Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agreed to split based on capital contribution?
A.
60% to A and 40% to B
B.
50% to A and 50% to B
C.
70% to A and 30% to B
D.
40% to A and 60% to B
Show solution
Solution
Profits should be divided in accordance with their capital contributions, hence 60% to A and 40% to B.
Correct Answer:
A
— 60% to A and 40% to B
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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agree to split them equally?
A.
60% to Partner A and 40% to Partner B
B.
50% to each partner
C.
70% to Partner A and 30% to Partner B
D.
40% to Partner A and 60% to Partner B
Show solution
Solution
Despite the capital contribution, the partners agreed to split profits equally, hence 50% to each.
Correct Answer:
B
— 50% to each partner
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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agree to split them based on capital contribution?
A.
60% to A and 40% to B
B.
50% to A and 50% to B
C.
70% to A and 30% to B
D.
40% to A and 60% to B
Show solution
Solution
Profits should be divided in accordance with their capital contributions, so A receives 60% and B receives 40%.
Correct Answer:
A
— 60% to A and 40% to B
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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if not stated otherwise?
A.
Equally among partners
B.
In the ratio of their capital contributions
C.
Based on the time invested in the business
D.
According to a pre-agreed percentage
Show solution
Solution
In the absence of any other agreement, profits are typically divided in the ratio of capital contributions.
Correct Answer:
B
— In the ratio of their capital contributions
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Q. If Product A's sales in Q4 are $3000, what is the total sales for Product A across all quarters?
A.
$8000
B.
$9000
C.
$10000
D.
$11000
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Solution
Product A's sales across all quarters total $9000 ($1000 + $2000 + $2500 + $3000).
Correct Answer:
B
— $9000
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Q. If Product A's sales increase by 20% in Q3, what will be the new sales figure?
A.
$1200
B.
$1400
C.
$1600
D.
$1800
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Solution
Product A's Q3 sales are $1000. A 20% increase results in $1200.
Correct Answer:
C
— $1600
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Q. If Product B's sales in Q4 are projected to be 10% higher than in Q3, what will be the sales figure?
A.
330 units
B.
360 units
C.
390 units
D.
420 units
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Solution
If Product B's sales in Q3 were 327 units, a 10% increase would result in approximately 360 units.
Correct Answer:
B
— 360 units
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Q. If Product C's sales in Q4 are projected to be 400 units, what is the expected growth rate from Q3?
A.
20%
B.
25%
C.
30%
D.
15%
Show solution
Solution
The expected growth rate from Q3 (320 units) to Q4 (400 units) is 25%.
Correct Answer:
B
— 25%
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Q. If Product D's sales in Q1 were 200 units and increased by 25% in Q2, what were the sales in Q2?
A.
250
B.
300
C.
225
D.
275
Show solution
Solution
Sales in Q2 were 200 + (25% of 200) = 200 + 50 = 250 units.
Correct Answer:
C
— 225
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Q. If Product D's sales in Q1 were 200 units, what percentage increase is observed in Q2?
A.
25%
B.
50%
C.
75%
D.
100%
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Solution
Product D's sales increased from 200 units in Q1 to 300 units in Q2, which is a 50% increase.
Correct Answer:
B
— 50%
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Q. If Product D's sales in Q1 were 300 units, what was the percentage increase in Q2?
A.
20%
B.
30%
C.
50%
D.
60%
Show solution
Solution
The sales in Q2 were 390 units, which is a 30% increase from Q1.
Correct Answer:
B
— 30%
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Q. If Product D's sales in Q1 were 300 units, what was the percentage increase in sales by Q2?
A.
10%
B.
20%
C.
30%
D.
40%
Show solution
Solution
The sales increased to 390 units in Q2, which is a 30% increase from Q1.
Correct Answer:
C
— 30%
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Q. If Product D's sales in Q3 were $2000, what is the sales growth percentage from Q3 to Q4?
A.
25%
B.
50%
C.
75%
D.
100%
Show solution
Solution
Sales grew from $2000 in Q3 to $3000 in Q4, which is a 50% growth.
Correct Answer:
B
— 50%
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Q. If Q is to the left of R and S is to the right of R, who is sitting in the middle?
A.
Q
B.
R
C.
S
D.
None of the above
Show solution
Solution
R is in the middle as Q is to the left and S is to the right.
Correct Answer:
B
— R
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Q. If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?
A.
Yes
B.
No
C.
Depends on A
D.
Not enough information
Show solution
Solution
A relation is a function if every element in the domain (set A) maps to exactly one element in the codomain. Here, 1 maps to 2, and 2 maps to 3, but 3 has no mapping, so R is not a function.
Correct Answer:
B
— No
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Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R symmetric?
A.
Yes
B.
No
C.
Depends on A
D.
None of the above
Show solution
Solution
A relation is symmetric if for every (a, b) in R, (b, a) is also in R. Since R only contains pairs of the form (a, a), it is symmetric.
Correct Answer:
A
— Yes
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Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R reflexive?
A.
Yes
B.
No
C.
Depends on A
D.
None of the above
Show solution
Solution
A relation R is reflexive if every element in set A is related to itself. Since R contains (1, 1), (2, 2), and (3, 3), R is reflexive.
Correct Answer:
A
— Yes
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Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 2), (2, 3)}, is R transitive?
A.
Yes
B.
No
C.
Not enough information
D.
None of the above
Show solution
Solution
A relation R is transitive if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) must also be in R. Here, (1, 2) and (2, 3) are in R, but (1, 3) is not, so R is not transitive.
Correct Answer:
B
— No
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Q. If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 1)}, which of the following properties does R possess?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
All of the above
Show solution
Solution
R is not reflexive as (1,1), (2,2), (3,3) are not in R. It is symmetric as (2,3) implies (3,2) is not in R. It is transitive as (1,2) and (2,3) implies (1,3) is not in R. Thus, R is not all of the above.
Correct Answer:
C
— Transitive
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Q. If R is a relation on the set {1, 2, 3, 4} defined by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1)}, what type of relation is R?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
Both reflexive and symmetric
Show solution
Solution
R is reflexive because it contains all pairs (a, a) and symmetric because (1,2) implies (2,1).
Correct Answer:
D
— Both reflexive and symmetric
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Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, which of the following is true?
A.
R is reflexive
B.
R is symmetric
C.
R is transitive
D.
Both 1 and 2
Show solution
Solution
R is reflexive and symmetric, but not transitive. Thus, both 1 and 2 are true.
Correct Answer:
D
— Both 1 and 2
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Q. If R is a relation on the set {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3), (1, 2)}, is R a partial order?
A.
Yes
B.
No
C.
Only reflexive
D.
Only transitive
Show solution
Solution
R is not a partial order because it is not transitive; (1,2) and (2,2) do not imply (1,2).
Correct Answer:
B
— No
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Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, what can be said about R?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
None of the above
Show solution
Solution
R is neither reflexive, symmetric, nor transitive as it does not satisfy any of the properties.
Correct Answer:
D
— None of the above
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Q. If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
None of the above
Show solution
Solution
R is not symmetric as (b,c) does not imply (c,b) is in R. It is reflexive and transitive.
Correct Answer:
B
— Symmetric
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Q. If R is a relation on the set {x, y, z} defined by R = {(x, y), (y, z), (z, x)}, what can be said about R?
A.
Reflexive
B.
Symmetric
C.
Transitive
D.
None of the above
Show solution
Solution
R is neither reflexive, symmetric, nor transitive.
Correct Answer:
D
— None of the above
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Q. If R is sitting between S and T in a circular arrangement, and U is sitting opposite S, who is sitting next to U?
Show solution
Solution
Since R is between S and T, and U is opposite S, T must be next to U.
Correct Answer:
C
— T
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Q. If R is sitting to the left of S and T is sitting opposite R, who is sitting to the right of S?
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Solution
Since R is to the left of S, R is also to the right of S, making R the one sitting to the right of S.
Correct Answer:
A
— R
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Q. If R is to the right of S and T is to the left of S, which of the following is true?
A.
R is to the left of T
B.
S is in the middle
C.
T is to the right of R
D.
R is at the end
Show solution
Solution
The arrangement is T, S, R. Thus, S is in the middle.
Correct Answer:
B
— S is in the middle
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Q. If R1 = 10Ω, R2 = 15Ω, R3 = 5Ω, what should R4 be for the Wheatstone bridge to be balanced?
A.
7.5Ω
B.
10Ω
C.
12.5Ω
D.
15Ω
Show solution
Solution
Using the balance condition R1/R2 = R3/R4, we find R4 = (R2 * R3) / R1 = (15 * 5) / 10 = 7.5Ω.
Correct Answer:
C
— 12.5Ω
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Q. If R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω in a Wheatstone bridge, what should R4 be for the bridge to be balanced?
A.
15Ω
B.
20Ω
C.
25Ω
D.
30Ω
Show solution
Solution
For balance, R1/R2 = R3/R4, thus R4 = (R2 * R3) / R1 = (20 * 30) / 10 = 60Ω.
Correct Answer:
B
— 20Ω
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