Q. In a certain number system, the number 12 is represented as 'A' and the number 18 as 'B'. If 'A' is a factor of 'B', which of the following statements is true?
A.A is greater than B
B.B is a multiple of A
C.A and B are equal
D.A is a multiple of B
Solution
'B' (18) is a multiple of 'A' (12) since 18 can be expressed as 12 multiplied by 1.5.
Q. In a certain number system, the number 12 is represented as 'AB'. If 'A' is a factor of 12 and 'B' is a multiple of 3, which of the following could be the value of 'AB'?
A.24
B.36
C.48
D.60
Solution
'A' can be 1, 2, 3, 4, 6, or 12 (factors of 12) and 'B' can be 3, 6, 9, 12, etc. The only combination that fits is A=3 and B=12, which gives us 36.
Q. In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?
A.6
B.5
C.8
D.7
Solution
In a regular polygon, each interior angle can be calculated using the formula (n-2) * 180/n. Setting this equal to 120 degrees and solving for n gives n = 6, indicating a hexagon.
Q. In a certain town, the ratio of the number of men to women is 3:2. If there are 120 men, how many women are there?
A.80
B.60
C.40
D.100
Solution
If the ratio of men to women is 3:2, then for every 3 men, there are 2 women. If there are 120 men, we can set up the proportion: 3/2 = 120/x. Solving for x gives x = 80. Therefore, there are 80 women.
Q. In a certain town, the ratio of the number of men to women is 3:4. If there are 120 men in the town, how many women are there?
A.80
B.90
C.100
D.110
Solution
If the ratio of men to women is 3:4, then for every 3 men, there are 4 women. If there are 120 men, we can set up the proportion: 3/4 = 120/x. Solving for x gives x = 160. Therefore, there are 160 women.
Q. In a certain town, the ratio of the number of men to women is 3:4. If there are 120 men, how many women are there?
A.80
B.90
C.100
D.110
Solution
If the ratio of men to women is 3:4, then for every 3 men, there are 4 women. If there are 120 men, we can set up the proportion: 3/4 = 120/x. Cross-multiplying gives us 3x = 480, so x = 160. Therefore, there are 160 women.
Q. In a circle, if an angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the circumference?
A.20 degrees
B.40 degrees
C.80 degrees
D.160 degrees
Solution
The angle subtended at the circumference is half the angle subtended at the center. Therefore, the angle at the circumference is 80/2 = 40 degrees.
Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the remaining part of the circle?
A.30 degrees
B.60 degrees
C.90 degrees
D.120 degrees
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Q. In a class of 30 students, 18 students study Mathematics, 15 study Science, and 10 study both subjects. How many students study only Mathematics?
A.8
B.10
C.15
D.18
Solution
To find the number of students who study only Mathematics, we use the formula: Only Mathematics = Total Mathematics - Both subjects. Thus, 18 - 10 = 8.
Q. In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
A.10
B.15
C.20
D.25
Solution
Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.
Q. In a class of 50 students, 20 study English, 25 study Mathematics, and 10 study both. How many students study only one subject?
A.35
B.25
C.15
D.45
Solution
The number of students studying only English is 20 - 10 = 10, and only Mathematics is 25 - 10 = 15. Thus, total studying only one subject is 10 + 15 = 25.
