Q. If a mixture is made by combining 3 parts of liquid A and 5 parts of liquid B, what is the ratio of liquid A to the total mixture?
A.
3:8
B.
3:5
C.
5:3
D.
5:8
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Solution
Total parts = 3 + 5 = 8. Ratio of A = 3:8.
Correct Answer: A — 3:8
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Q. If a mixture of two liquids A and B is made in the ratio 1:4, what is the percentage of liquid A in the mixture?
A.
20%
B.
25%
C.
30%
D.
15%
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Solution
Total parts = 1 + 4 = 5. Percentage of A = (1/5) * 100 = 20%.
Correct Answer: B — 25%
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Q. If a mixture of two types of nuts contains 70% cashews and 30% almonds, how many kilograms of almonds are there in a 20 kg mixture?
A.
6 kg
B.
7 kg
C.
8 kg
D.
9 kg
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Solution
30% of 20 kg = 0.3 * 20 = 6 kg of almonds.
Correct Answer: B — 7 kg
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Q. If a number in base-3 is represented as '210', what is its decimal equivalent?
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Solution
'210' in base-3 is 2*3^2 + 1*3^1 + 0*3^0 = 18 + 3 + 0 = 21.
Correct Answer: B — 19
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Q. If a number in base-6 is represented as '54', what is its decimal equivalent?
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Solution
'54' in base 6 is calculated as 5*6^1 + 4*6^0 = 30 + 4 = 34.
Correct Answer: B — 32
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Q. If a number is a factor of 36, which of the following numbers is NOT a factor?
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Solution
All options are factors of 36 except for 9, which is a factor but not a multiple of 4.
Correct Answer: D — 9
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Q. If a number is a multiple of 9, which of the following must also be true?
A.
It is a multiple of 3.
B.
It is a multiple of 27.
C.
It is a prime number.
D.
It is an even number.
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Solution
All multiples of 9 are also multiples of 3.
Correct Answer: A — It is a multiple of 3.
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Q. If a number is a multiple of both 4 and 6, which of the following must it also be a multiple of?
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Solution
The least common multiple of 4 and 6 is 12, so any multiple of both must also be a multiple of 12.
Correct Answer: A — 12
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Q. If a number is a multiple of both 7 and 9, which of the following numbers is a possible candidate?
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Solution
63 is a multiple of both 7 (7x9) and 9 (9x7).
Correct Answer: A — 63
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Q. If a number is congruent to 0 modulo 6, which of the following could be a possible value?
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Solution
A number congruent to 0 mod 6 must be a multiple of 6. 12 is a multiple of 6.
Correct Answer: B — 12
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Q. If a number is divided by 9 and gives a remainder of 2, which of the following numbers will also give the same remainder when divided by 9?
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Solution
29 gives a remainder of 2 when divided by 9 (9*3 + 2 = 29).
Correct Answer: C — 29
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Q. If a number is divisible by 12, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 5
C.
It is divisible by 10
D.
It is a prime number
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Solution
A number divisible by 12 is also divisible by both 3 and 4.
Correct Answer: A — It is divisible by 3
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Q. If a number is divisible by 4, which of the following must also be true?
A.
It is even
B.
It is divisible by 8
C.
It is divisible by 2
D.
It is a multiple of 10
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Solution
Any number divisible by 4 is even, as 4 itself is an even number.
Correct Answer: A — It is even
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Q. If a number is divisible by 7, which of the following is NOT necessarily true?
A.
It is odd
B.
It is not a prime number
C.
It can be a multiple of 14
D.
It can be a two-digit number
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Solution
A number can be divisible by 7 and still be even, such as 14.
Correct Answer: A — It is odd
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Q. If a number is divisible by 8, which of the following must also be true?
A.
It is divisible by 2
B.
It is divisible by 4
C.
It is a multiple of 16
D.
It is a prime number
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Solution
Any number divisible by 8 is also divisible by 4, as 8 is a multiple of 4.
Correct Answer: B — It is divisible by 4
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Q. If a number is divisible by both 2 and 3, which of the following must it also be divisible by?
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Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer: B — 6
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Q. If a number is divisible by both 3 and 5, which of the following must also be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is not divisible by 6
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Solution
A number divisible by both 3 and 5 is also divisible by their LCM, which is 15.
Correct Answer: A — It is divisible by 15
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Q. If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
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Solution
The least common multiple of 8 and 12 is 24, so the number must be divisible by 24.
Correct Answer: B — 24
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Q. If a number is expressed as 5k + 3, where k is an integer, what is the remainder when this number is divided by 5?
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Solution
The remainder is 3, as 5k is divisible by 5.
Correct Answer: D — 3
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Q. If a number leaves a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5, what is the smallest positive integer that satisfies these conditions?
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Solution
The smallest number satisfying both conditions is 9, as 9 mod 4 = 1 and 9 mod 5 = 4.
Correct Answer: A — 6
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Q. If a number leaves a remainder of 2 when divided by 5 and a remainder of 3 when divided by 7, what is the smallest such number?
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Solution
The smallest number satisfying both conditions is 12, as 12 mod 5 = 2 and 12 mod 7 = 5.
Correct Answer: A — 12
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Q. If a number leaves a remainder of 4 when divided by 8, which of the following numbers will also leave the same remainder when divided by 8?
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Solution
20 leaves a remainder of 4 when divided by 8 (8*2 + 4 = 20).
Correct Answer: B — 20
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Q. If a number leaves a remainder of 5 when divided by 12, what will be the remainder when the same number is divided by 4?
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Solution
The number can be expressed as 12k + 5. When divided by 4, the remainder is 5 mod 4, which is 1.
Correct Answer: B — 2
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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 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 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 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 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 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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