Mathematics Test Questions

The mean score of class A of 40 students in the mathematics test of 30 marks is 23. The mean score of class B of 45 students in the same test is 22. What is the ratio of the mean score of both the classes to that of class A?

• 380 : 391

• 390 : 382

• 382 : 391

• 391 : 382

Answer explanation

To find the ratio of the mean scores, first calculate the total mean score: (23 * 40 + 22 * 45) / (40 + 45) = 22.5. The ratio of the mean score of both classes to class A is 382:391, making option 382:391 the correct choice.

The average of five students in a class test is 39.20 and the average of three of them is 41. What is the average of the remaining two students?

• 37.5

• 36.5

• 39.5

• 38.5

Answer explanation

The total score of five students is 39.20 * 5 = 196. The total score of three students is 41 * 3 = 123. The remaining two students' total score is 196 - 123 = 73. Their average is 73 / 2 = 36.5.

In a class of 100 students, the mean marks obtained in a certain subject is 25 and in another class of 50 students, the mean marks obtained in the same subject is 70. The mean marks obtained by the students of both the classes taken together.

• 25

• 60

• 30

• 40

Answer explanation

To find the combined mean, calculate the total marks for both classes. Class 1: 100 students * 25 marks = 2500. Class 2: 50 students * 70 marks = 3500. Total marks = 2500 + 3500 = 6000. Total students = 100 + 50 = 150. Mean = 6000 / 150 = 40.

The average marks obtained by a group of 25 students was 36. One student left the group, as a result of which the average of the remaining students grow to 37.5. Soon after another joined the same group, as a result of which the average marks dropped to 37.2. Find the average marks of the student who left and the student who joined the group.

• 37.5

• 22.5

• 30

• 15

Answer explanation

The total marks of 25 students = 25 * 36 = 900. After one left, total marks = 37.5 * 24 = 900 - x, where x is the marks of the student who left. Solving gives x = 15. The new student must have marks = 37.2 * 25 - 885 = 15.

The mean of the marks scored by 40 students is 68. Later on, it was found that a score of 25 was misread as 45. Find the correct mean:

• 68.5

• 28

• 15

• 67.5

Answer explanation

To find the correct mean, first calculate the total marks: 40 students * 68 mean = 2720. Adjust for the misread score: subtract 45 and add 25, resulting in 2700. The new mean is 2700 / 40 = 67.5.

The average marks of 3 students of a class in an examination is 18 out of 25. Two new students appeared in the exam. What is the minimum marks which can be obtained by a new student and it is less than other students and the total average of all the five students increases to 20?

• 23

• 20

• 21

• 22

Answer explanation

The total marks for 5 students to average 20 is 100. The current total for 3 students is 54 (3*18). The 2 new students must score a total of 46. If one scores 21, the other can score 25, meeting the conditions.

The number of students of three groups of a college G1, G2 and G3 is 20, 40 and 60 respectively. The average marks obtained by group G1, G2 and G3 is 50%, 60% and 70% respectively. What is the average marks of all the students of the college?

• 62%

• 61%

• 60%

• 63%

Answer explanation

To find the average marks of all students, calculate the total marks: (20*50 + 40*60 + 60*70) / (20 + 40 + 60) = (1000 + 2400 + 4200) / 120 = 7600 / 120 = 63%. Thus, the correct answer is 63%.

The average marks obtained by Reena in 16 exams is 26. The average marks obtained by shreya till now is 24, but she has taken only 12 tests till now. What is the average marks that Shreya has to be obtained in the remaining 4 exams to perform as well as Reena?

• 28

• 32

• 30

• 26

Answer explanation

Reena's total marks = 16 * 26 = 416. Shreya's total marks = 12 * 24 = 288. To match Reena's average in 16 exams, Shreya needs 416 marks. For 4 more exams, she needs 416 - 288 = 128 marks. Average needed = 128 / 4 = 32.

In a class there were 9 boys and some girls. In a test, the mean score obtained by the boys was 13 while that obtained by the girls was 15. If the overall average was 14.28, what was the total number of students in the class?

• 24

• 25

• 26

• 27

Answer explanation

Let the number of girls be x. Total score of boys = 9 * 13 = 117. Total score of girls = x * 15. Overall average = (117 + 15x) / (9 + x) = 14.28. Solving gives x = 16, so total students = 9 + 16 = 25.

The average of the marks of three students in an examination of 25 marks is 16. Two new students appeared in the examination. In order to make the average marks of all the five students is 19, what is the minimum marks that the who got less marks than the second new student must get?

• 22

• 21

• 20

• 23

Answer explanation

The total marks for three students is 48 (3*16). For five students to average 19, total marks must be 95 (5*19). Thus, the two new students must score 47. If one scores 22, the other must score 25, making 22 the minimum for the lower scorer.