Q. If a number leaves a remainder of 5 when divided by 12, which of the following could be the number?
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Solution
17 leaves a remainder of 5 when divided by 12 (12*1 + 5 = 17).
Correct Answer:
A
— 17
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Q. If a number leaves a remainder of 5 when divided by 8, what will be the remainder when this number is divided by 4?
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Solution
If the number is 8k + 5, then when divided by 4, the remainder is 1 (5 % 4 = 1).
Correct Answer:
B
— 1
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Q. If a number leaves a remainder of 5 when divided by 8, which of the following could be the number?
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Solution
13 leaves a remainder of 5 when divided by 8 (8*1 + 5 = 13).
Correct Answer:
A
— 13
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Q. If a number leaves a remainder of 7 when divided by 10, what will be the remainder when the same number is divided by 5?
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Solution
The number can be expressed as 10k + 7. When divided by 5, the remainder is 7 mod 5, which is 2.
Correct Answer:
C
— 2
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Q. If a number x is congruent to 5 modulo 8, which of the following could be a possible value of x?
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Solution
x = 5 + 8k for some integer k. 13 is 5 + 8(1), so it is congruent to 5 modulo 8.
Correct Answer:
A
— 13
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Q. If a partner contributes capital but does not participate in management, they are known as a:
A.
General partner
B.
Silent partner
C.
Active partner
D.
Managing partner
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Solution
A silent partner contributes capital but does not take part in the management of the business.
Correct Answer:
B
— Silent partner
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Q. If a partner contributes capital but does not participate in management, they are likely a: (2023)
A.
General partner
B.
Silent partner
C.
Active partner
D.
Managing partner
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Solution
A silent partner contributes capital but does not take part in the management of the business.
Correct Answer:
B
— Silent partner
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Q. If a partner wishes to leave a partnership, what is the most common procedure?
A.
Notify the other partners verbally
B.
Sell their share to an outsider
C.
Follow the terms outlined in the partnership agreement
D.
Leave without any formalities
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Solution
The most common procedure is to follow the terms outlined in the partnership agreement regarding withdrawal.
Correct Answer:
C
— Follow the terms outlined in the partnership agreement
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Q. If a partner wishes to leave the partnership, what is typically required?
A.
A unanimous decision from all partners
B.
A written notice to the remaining partners
C.
Immediate withdrawal without notice
D.
A financial penalty
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Solution
Typically, a partner must provide written notice to the remaining partners if they wish to leave.
Correct Answer:
B
— A written notice to the remaining partners
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Q. If a partner withdraws from a partnership, what is the term used to describe this process?
A.
Dissolution
B.
Retirement
C.
Liquidation
D.
Termination
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Solution
The process of a partner withdrawing from a partnership is commonly referred to as retirement.
Correct Answer:
B
— Retirement
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Q. If a partnership agreement is silent on profit sharing, how are profits typically divided?
A.
Equally among all partners
B.
Based on the capital contribution of each partner
C.
According to the seniority of the partners
D.
By mutual agreement only
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Solution
In the absence of a specific agreement, profits are typically divided equally among all partners.
Correct Answer:
A
— Equally among all partners
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 3 letters of the alphabet and the first 5 digits?
A.
150
B.
180
C.
120
D.
100
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Solution
The number of ways to choose 3 letters from 3 is 3! and 2 digits from 5 is 5P2. Total = 3! * 5P2 = 6 * 20 = 120.
Correct Answer:
B
— 180
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the English alphabet and digits?
A.
17576000
B.
456976
C.
100000
D.
1000
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Solution
There are 26 letters and 10 digits. The total combinations are 26^3 * 10^2 = 17576000.
Correct Answer:
A
— 17576000
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using 26 letters and 10 digits?
A.
676000
B.
6760000
C.
67600
D.
6760
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Solution
The number of passwords is 26^3 * 10^2 = 17576000.
Correct Answer:
A
— 676000
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Q. If a pentagon has one angle measuring 120 degrees, what can be inferred about the other angles?
A.
All other angles must also be 120 degrees.
B.
The sum of the other angles must be 360 degrees.
C.
At least one angle must be less than 60 degrees.
D.
The pentagon cannot exist.
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Solution
The sum of the interior angles of a pentagon is 540 degrees. If one angle is 120 degrees, the sum of the other four angles must be 540 - 120 = 420 degrees.
Correct Answer:
B
— The sum of the other angles must be 360 degrees.
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Q. If a person can run 10 km in 50 minutes, what is his speed in km/h?
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Solution
Speed = Distance / Time = 10 km / (50/60) h = 10 * (60/50) = 12 km/h.
Correct Answer:
B
— 12
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Q. If a person saves 15% of his monthly income of $2000, how much does he save? (2000)
A.
$300
B.
$250
C.
$200
D.
$350
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Solution
Savings = 15% of $2000 = 0.15 × 2000 = $300.
Correct Answer:
A
— $300
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Q. If a person saves 15% of his monthly salary and his monthly salary is $2000, how much does he save in a year? (2000)
A.
$2400
B.
$3600
C.
$1800
D.
$3000
Show solution
Solution
Monthly savings = 15% of 2000 = 0.15 * 2000 = 300. Annual savings = 300 * 12 = 3600.
Correct Answer:
B
— $3600
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Q. If a person saves 15% of his monthly salary and his savings amount to $300, what is his monthly salary? (2000)
A.
$2000
B.
$2500
C.
$3000
D.
$3500
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Solution
Let the monthly salary be x. Then 0.15x = 300, leading to x = 300/0.15 = 2000.
Correct Answer:
A
— $2000
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Q. If a person saves 15% of his monthly salary of $800, how much does he save?
A.
$120
B.
$100
C.
$80
D.
$60
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Solution
Savings = 15% of $800 = 0.15 × 800 = $120.
Correct Answer:
A
— $120
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Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular decagon? (2023)
A.
144 degrees
B.
120 degrees
C.
108 degrees
D.
135 degrees
Show solution
Solution
The measure of each interior angle in a regular polygon is given by the formula [(n-2) * 180] / n. For a decagon (n=10), it is [(10-2) * 180] / 10 = 144 degrees.
Correct Answer:
A
— 144 degrees
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Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular polygon? (2023)
A.
144 degrees
B.
156 degrees
C.
180 degrees
D.
120 degrees
Show solution
Solution
The measure of each interior angle in a regular polygon can be calculated using the formula [(n-2) * 180] / n. For n=10, it is 144 degrees.
Correct Answer:
A
— 144 degrees
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Q. If a polygon has 12 sides, how many diagonals can be drawn from one vertex?
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Solution
The number of diagonals that can be drawn from one vertex of an n-sided polygon is given by (n-3). For a dodecagon (12-sided polygon), it is 12-3 = 9.
Correct Answer:
B
— 10
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Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular polygon?
A.
30 degrees
B.
36 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
The measure of each exterior angle of a regular polygon is calculated as 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.
Correct Answer:
B
— 36 degrees
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Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular dodecagon?
A.
30 degrees
B.
36 degrees
C.
15 degrees
D.
45 degrees
Show solution
Solution
The measure of each exterior angle of a regular polygon can be calculated using the formula 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.
Correct Answer:
B
— 36 degrees
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Q. If a polygon has 8 sides, how many diagonals does it have?
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Solution
Using the formula n(n-3)/2, for an octagon (n=8), the number of diagonals is 8(8-3)/2 = 20.
Correct Answer:
A
— 20
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Q. If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
A.
135 degrees
B.
120 degrees
C.
108 degrees
D.
150 degrees
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Solution
The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.
Correct Answer:
C
— 108 degrees
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Q. If a polygon has 8 sides, what is the sum of its interior angles?
A.
720 degrees
B.
1080 degrees
C.
900 degrees
D.
1440 degrees
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Solution
The sum of the interior angles of an octagon (8-sided polygon) is calculated using the formula (n-2) * 180, which gives (8-2) * 180 = 1080 degrees.
Correct Answer:
B
— 1080 degrees
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Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of the x^2 term?
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Solution
In the polynomial P(x), the coefficient of the x^2 term is -4.
Correct Answer:
B
— -4
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Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of x^2?
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Solution
In the polynomial P(x), the coefficient of x^2 is -4.
Correct Answer:
B
— -4
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