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

Imagine that there are four hundred and fifty-nine managers in a hotel. If the number of managers is enlarged by 36, the expenses of the food increased by Rs. eighty-one per day while the average spending per head decreased by one. Find the original spending of the hotel on food.

  1. 7344

  2. 7244

  3. 7044

  4. 7444
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original spending be S and number of managers be 459. Average = S/459. New average = (S+81)/(459+36) = S/459 - 1. Solving (S+81)/495 = (S-459)/459 gives 459S + 37179 = 495S - 227070, leading to 36S = 264249, S = 7340.25. The closest integer option is 7344.

Multiple choice

In a class test, the average marks were 60. If 20% of the students scored 85 marks and 25% scored 95 marks, what were the average marks of the remaining students in the test?

  1. 35

  2. 25

  3. 20

  4. 32

  5. 45
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the total number of students be 100. Total marks = 60 * 100 = 6000. Marks from 20% (20 students) = 20 * 85 = 1700. Marks from 25% (25 students) = 25 * 95 = 2375. Remaining students = 55. Remaining marks = 6000 - 1700 - 2375 = 1925. Average = 1925 / 55 = 35.

Multiple choice

A body travelling along a straight line traversed one third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 2 m/s for half the time and with velocity 6 m/s for the other half of time. The mean velocity averaged

  1. 5 m/s

  2. 4 m/s

  3. 4.5 m/s

  4. 3.5 m/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be 3D. First D is covered at 4 m/s (time = D/4). Remaining 2D is covered in time T, where D/T = (2+6)/2 = 4 m/s. So T = 2D/4 = D/2. Total time = D/4 + D/2 = 3D/4. Mean velocity = Total Distance / Total Time = 3D / (3D/4) = 4 m/s.

Multiple choice

In April, Jennifer sold on an average 15 ice creams daily. In the first 20 days of May, she sold on an average 20 ice creams. Which of the following is true regarding the average number of ice creams sold over the whole period?

  1. More than 15

  2. Less than 15

  3. Equal to 10

  4. More than 20

  5. Less than 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

April has 30 days, May has 31. The average for April is 15. The average for the first 20 days of May is 20. The overall average is (15*30 + 20*20) / (30 + 20) = (450 + 400) / 50 = 850 / 50 = 17. Since 17 > 15, the average is more than 15.

Multiple choice

Does the average age of the class decrease if ten new students join the class? (1) Nine out of ten new students have age greater than the average of the class. (2) The eldest among the ten has age less than the new average (i.e. the average ages including these students).

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original sum be S and count be n. Average = S/n. New average = (S + sum of 10)/(n+10). Statement 2 says the eldest of the 10 is less than the new average. If the largest of the new items is less than the new average, then all new items are less than the new average, which forces the average to decrease.

Multiple choice

Mr. Samson is a motorbike manufacturer who has agreed to donate a percentage of the revenue that he earns from sales of his products to improve the level of child healthcare provided in his town. Each of his motorbikes are sold for an average of \$12,500. Calculate the number of bikes sold by Mr. Samson. (1) Total amount of revenue generated by Mr. Samson's company is \$1.5 million. (2) He donated 7.5% of total revenue generated by the company.

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (1) gives total revenue (1.5 million) and the price per bike (12,500). Dividing 1,500,000 by 12,500 gives 120 bikes. Statement (2) provides only a percentage of revenue donated, which is insufficient to find the number of bikes.

Multiple choice

In the Grade 3 classroom library of Springfield Primary School, there are 34 short story books, and the average number of pages in each of the books is 32. Ms. Williamson, the class incharge, purchases a new book and keeps in the library; so, the average number of pages in each book increases by 1. Find the number of pages in the new book purchased by Ms. Williamson.

  1. 59

  2. 67

  3. 68

  4. 71

  5. 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial total pages = 34 * 32 = 1088. New number of books = 35. New average = 33. New total pages = 35 * 33 = 1155. Pages in the new book = 1155 - 1088 = 67.

Multiple choice

The average (arithmetic mean) of k, l, m and n is 10. Quantity A Average of k and l, if the sum of m and n is 20 Quantity B Value of k, if the sum of l, m and n is 30

  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
C Correct answer
Explanation

Average of k, l, m, n = 10 implies k+l+m+n = 40. Quantity A: (k+l)/2. If m+n=20, then k+l=20, so A=10. Quantity B: k. If l+m+n=30, then k=10. Both are 10.

Multiple choice

A shopkeeper made the payment of \$150 for a shipment of n identical Christmas gifts. He kept one gift for his friend and sold each of the others for \$5 more than the average cost of n gifts. The total revenue from the sale of the gifts was $60 more than the cost of the shipment. Quantity A Number of gifts sold Quantity B 15

  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

Cost per gift = 150/n. Selling price = (150/n) + 5. Total revenue = (n-1)(150/n + 5) = 150 + 5n - 150/n - 5 = 145 + 5n - 150/n. Revenue = Cost + 60 = 150 + 60 = 210. So, 145 + 5n - 150/n = 210, 5n - 150/n = 65, n^2 - 13n - 30 = 0. Solving (n-15)(n+2) = 0 gives n = 15. Number of gifts sold is n-1 = 14. Quantity A (14) < Quantity B (15).

Multiple choice

The average (arithmetic mean) weight of 4 boys is 90 pounds. Two of the four boys among them weigh 80 and 100 pounds, respectively. Quantity A The average weight of the other two boys (in pounds) Quantity B 90

  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
C Correct answer
Explanation

Total weight of 4 boys = 4 * 90 = 360. Sum of two boys = 80 + 100 = 180. Sum of other two = 360 - 180 = 180. Average of other two = 180 / 2 = 90. Quantity A = 90, Quantity B = 90.

Multiple choice

There are some chocolates and packets of biscuits kept in a big box. The average weight of the packets of biscuits in the box is 88 grams, and the average weight of the chocolates in the box is 60 grams. The average weight of both a chocolate and a packet of biscuits is 81 grams. Quantity A Number of packets of biscuits in the box Quantity B Number of chocolates in the box

  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
A Correct answer
Explanation

Using the alligation method: Biscuits (88) and Chocolates (60) average to 81. The ratio of biscuits to chocolates is (81-60) : (88-81) = 21 : 7 = 3 : 1. Since the ratio of biscuits to chocolates is 3:1, there are more biscuits than chocolates.

Multiple choice

What is the weight of Bob, if the average weight of Albert, Bob and Caitlin is 45 pounds? (1) The average weight of Albert and Bob is 40 pounds. (2) The average weight of Bob and Caitlin is 43 pounds.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A, B, C be the weights. (A+B+C)/3 = 45 => A+B+C = 135. (1) A+B = 80. (2) B+C = 86. With (1), C = 135-80 = 55. With (2), A = 135-86 = 49. Neither alone gives B, but together we can solve for A and C, then B = 135 - (A+C).