Q. If the LCM of three numbers is 180 and their HCF is 3, what is the product of the three numbers? (2023)
A.
540
B.
1800
C.
5400
D.
18000
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Solution
The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.
Correct Answer: C — 5400
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Q. If the LCM of two numbers is 120 and their HCF is 10, what is the product of the two numbers? (2023)
A.
1200
B.
1000
C.
2400
D.
600
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Solution
The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 10 = 1200.
Correct Answer: A — 1200
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Q. If the LCM of two numbers is 120 and their HCF is 5, what is the product of the two numbers? (2023)
A.
600
B.
1200
C.
240
D.
300
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Solution
The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 5 = 600.
Correct Answer: A — 600
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Q. If the LCM of two numbers is 180 and their HCF is 15, what is the sum of the two numbers? (2023)
A.
75
B.
90
C.
105
D.
120
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Solution
Let the two numbers be 15a and 15b. Then, LCM = 15ab = 180, so ab = 12. The pairs (3, 4) give the numbers 45 and 60, summing to 105.
Correct Answer: C — 105
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Q. If the LCM of two numbers is 60 and their HCF is 4, what is the product of the two numbers? (2023)
A.
240
B.
120
C.
300
D.
180
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Solution
The product of two numbers is equal to the product of their LCM and HCF. Therefore, 60 * 4 = 240.
Correct Answer: A — 240
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Q. If the LCM of two numbers is 72 and one of the numbers is 24, what is the other number? (2023)
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Solution
Using the relationship between LCM and the numbers: (24 * x) / HCF = 72. The other number is 36.
Correct Answer: B — 36
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Q. If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
A.
It is 216.
B.
It is 72.
C.
It is 36.
D.
It is 6.
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Solution
The product of two numbers is equal to the product of their LCM and GCD: 36 * 6 = 216.
Correct Answer: A — It is 216.
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, what is the product of the two numbers?
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Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 5 = 300.
Correct Answer: A — 300
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
A.
720
B.
180
C.
120
D.
60
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Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Correct Answer: A — 720
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Q. If the lengths of the diagonals of a rhombus are 10 cm and 24 cm, what is the area of the rhombus?
A.
120 cm²
B.
240 cm²
C.
60 cm²
D.
300 cm²
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Solution
The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².
Correct Answer: B — 240 cm²
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Q. If the lengths of the sides of a triangle are in the ratio 3:4:5, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
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Solution
A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, thus it is a right triangle.
Correct Answer: D — Right
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Q. If the linear equation 3x + 4y = 12 is graphed, what is the y-intercept?
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Solution
Setting x = 0 in the equation gives y = 3, so the y-intercept is 3.
Correct Answer: B — 3
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Q. If the linear equation 3x - 4y = 12 is graphed, what is the y-coordinate of the point where it intersects the y-axis?
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Solution
To find the y-intercept, set x = 0: 3(0) - 4y = 12, which gives y = -3.
Correct Answer: D — -4
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Q. If the linear equation 5x + 2y = 10 is graphed, what is the point where it intersects the x-axis?
A.
(2, 0)
B.
(0, 5)
C.
(5, 0)
D.
(0, 2)
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Solution
To find the x-intercept, set y = 0. Solving gives x = 2, so the intersection point is (2, 0).
Correct Answer: A — (2, 0)
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Q. If the linear equation 5x - 2y = 10 is graphed, what is the point of intersection with the x-axis?
A.
(2, 0)
B.
(0, 5)
C.
(0, -5)
D.
(5, 0)
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Solution
Setting y to 0 in the equation gives x = 2, so the intersection with the x-axis is (2, 0).
Correct Answer: A — (2, 0)
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Q. If the linear equation 5x - 2y = 10 is graphed, what is the y-intercept?
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Solution
Setting x = 0 in the equation gives y = -5, so the y-intercept is -5.
Correct Answer: B — 2
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Q. If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?
A.
20 degrees
B.
30 degrees
C.
40 degrees
D.
60 degrees
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Solution
Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.
Correct Answer: B — 30 degrees
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?
A.
(6, 7)
B.
(8, 9)
C.
(4, 5)
D.
(0, 1)
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Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer: A — (6, 7)
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?
A.
(6, 7)
B.
(8, 9)
C.
(4, 5)
D.
(2, 3)
Show solution
Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer: A — (6, 7)
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Q. If the nth term of a harmonic progression is given by 1/(1/n + 1/a), what does 'a' represent?
A.
The first term
B.
The last term
C.
The common difference
D.
The sum of the terms
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Solution
'a' represents the first term of the harmonic progression in the formula for the nth term.
Correct Answer: A — The first term
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Q. If the nth term of a harmonic progression is given by 1/(1/n + 1/m), what does this represent?
A.
The average of n and m
B.
The product of n and m
C.
The sum of n and m
D.
The difference of n and m
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Solution
The nth term of a harmonic progression can be expressed as the harmonic mean of n and m, which is 1/(1/n + 1/m).
Correct Answer: A — The average of n and m
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Q. If the nth term of a sequence is given by a_n = 5n - 3, what is the value of a_7? (2023)
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Solution
Substituting n = 7 into the formula gives a_7 = 5*7 - 3 = 35 - 3 = 32.
Correct Answer: B — 34
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Q. If the nth term of a sequence is given by n^2 + n, what is the 4th term? (2023)
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Solution
The 4th term is 4^2 + 4 = 16 + 4 = 20.
Correct Answer: A — 20
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Q. If the number 'A' in a base-6 system is equal to 30 in decimal, what is the value of 'A'?
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Solution
In base-6, 'A' = 3*6^1 + 0*6^0 = 18 + 0 = 18. Therefore, 'A' is 42 in decimal.
Correct Answer: B — 42
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Q. If the number 'XYZ' in base-5 equals 100 in decimal, what is the value of 'X'?
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Solution
In base-5, 'XYZ' = X*5^2 + Y*5^1 + Z*5^0 = 100. Solving gives X = 3.
Correct Answer: B — 3
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Q. If the number 1011 in binary is converted to decimal, what is its value?
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Solution
The binary number 1011 converts to decimal as follows: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.
Correct Answer: A — 11
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Q. If the number 36 is expressed in terms of its prime factors, which of the following is correct?
A.
2^2 * 3^2
B.
2^3 * 3^1
C.
3^2 * 4^1
D.
6^2
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Solution
The prime factorization of 36 is 2^2 * 3^2, as 36 = 2 * 2 * 3 * 3.
Correct Answer: A — 2^2 * 3^2
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Q. If the perimeter of a regular hexagon is 72 cm, what is the length of each side?
A.
10 cm
B.
12 cm
C.
14 cm
D.
8 cm
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Solution
The perimeter of a regular hexagon is the sum of the lengths of its 6 equal sides. Therefore, each side is 72 cm / 6 = 12 cm.
Correct Answer: B — 12 cm
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Q. If the perimeter of a regular octagon is 64 cm, what is the length of each side? (2023)
A.
6 cm
B.
8 cm
C.
10 cm
D.
12 cm
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Solution
The perimeter of a regular octagon is 8 times the length of one side. Therefore, each side is 64 cm / 8 = 8 cm.
Correct Answer: B — 8 cm
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Q. If the perimeter of an equilateral triangle is 36 cm, what is the length of each side?
A.
9 cm
B.
12 cm
C.
15 cm
D.
18 cm
Show solution
Solution
In an equilateral triangle, all sides are equal. Therefore, if the perimeter is 36 cm, each side is 36/3 = 12 cm.
Correct Answer: B — 12 cm
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