Q. If P is heavier than Q and R is lighter than S, which of the following is true? (2020)
A.
P > Q
B.
R < S
C.
P < S
D.
Q > R
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Solution
P is heavier than Q is a direct statement from the given information.
Correct Answer: A — P > Q
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Q. If P is scheduled after Q and R is scheduled before P, which of the following is true? (2022)
A.
Q is first
B.
R is last
C.
P is first
D.
R is first
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Solution
Q must be first since P is after Q and R is before P.
Correct Answer: A — Q is first
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Q. If P is the aunt of Q and R is the brother of Q, how is P related to R? (2023)
A.
Sister
B.
Aunt
C.
Mother
D.
Cousin
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Solution
P is the aunt of R as well, since R and Q are siblings.
Correct Answer: B — Aunt
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Q. If P is the father of Q and R is the sister of Q, what is R's relationship to P?
A.
Daughter
B.
Son
C.
Niece
D.
Sister
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Solution
R is the daughter of P as she is the sister of Q, who is the child of P.
Correct Answer: A — Daughter
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Q. If P is the grandfather of Q and R is the father of Q, what is P's relationship to R? (2022)
A.
Son
B.
Father
C.
Brother
D.
Uncle
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Solution
P is the grandfather of Q, and since R is the father of Q, P is R's father.
Correct Answer: B — Father
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Q. If P is the son of Q and R is the daughter of Q, how is R related to P? (2019)
A.
Sister
B.
Cousin
C.
Aunt
D.
Mother
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Solution
P and R are both children of Q, making R the sister of P.
Correct Answer: A — Sister
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Q. If P ≤ Q and Q < R, which of the following is true?
A.
P < R
B.
P = R
C.
Q = P
D.
R < P
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Solution
Since P ≤ Q and Q < R, it follows that P < R.
Correct Answer: A — P < R
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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 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
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Solution
Profits should be divided in accordance with their capital contributions, which are 60% for A and 40% for 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 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
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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 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 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
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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 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 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%
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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
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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 300 units, what was the percentage increase in Q2?
A.
20%
B.
30%
C.
50%
D.
60%
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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 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
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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 reflexive?
A.
Yes
B.
No
C.
Depends on A
D.
None of the above
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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, 1), (2, 2), (3, 3)}, is R symmetric?
A.
Yes
B.
No
C.
Depends on A
D.
None of the above
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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, 2), (2, 3)}, is R transitive?
A.
Yes
B.
No
C.
Not enough information
D.
None of the above
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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
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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
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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)}, is R a partial order?
A.
Yes
B.
No
C.
Only reflexive
D.
Only transitive
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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 {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 {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?
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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 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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