Q. In a survey, 60% of the participants preferred Brand A over Brand B. If 240 participants preferred Brand A, how many participants were surveyed in total? (2023)
A.
400
B.
480
C.
600
D.
720
Solution
Let the total number of participants be x. According to the problem, 60% of x = 240. Therefore, x = 240 / 0.6 = 400.
Q. In a survey, 60% of the participants preferred Brand A over Brand B. If 240 participants preferred Brand B, how many participants were surveyed in total?
A.
400
B.
600
C.
800
D.
1000
Solution
Let the total number of participants be x. According to the problem, 40% of x = 240. Therefore, x = 240 / 0.4 = 600.
Q. In a survey, the average age of a group of people is 30 years. If one person aged 40 leaves the group, what will be the new average age if the group originally had 10 people? (2023)
A.
28
B.
29
C.
30
D.
31
Solution
New total age = (30 × 10) - 40 = 260. New average = 260 / 9 = 28.89, which rounds to 29.
Q. In a survey, the average age of a group of people is 40 years. If one person aged 60 leaves the group, what will be the new average age if the group originally had 10 people?
A.
38
B.
39
C.
40
D.
41
Solution
Total age = 40 × 10 = 400. New total age = 400 - 60 = 340. New average = 340 / 9 = 37.78, which rounds to 38.
Q. In a survey, the average age of a group of people is 40 years. If one person aged 60 leaves the group, what will be the new average age if the group originally had 10 members? (2023)
A.
38
B.
39
C.
40
D.
41
Solution
Total age = 40 × 10 = 400. New total age = 400 - 60 = 340. New average = 340 / 9 = 37.78, which rounds to 38.
Q. In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the first angle, what is the measure of the smallest angle?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Solution
Let the smallest angle be x. Then the second angle is 2x and the third angle is x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (x - 30) = 180. Solving this gives x = 30 degrees.
Q. In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the largest angle, what is the measure of the smallest angle?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Solution
Let the smallest angle be x. Then the second angle is 2x and the largest angle is 2x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (2x - 30) = 180. Solving this gives x = 30 degrees.
Q. In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the maximum length of the third side?
A.
16 cm
B.
17 cm
C.
18 cm
D.
19 cm
Solution
According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, the maximum length of the third side can be 16 cm (7 + 10 - 1). Hence, the answer is 17 cm.
Q. In a triangle, if the lengths of two sides are 7 cm and 10 cm, what is the range of possible lengths for the third side?
A.
3 cm to 17 cm
B.
3 cm to 10 cm
C.
10 cm to 17 cm
D.
7 cm to 10 cm
Solution
According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides and greater than the difference of the two sides. Therefore, the range is 3 cm to 17 cm.
Q. In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
A.
3 cm
B.
15 cm
C.
5 cm
D.
17 cm
Solution
According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.
