Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers? (2023)
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Solution
Let the two numbers be 5x and 5y. Then, HCF(5x, 5y) = 5 and LCM(5x, 5y) = 100. This gives xy = 20. The pairs (x, y) that satisfy this are (4, 5) or (5, 4), leading to the sum 5(4 + 5) = 45.
Correct Answer:
A
— 30
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Q. If the HCF of two numbers is 5 and their product is 100, what could be the two numbers? (2023)
A.
5 and 20
B.
10 and 10
C.
15 and 5
D.
25 and 4
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Solution
If HCF is 5, the two numbers can be expressed as 5a and 5b. Thus, 5a * 5b = 100 implies ab = 4. The pair (1, 4) gives us 5 and 20.
Correct Answer:
A
— 5 and 20
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Q. If the HCF of two numbers is 5 and their product is 100, what is their LCM?
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Solution
Using the relationship between HCF, LCM, and product: HCF * LCM = Product. Thus, LCM = 100 / 5 = 20.
Correct Answer:
B
— 25
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Q. If the HCF of two numbers is 5 and their product is 1000, what is their LCM? (2023)
A.
200
B.
100
C.
250
D.
150
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Solution
Using the relation HCF * LCM = Product of the numbers, we have LCM = 1000 / 5 = 200.
Correct Answer:
A
— 200
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Q. If the HCF of two numbers is 8 and their LCM is 48, what could be one of the possible pairs of numbers? (2023)
A.
16 and 24
B.
8 and 32
C.
4 and 12
D.
20 and 16
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Solution
The numbers can be 16 and 24, as their HCF is 8 and LCM is 48.
Correct Answer:
A
— 16 and 24
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Q. If the HCF of two numbers is 8 and their product is 288, what is their LCM? (2023)
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Solution
Using the relationship between HCF, LCM, and the product of two numbers: LCM = Product / HCF = 288 / 8 = 36.
Correct Answer:
A
— 36
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Q. If the height of a cylinder is doubled while keeping the radius constant, how does the volume change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
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Solution
Volume of a cylinder = πr²h. If height is doubled, volume becomes 2πr²h, which is double the original volume.
Correct Answer:
B
— It doubles
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Q. If the hexadecimal number A3 is converted to decimal, what is its value? (2023)
A.
163
B.
1630
C.
103
D.
83
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Solution
A3 in hexadecimal is calculated as 10*16^1 + 3*16^0 = 160 + 3 = 163.
Correct Answer:
A
— 163
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Q. If the LCM of three numbers is 120 and their HCF is 2, what is the maximum possible product of the three numbers? (2023)
A.
240
B.
480
C.
600
D.
720
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Solution
The maximum product occurs when the numbers are 2, 10, and 6, giving a product of 120.
Correct Answer:
C
— 600
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Q. If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)
A.
540
B.
1800
C.
5400
D.
18000
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Solution
The maximum product of the three numbers can be calculated as (LCM * HCF^2) = 180 * 3^2 = 5400.
Correct Answer:
C
— 5400
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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 one of the numbers is 15, what is the other number?
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Solution
Using the relation LCM(a, b) = (a * b) / HCF(a, b), we can find the other number. Here, 60 = (15 * x) / HCF(15, x). The other number is 60 / 15 = 4.
Correct Answer:
A
— 30
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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 60 and their HCF is 5, what is the sum of the two numbers if they are both less than 30? (2023)
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Solution
Let the two numbers be 5a and 5b. Then, LCM(5a, 5b) = 5 * LCM(a, b) = 60, which gives LCM(a, b) = 12. The pairs (3, 4) work, giving numbers 15 and 20, which sum to 35.
Correct Answer:
D
— 30
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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 LCM of two numbers is 84 and their HCF is 7, what is the sum of the two numbers if one of them is 21? (2023)
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Solution
Let the other number be x. Then, 84 = (21 * x) / 7. Solving gives x = 28. The sum is 21 + 28 = 49.
Correct Answer:
B
— 63
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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 one of the numbers is 15, what could be the other number?
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Solution
The LCM of 15 and 20 is 60, making 20 a valid option. 30 and 60 would not work as they would exceed the LCM.
Correct Answer:
B
— 30
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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 least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
A.
(5, 12)
B.
(10, 30)
C.
(15, 20)
D.
(5, 15)
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Solution
The product of the two numbers is equal to the LCM multiplied by the GCD. Thus, 60 * 5 = 300. The pair (15, 20) satisfies this condition since 15 * 20 = 300.
Correct Answer:
C
— (15, 20)
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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 can be inferred about the product of the two numbers?
A.
It is 720.
B.
It is 60.
C.
It is 12.
D.
It is 5.
Show solution
Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Correct Answer:
A
— It is 720.
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Q. If the length of a rectangle is increased by 20% and the width is decreased by 10%, what is the percentage change in the area?
A.
8% increase
B.
10% decrease
C.
12% increase
D.
2% decrease
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Solution
Let the original length be L and width be W. The new length is 1.2L and the new width is 0.9W. The original area is LW and the new area is (1.2L)(0.9W) = 1.08LW. The percentage change in area is ((1.08LW - LW) / LW) * 100 = 8% increase.
Correct Answer:
D
— 2% decrease
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Q. If the lengths of the diagonals of a quadrilateral are equal, which of the following can be concluded?
A.
The quadrilateral is a rectangle.
B.
The quadrilateral is a rhombus.
C.
The quadrilateral is a square.
D.
The quadrilateral is a parallelogram.
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Solution
If the diagonals of a quadrilateral are equal, it can be concluded that the quadrilateral is a rectangle.
Correct Answer:
A
— The quadrilateral is a rectangle.
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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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