)/21 = 350/21 = 50/3 hours. Average speed = 400 / (50/3) = 400 * 3 / 50 = 24 km/h.

Multiple choice

The average weight of 5 people in a group is 60 kg. A new person joins, and the average increases to 61 kg. Now, a person left the group, such that the weight of the person who left and the weight of the new person were in the ratio of 3:4 . What was the weight of the person who left?

  1. 48.8

  2. 58.8

  3. 89.4

  4. 49.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial total = 5 * 60 = 300. After new person (weight Wn), total = 6 * 61 = 366. So Wn = 66. Ratio of left person (Wl) to Wn is 3:4. Wl = (3/4) * 66 = 49.5.

Multiple choice

In a school, there are two sections, X and Y, each with a certain number of students. In Section X, there are 30 students with an average score of 75, while in Section Y, there are 40 students with an average score of 80. The highest and lowest scores in Section X are 90 and 60, respectively, and in Section Y, they are 95 and 70, respectively. If 10 students from Section Y transfer to Section X, what could be the new minimum and maximum average scores for Section X, respectively?

  1. 63.75 and 75

  2. 67.75 and 75

  3. 73.75 and 80

  4. 83.75 and 90

  5. 87.75 and 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Section X: 30 students, avg 75, total 2250. Section Y: 40 students, avg 80, total 3200. Transfer 10 students from Y to X. New X total = 2250 + sum(10 students from Y). New X count = 40. Min sum of 10 students from Y = 10 * 70 = 700. Max sum = 10 * 95 = 950. Min avg = (2250+700)/40 = 2950/40 = 73.75. Max avg = (2250+950)/40 = 3200/40 = 80.

Multiple choice

A weather analyst recorded the daily temperature deviations (in degrees Celsius) from the average, over several days. The deviations were all integral values from −20 to 18, inclusive. What is the sum of all these deviations, in degrees Celsius?

  1. 0

  2. −1

  3. −19

  4. −39

  5. −41
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sum of integers from -20 to 18 is the sum of -20, -19, and the sum of integers from -18 to 18. The sum from -18 to 18 is 0. Thus, the total sum is -20 + (-19) = -39.