Q. If the sum of two numbers is 30 and one of the numbers is a multiple of 5, which of the following could be the other number?
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Solution
If one number is 20 (a multiple of 5), the other number would be 10, making it a valid option.
Correct Answer:
C
— 20
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Q. If the sum of two numbers is 30 and one of them is a multiple of 5, which of the following could be the two numbers?
A.
10 and 20
B.
15 and 15
C.
5 and 25
D.
12 and 18
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Solution
5 and 25 add up to 30, and 25 is a multiple of 5.
Correct Answer:
C
— 5 and 25
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Q. If the sum of two numbers is 30 and one of them is a multiple of 5, which of the following pairs could represent these numbers?
A.
10 and 20
B.
15 and 15
C.
5 and 25
D.
12 and 18
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Solution
5 and 25 add up to 30, and 5 is a multiple of 5.
Correct Answer:
C
— 5 and 25
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Q. If the sum of two numbers is 30 and one of them is a multiple of 6, which of the following could be the two numbers?
A.
12 and 18
B.
10 and 20
C.
6 and 24
D.
15 and 15
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Solution
12 is a multiple of 6, and 12 + 18 = 30.
Correct Answer:
A
— 12 and 18
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Q. If the sum of two numbers is 50 and both leave a remainder of 4 when divided by 6, what is the remainder when their sum is divided by 6? (2023)
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Solution
Both numbers can be expressed as 6k + 4. Their sum is 12k + 8, which gives a remainder of 2 when divided by 6.
Correct Answer:
A
— 0
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Q. If the sum of two numbers is a multiple of 10, which of the following can be inferred?
A.
Both numbers are even.
B.
Both numbers are odd.
C.
At least one number is even.
D.
At least one number is odd.
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Solution
For the sum to be a multiple of 10, at least one of the numbers must be even.
Correct Answer:
C
— At least one number is even.
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Q. If the surface area of a cube is 216 square meters, what is the length of one side of the cube?
A.
6 meters
B.
9 meters
C.
12 meters
D.
15 meters
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Solution
The surface area of a cube is given by the formula SA = 6a². Setting 6a² = 216, we find a² = 36, thus a = 6 meters.
Correct Answer:
B
— 9 meters
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Q. If the surface area of a cylinder is 150π cm² and the height is 10 cm, what is the radius?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
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Solution
The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(10 + r), we find r = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the surface area of a cylinder is 150π cm² and the height is 5 cm, what is the radius?
A.
5 cm
B.
3 cm
C.
4 cm
D.
2 cm
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Solution
The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(5 + r), we find r = 4 cm.
Correct Answer:
C
— 4 cm
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Q. If the system of equations 2x + 3y = 6 and 4x + 6y = 12 is given, what can be inferred about the lines represented by these equations?
A.
They intersect at one point.
B.
They are parallel.
C.
They are the same line.
D.
They have no solutions.
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Solution
The second equation is a multiple of the first, indicating that both equations represent the same line.
Correct Answer:
C
— They are the same line.
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Q. If the terms of a harmonic progression are 1, 1/4, and 1/9, what is the common difference of the corresponding arithmetic progression?
A.
1/36
B.
1/12
C.
1/9
D.
1/4
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Solution
The reciprocals are 1, 4, and 9. The common difference is 4 - 1 = 3.
Correct Answer:
B
— 1/12
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Q. If the terms of a harmonic progression are 3, 6, and x, what is the value of x?
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Solution
The reciprocals of the terms are 1/3, 1/6, and 1/x. Since they form an arithmetic progression, we can set up the equation: 1/6 - 1/3 = 1/x - 1/6, solving gives x = 12.
Correct Answer:
B
— 12
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Q. If the terms of a harmonic progression are 4, 2, and x, what is the value of x?
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Solution
The reciprocals are 1/4, 1/2, and 1/x. The common difference is 1/2 - 1/4 = 1/4, so 1/x = 1/2 + 1/4 = 3/4, thus x = 4/3.
Correct Answer:
D
— 3
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Q. If the total sales for all products in Q4 were 1500 units, what percentage of total sales did Product B represent?
A.
20%
B.
30%
C.
40%
D.
50%
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Solution
Product B represented 40% of total sales in Q4, selling 600 units.
Correct Answer:
C
— 40%
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Q. If the total sales for Product A over the four quarters were 1200 units, what was the average sales per quarter?
A.
300
B.
350
C.
400
D.
450
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Solution
The average sales per quarter for Product A is 1200 / 4 = 300 units.
Correct Answer:
A
— 300
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Q. If the total sales of all fruits in the bar graph is 5000 units, and apples account for 30% of the total, how many units were sold? (2000)
A.
1500
B.
1000
C.
2000
D.
500
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Solution
30% of 5000 units is 1500 units sold for apples.
Correct Answer:
A
— 1500
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Q. If the total sales of all fruits in the bar graph is 5000 units, what percentage of total sales do apples represent if their sales are 1500 units?
A.
20%
B.
30%
C.
25%
D.
15%
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Solution
Apples represent 1500 out of 5000 units, which is 30% of total sales.
Correct Answer:
B
— 30%
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Q. If the trend continues as shown in the table, which product is likely to see the most significant increase in sales by Q4?
A.
Product A
B.
Product B
C.
Product C
D.
Product D
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Solution
Product A shows a consistent upward trend, indicating a significant increase by Q4.
Correct Answer:
A
— Product A
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Q. If the trend continues, which product is likely to see the most significant increase in sales by Q4?
A.
Product A
B.
Product B
C.
Product C
D.
Product D
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Solution
Product A shows a consistent upward trend, indicating a likely increase in sales by Q4.
Correct Answer:
A
— Product A
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Q. If the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set A = {2, 4, 6, 8}, and set B = {1, 2, 3}, what is the complement of A?
A.
{1, 3, 5, 7, 9, 10}
B.
{1, 3, 5, 7, 9}
C.
{2, 4, 6, 8}
D.
{1, 2, 3}
Show solution
Solution
The complement of A in U is the set of elements in U that are not in A, which is {1, 3, 5, 7, 9, 10}.
Correct Answer:
A
— {1, 3, 5, 7, 9, 10}
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Q. If the universal set U = {1, 2, 3, 4, 5, 6} and set A = {2, 4, 6}, what is the complement of set A?
A.
{1, 2, 3}
B.
{1, 3, 5}
C.
{2, 4, 6}
D.
{4, 5, 6}
Show solution
Solution
The complement of set A consists of elements in the universal set U that are not in set A. Therefore, the complement is {1, 3, 5}.
Correct Answer:
B
— {1, 3, 5}
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Q. If the universal set U has 100 elements, set A has 40 elements, and set B has 30 elements with 10 elements in both A and B, how many elements are in neither A nor B?
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Solution
Using the principle of inclusion-exclusion, the number of elements in either A or B is: (A + B - Both) = 40 + 30 - 10 = 60. Therefore, elements in neither = U - (A ∪ B) = 100 - 60 = 40.
Correct Answer:
A
— 60
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Q. If the words 'apple', 'banana', 'cherry', and 'date' are arranged in reverse alphabetical order, which word comes first?
A.
date
B.
cherry
C.
banana
D.
apple
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Solution
In reverse alphabetical order, 'date' comes first.
Correct Answer:
A
— date
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Q. If the words 'cat', 'bat', 'rat', and 'hat' are arranged in alphabetical order, which word comes second?
A.
bat
B.
cat
C.
hat
D.
rat
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Solution
In alphabetical order, 'bat' comes before 'cat', making it the second word.
Correct Answer:
A
— bat
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Q. If the words 'quick', 'brown', and 'fox' are arranged to form a coherent sentence, which of the following is the correct arrangement?
A.
The quick brown fox
B.
Brown quick the fox
C.
Fox the quick brown
D.
Quick the brown fox
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Solution
The correct arrangement that forms a coherent sentence is 'The quick brown fox'.
Correct Answer:
A
— The quick brown fox
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Q. If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the two angles?
A.
40 and 50 degrees
B.
45 and 45 degrees
C.
35 and 55 degrees
D.
30 and 60 degrees
Show solution
Solution
Let the two angles be x and x - 10. Since they are complementary, x + (x - 10) = 90. Solving gives x = 50 degrees, and the other angle is 40 degrees.
Correct Answer:
A
— 40 and 50 degrees
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Q. If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the angles? (2023)
A.
40 degrees and 50 degrees
B.
45 degrees and 45 degrees
C.
35 degrees and 55 degrees
D.
30 degrees and 60 degrees
Show solution
Solution
Let the angles be x and x - 10. Then, x + (x - 10) = 90. Solving gives x = 50 degrees and the other angle is 40 degrees.
Correct Answer:
A
— 40 degrees and 50 degrees
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Q. If two angles are complementary and one angle is 10 degrees more than the other, what are the measures of the two angles?
A.
40 and 50 degrees
B.
45 and 45 degrees
C.
30 and 60 degrees
D.
35 and 55 degrees
Show solution
Solution
Let the smaller angle be x. Then the larger angle is x + 10. Since they are complementary, x + (x + 10) = 90. Solving gives x = 40 degrees, so the angles are 40 and 50 degrees.
Correct Answer:
A
— 40 and 50 degrees
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Q. If two angles are complementary and one angle is twice the other, what are the measures of the angles?
A.
30 degrees and 60 degrees
B.
20 degrees and 70 degrees
C.
45 degrees and 45 degrees
D.
10 degrees and 80 degrees
Show solution
Solution
Let the smaller angle be x. Then the larger angle is 2x. The equation x + 2x = 90 gives x = 30 degrees and 2x = 60 degrees.
Correct Answer:
A
— 30 degrees and 60 degrees
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Q. If two angles are complementary and one angle measures 25 degrees, what is the measure of the other angle?
A.
55 degrees
B.
65 degrees
C.
75 degrees
D.
85 degrees
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Solution
Complementary angles add up to 90 degrees. Therefore, the other angle is 90 - 25 = 65 degrees.
Correct Answer:
A
— 55 degrees
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