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

Passage

Directions: Read the following information and answer the question that follows: The average weight of 25 students of class A is Z kg. The average weight of 35 students of class B is (Z + 8) kg, and the average weight of 20 students of class C is (Z + 5)kg. The average weight of students of class A and B is 55 kg.

The average weight of students of classes A, B and C is approximate what percent of average weight of students of Class A and C?

  1. 95%

  2. 105%

  3. 115%

  4. 85%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average of A and B is 55. (25Z + 35(Z+8))/60 = 55 => 60Z + 280 = 3300 => 60Z = 3020 => Z = 50.33. Average A, B, C = (25*50.33 + 35*58.33 + 20*55.33) / 80 = (1258.25 + 2041.55 + 1106.6) / 80 = 4406.4 / 80 = 55.08. Average A and C = (25*50.33 + 20*55.33) / 45 = (1258.25 + 1106.6) / 45 = 52.55. Ratio = 55.08 / 52.55 = 1.048, which is approximately 105%.

Multiple choice

Passage

Directions: Read the following information carefully and answer the question given below. Average Marks by Students of Different Grades in Different Subjects Grade / Subject English Hindi Geography Maths Physics Grade 1 75 76 58 72 86 Grade 2 65 84 84 74 78 Grade 3 87 48 94 88 82 Grade 4 53 76 89 58 84 Grade 5 49 84 64 59 79 Grade 6 59 74 38 91 47 Grade 7 81 85 69 68 76

The total average marks of Grade 6 students in all the five subjects are

  1. 424

  2. 315

  3. 309

  4. 420

  5. 306
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of marks for Grade 6: 59 (English) + 74 (Hindi) + 38 (Geography) + 91 (Maths) + 47 (Physics) = 309.

Multiple choice

Passage

Directions: Read the following information carefully and answer the question given below. Average Marks by Students of Different Grades in Different Subjects Grade / Subject English Hindi Geography Maths Physics Grade 1 75 76 58 72 86 Grade 2 65 84 84 74 78 Grade 3 87 48 94 88 82 Grade 4 53 76 89 58 84 Grade 5 49 84 64 59 79 Grade 6 59 74 38 91 47 Grade 7 81 85 69 68 76

What is the ratio of the average marks of Grade 7 students in Geography and Physics to the average marks of Grade 3 students in Maths and English?

  1. 29 : 31

  2. 33 : 31

  3. 35 : 29

  4. 29 : 35

  5. 35 : 37
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Grade 7 (Geo + Phys) = (69 + 76) / 2 = 145 / 2 = 72.5. Grade 3 (Maths + Eng) = (88 + 87) / 2 = 175 / 2 = 87.5. Ratio = 72.5 / 87.5 = 725 / 875 = 29 / 35.

Multiple choice

Passage

Directions: Read the following information carefully and answer the question given below. Average Marks by Students of Different Grades in Different Subjects Grade / Subject English Hindi Geography Maths Physics Grade 1 75 76 58 72 86 Grade 2 65 84 84 74 78 Grade 3 87 48 94 88 82 Grade 4 53 76 89 58 84 Grade 5 49 84 64 59 79 Grade 6 59 74 38 91 47 Grade 7 81 85 69 68 76

Average marks of Grade 5 students in Hindi are what percentage of average marks of Grade 2 students in Maths and Physics?

  1. 65.79%

  2. 48.54%

  3. 53.78%

  4. 55.26%

  5. 59.91%
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Read the following information carefully and answer the question given below. Average Marks by Students of Different Grades in Different Subjects Grade / Subject English Hindi Geography Maths Physics Grade 1 75 76 58 72 86 Grade 2 65 84 84 74 78 Grade 3 87 48 94 88 82 Grade 4 53 76 89 58 84 Grade 5 49 84 64 59 79 Grade 6 59 74 38 91 47 Grade 7 81 85 69 68 76

What are the average marks in Physics scored by all the seven grades?

  1. 75.4

  2. 72.5

  3. 73

  4. 76

  5. 77
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of physics marks: 86 + 78 + 82 + 84 + 79 + 47 + 76 = 532. Average = 532 / 7 = 76.

Multiple choice

Passage

Directions: A table is given below which shows the percentage of students from five different colleges who got placement offer and those who opted for higher studies after completing their graduation. Colleges Total number of pass out students % of students who got placed opted for high studies A 960 35 25 B 1080 30 15 C 1450 24 32 D 800 19 21 E 1250 34 28

What is the average number of students who got placed from colleges A, B and C?

  1. 288

  2. 336

  3. 348

  4. 372

  5. 401
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Placed students: A = 35% of 960 = 336. B = 30% of 1080 = 324. C = 24% of 1450 = 348. Average = (336 + 324 + 348) / 3 = 1008 / 3 = 336.

Multiple choice

Passage

Directions: Based on the information below, answer the question which follows. Six friends Albert, Betty, Claire, Daisy, Evan and Fred who are working in different organisations, are looking for a switch in their jobs. They come across an advertisement in the newspaper regarding a job fair being organised in New Delhi. After enrolling for the fair, different days are allotted to each one of them from Monday to Saturday, not necessarily in the same order, starting from Monday. They also have to arrange for their stay in different hotels to concentrate well while preparing for the upcoming interviews namely Taj, Hilton, Crowne Plaza, Radisson, Hyatt and Marriott. Additional information provided is as follows: i. Albert prefers to stay in Taj but not in Hilton. Albert does not work in Whirlpool and participates in the job fair on Monday. The person who works in Whirlpool participates in the job fair on Saturday. ii. Fred does not stay in Hyatt but works in Himalaya. iii. Betty and Daisy participate in the job fair on consecutive days. iv. Claire participates in the job fair on the day before the person staying in Crowne Plaza but on the next day of the Pepsi employee. v. The person working with Oppo participates in the job fair on Friday and does not stay in Hilton. vi. Claire, who is working with Nestle, participates in the job fair at a gap of one day prior to Evan. vii. Daisy stays in Marriott and attends the fair on the last day of the week. viii. The person working with Apple stays in Radisson.

If the current salary packages of the friends working in Whirlpool, Nestle, Himalaya, Pepsi, Oppo and Apple are 20, 30, 40; 50, 60 and 70 lakhs per annum in the same order, then at the time of participating in the job fair, find the average annual package of Albert, Betty and Fred.

  1. 30 lakhs per annum

  2. 90 lakhs per annum

  3. 20 lakhs per annum

  4. 60 lakhs per annum
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both the statements and Give answer

What is the average weight of the three new members who are recently included into the team? I. The average weight of the team increases by 20 kg. II. The three new men substitute earlier members whose weights are 64 kg, 75 kg and 66 kg.

  1. if the data in statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question

  2. if the data in statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question

  3. if the data either in statement I or in Statement II alone are sufficient to answer the question

  4. if the data even in both statements I and II together are not sufficient to answer the question

  5. if the data in both statements I and II together are necessary to answer the question
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I tells us the total weight increases by 20kg, but we don't know the number of team members, so we can't find the total weight change. Statement II lists the weights of the replaced members, but we don't know the weight of the new members. Even together, we lack the number of members to calculate the average.

Multiple choice

Passage

Directions: Study the following information carefully and answer the given question carefully. In a railway station, three trains A, B and C would arrive and leave from the respective platforms. All the trains has different number of bogies and people in them. No two trains have the same number of bogies in them and no two trains would arrive or leave from the same platform. There are three platforms P1, P2 and P3. It is not necessary for the trains to arrive at the platforms in same order. The train which leaves from the platform with the odd prime number carries an average of 117 people in each bogie. The train which has 21 bogies arrives at P1. Train C arrives at P3. Train B leaves the platform at 8:30 p.m. The difference between the time Train A and the time Train C leave from their respective platforms is one hour. The maximum number of bogies in a train is 24. The total number of people in the train arriving at P2 is 2,618. Train A has 22 bogies. The train with the maximum number of bogies leaves the platform at 8:15 p.m. The train which leaves from P2 would leave after all the trains has left. The total number of people in all the trains altogether is 7,862 people.

What is the average number of people in each bogie of the train with 21 bogies?

  1. 117

  2. 120

  3. 112

  4. 116

  5. 119
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Based on the passage, the train with 21 bogies arrives at P1. The train leaving from an odd prime platform (P3 is prime) carries 117 people per bogie. Train C arrives at P3. Through deduction of the remaining constraints, the average for the 21-bogie train is determined to be 116.

Multiple choice

Passage

Directions: Read the following data carefully and answer the question. The table below shows the total number of students who enrolled in five finance courses in a Business Management School from 2015 to 2019. Note: Some data is missing in the following table, and a, b, c, x, y and z are also some missing values. Courses 2015 2016 2017 2018 2019 Accounting, Finance & Economics 120 - 150 160 - Marketing & Accounting x 140 - 150 a Supply Chain Management 140 - 150 160 - Finance Risk Management - b 155 160 y Entrepreneurship in Applied Technologies c 125 150 z 160

The total number of students who enrolled in Marketing & Accounting in 2017 is equal to the average of the total number of students who enrolled in the same course in 2015 and 2019 together. The number of students who enrolled in Marketing & Accounting in 2019 is 35/32 of the number of students who enrolled in the same course in 2015. The total number of students who enrolled in Marketing & Accounting from 2015 to 2019 in the Business Management School is 692. Then the number of students who enrolled in Marketing & Accounting in 2017 is what percent of the number of students who enrolled in the same course in 2016?

  1. 95.71%

  2. 85.50%

  3. 90.20%

  4. 82.72%

  5. 80.21%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M(y) be Marketing & Accounting in year y. M(2017) = (M(2015) + M(2019))/2. M(2019) = (35/32) * M(2015). Total = M(2015) + 140 + M(2017) + 150 + M(2019) = 692. Substituting M(2017) and M(2019) in terms of M(2015): M(2015) + 140 + (M(2015) + (35/32)M(2015))/2 + 150 + (35/32)M(2015) = 692. Solving for M(2015) gives 128. Then M(2017) = (128 + 140)/2 = 134. M(2016) = 140. Percentage = (134/140) * 100 = 95.71%.

Multiple choice

Passage

Directions: Study the data and answer the question that follows. Given table shows the number of candidates that appeared in a competitive examination from Delhi, HP, UP, Punjab and Haryana over the years 2000 to 2004. Year/States Punjab Haryana Delhi HP UP 2000 450 455 451 451 511 2001 233 182 325 551 562 2002 560 478 529 822 321 2003 264 581 265 210 450 2004 752 841 856 378 896

What is the average number of students that appeared from Delhi?

  1. 485

  2. 355

  3. 499

  4. 658

  5. 458
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Passage

There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20, 25 and 30, respectively. If the three classes are represented by A, B and C and you have the following information about the three classes, answer the questions that follow: A A Highest score 22, Lowest score 18 B A Highest score 31, Lowest score 23 C A Highest score 33, Lowest score 26 If five students are transferred from A to B.

In a transfer of 5 students from A to B, the maximum possible average achievable for group B is

  1. 25

  2. 24.5

  3. 25.5

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Group B initially has 25 x 25 = 625 total marks. To maximize its new average, transfer five students scoring 22 each from A, giving a total of 735 marks for 30 students, so the average is 24.5.

Multiple choice

Passage

Study the following information carefully and answer the questions given beside. In an examination, six subjects - A, B, C, D, E, and F have equal maximum marks. The number of marks scored by one particular candidate in subject A is 20% less than his marks in subject F. The ratio of marks scored by the same candidate in subject B to that in C is 4 : 5 and that in D to E is 3 : 4. The number of marks scored by this candidate in subject E is 25% more than that of F. He scored 65 marks in the subject C. He scored 436/9 % in the examination and the average of marks scored by him in all the subjects is 218/3

What was the average of marks obtained by the candidate in the subject E and F together?

  1. 90

  2. 80

  3. 85

  4. 100

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Passage

Directions: Read the passage and answer the following question. Person A: House rent of 'A' is Rs. 4,000, which is 20% less than the expenditure on food. Transportation and other expenses together are 20% more than the expenses on house rent and food together. Transportation expenses of 'A' are Rs. 1,000 less than the expenditure of 'B' on food. Person B: House rent of 'B' is Rs. 30 more than 15% of the total expenditure of A. Expenditure of 'B' on food is the same as the average expenditure of 'A' on house rent and food. Expenditures of 'A' and 'B' on transportation are in ratio 7 : 9. Total expenditure of 'B' is Rs. 15,200. Person C: House rent of 'C' is the same as the difference between the total expenditure of 'A' and 'B'. Food and transportation expenses of 'C' together are the same as the transportation and other expenses of 'B'. Food and transportation expenses of 'C' are in ratio 5 : 2. Other expenses of 'C' are equal to 30% of his house rent.

Average expenses on other things of all three persons are what percent of the total expenditure of 'A'?

  1. 25%

  2. 20%

  3. 18%

  4. 16%

  5. 15%
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

[CAT 1997] Directions for Questions 24 to 26: Answer the questions based on the following information. A certain race is made up of three stretches: A, B and C, each 2 km long, and to be covered by a certain mode of transport. The following table gives these modes of transport for the stretches, and the minimum and maximum possible speeds (in km/hr) over these stretches. The speed over a particular stretch is assumed to be constant. The previous record for the race is 10 min.

Mr.Tortoise completes the race at an average speed of 20 km/hr. His average speed for the first two stretches is four times that for the last stretch. Find the speed over stretch C.

  1. 15 km/hr

  2. 12 km/hr

  3. 10 km/hr

  4. This is not possible
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 6 km. Total time = 10 min = 1/6 hr. Average speed = 20 km/hr. Total time = 6/20 = 0.3 hr = 18 min. The record is 10 min, but the question asks for the speed based on the 20 km/hr average. Let speeds be v1, v2, v3. v1=v2 (first two stretches). Average speed for first two = v1. Average speed for last = v3. v1 = 4 * v3. Total time = 2/v1 + 2/v1 + 2/v3 = 4/v1 + 2/v3 = 4/(4v3) + 2/v3 = 1/v3 + 2/v3 = 3/v3. Total time = 6/20 = 0.3 hr. 3/v3 = 0.3, so v3 = 10 km/hr.