Management Admissions
Q. If a hybrid set is defined as the combination of set R = {x, y} and set S = {y, z}, which of the following is the correct representation of the hybrid set?
A.
{x, y, z}
B.
{y}
C.
{x, y}
D.
{y, z}
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Solution
The hybrid set formed by combining set R and set S includes all unique elements from both sets, which are {x, y, z}.
Correct Answer: A — {x, y, z}
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Q. If A is to the left of B and C is to the right of A, which of the following is a valid conclusion?
A.
B is to the right of C
B.
C is to the left of B
C.
A is in the middle
D.
B is to the left of A
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Solution
Since A is to the left of B and C is to the right of A, it follows that C is to the left of B.
Correct Answer: B — C is to the left of B
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Q. If a line has the equation 3x - 4y = 12, what is the y-intercept of the line?
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Solution
To find the y-intercept, set x = 0. The equation becomes -4y = 12, thus y = -3. The y-intercept is (0, -3).
Correct Answer: A — 3
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Q. If a loan of $5000 is taken at a simple interest rate of 6% per annum, how much interest will be paid after 4 years?
A.
$1200
B.
$1000
C.
$800
D.
$600
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Solution
Using the simple interest formula, SI = (Principal * Rate * Time) / 100 = (5000 * 6 * 4) / 100 = $1200.
Correct Answer: B — $1000
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Q. If a mixture contains 20% sugar and 80% water, how much sugar is there in 50 liters of the mixture?
A.
5 liters
B.
10 liters
C.
15 liters
D.
20 liters
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Solution
20% of 50 liters = 0.2 * 50 = 10 liters of sugar.
Correct Answer: B — 10 liters
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Q. If a mixture contains 40% alcohol and 60% water, how much water is there in 15 liters of the mixture?
A.
6 liters
B.
9 liters
C.
7 liters
D.
8 liters
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Solution
Water in the mixture = 60% of 15 liters = 0.6 * 15 = 9 liters.
Correct Answer: B — 9 liters
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Q. If a mixture contains 40% sugar and 60% water, how much sugar is there in 200 grams of the mixture?
A.
80 grams
B.
60 grams
C.
40 grams
D.
100 grams
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Solution
40% of 200 grams = 0.4 * 200 = 80 grams of sugar.
Correct Answer: B — 60 grams
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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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