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CAT

Q. In a scheduling scenario, if task A takes longer than task B, which of the following can be inferred?

A. A must start before B.
B. B must start before A.
C. A cannot start until B is finished.
D. B can be completed while A is ongoing.

Solution

If A takes longer than B, it is possible for B to be completed while A is still ongoing.

Correct Answer: D — B can be completed while A is ongoing.

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Q. In a scheduling scenario, if task B cannot start until task A is finished, and task C cannot start until task B is finished, which of the following is a valid conclusion?

A. A must finish before C
B. B can start before A
C. C can start before B
D. A can start after C

Solution

A must finish before C can start, making the conclusion valid.

Correct Answer: A — A must finish before C

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Q. In a scheduling scenario, if task B is dependent on both tasks A and C being completed, which of the following sequences is valid?

A. C, A, B, D
B. A, B, C, D
C. B, A, C, D
D. A, C, D, B

Solution

C, A, B, D is valid as B starts after both A and C.

Correct Answer: A — C, A, B, D

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Q. In a scheduling scenario, if task E can only start after task D is completed, which of the following is a valid implication?

A. D can start after E
B. E can start before D
C. D must be completed before E
D. E and D can start simultaneously

Solution

E can only start after D is completed, making the implication true.

Correct Answer: C — D must be completed before E

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Q. In a scheduling scenario, if task F is dependent on tasks G and H, which of the following is a correct statement?

A. F can start before G and H
B. G and H must be completed before F
C. F can be completed at any time
D. H is independent of F

Solution

Task F can only start after both G and H are completed, making this statement correct.

Correct Answer: B — G and H must be completed before F

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Q. In a scheduling scenario, if task F must be completed before task G and task H can be done at any time, which of the following is true?

A. H must be done before F.
B. G can start before F.
C. F must be done before H.
D. G cannot start until F is done.

Solution

G cannot start until F is completed, as per the given condition.

Correct Answer: D — G cannot start until F is done.

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Q. In a scheduling scenario, if task J must be completed before task K, and task L can be done at any time, which of the following is true?

A. K can start before J.
B. L must be completed before J.
C. J must be completed before K, but L can be done anytime.
D. K must be completed before L.

Solution

J must be completed before K, while L's timing is independent of J and K.

Correct Answer: C — J must be completed before K, but L can be done anytime.

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Q. In a scheduling scenario, if task X must be completed before task Y, and task Y must be completed before task Z, which of the following sequences is valid?

A. Z, Y, X
B. X, Y, Z
C. Y, Z, X
D. Z, X, Y

Solution

The sequence X, Y, Z respects the order that X is before Y and Y is before Z.

Correct Answer: B — X, Y, Z

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Q. In a scheduling scenario, if task X must be completed before task Y, and task Y must be completed before task Z, which of the following is a valid inference?

A. X can start after Y
B. Z can start before Y
C. Y can start after X
D. Z must start after X

Solution

Z must start after X because X is a prerequisite for Y, which in turn is a prerequisite for Z.

Correct Answer: D — Z must start after X

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Q. In a scheduling set involving five friends, A, B, C, D, and E, if A cannot sit next to B, and C must sit between D and E, which of the following arrangements is valid?

A. A, C, D, E, B
B. B, A, C, E, D
C. D, C, E, A, B
D. C, D, A, B, E

Solution

The arrangement A, C, D, E, B satisfies the conditions as A is not next to B and C is between D and E.

Correct Answer: A — A, C, D, E, B

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Q. In a scheduling set involving five tasks A, B, C, D, and E, if task A must be completed before task B, and task C must be completed before task D, which of the following is a valid sequence?

A. A, B, C, D, E
B. C, D, A, B, E
C. B, A, D, C, E
D. E, A, C, D, B

Solution

The sequence A, B, C, D, E respects the constraints that A is before B and C is before D.

Correct Answer: A — A, B, C, D, E

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Q. In a scheduling set involving four tasks A, B, C, and D, if task A must be completed before task B, and task C cannot start until task D is finished, which of the following sequences is valid?

A. A, B, C, D
B. D, C, A, B
C. B, A, D, C
D. C, D, A, B

Solution

The only valid sequence is D, C, A, B, as it respects the constraints given.

Correct Answer: B — D, C, A, B

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Q. In a scheduling set, if task E can only start after both tasks A and D are completed, which of the following is a possible order?

A. A, D, E, B, C
B. D, A, B, C, E
C. E, A, D, B, C
D. B, C, A, D, E

Solution

The order A, D, E, B, C is valid as E starts after A and D.

Correct Answer: A — A, D, E, B, C

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Q. In a scheduling set, if task E can only start after task D and task D can only start after task C, which of the following is a valid order?

A. C, D, E, A
B. D, C, E, A
C. E, D, C, A
D. A, C, D, E

Solution

C, D, E, A is valid as E starts after D and D starts after C.

Correct Answer: A — C, D, E, A

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Q. In a scheduling set, if task E must be completed before task D, and task D must be completed before task C, which of the following sequences is valid?

A. C, D, E
B. E, D, C
C. D, C, E
D. E, C, D

Solution

The sequence E, D, C respects the order that E must be completed before D, and D must be completed before C.

Correct Answer: B — E, D, C

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Q. In a scheduling set, if task G must be completed before task H, and task H must be completed before task I, which of the following sequences is invalid?

A. G, H, I
B. H, G, I
C. G, I, H
D. I, H, G

Solution

The sequence H, G, I is invalid because H cannot precede G.

Correct Answer: B — H, G, I

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Q. In a scheduling set, if task J can only start after task K is completed, which of the following is a valid conclusion?

A. K can start after J
B. J can start at any time
C. K must be completed before J
D. J is independent of K

Solution

Task J can only start after K is completed, making this conclusion valid.

Correct Answer: C — K must be completed before J

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Q. In a school, the ratio of teachers to students is 1:20. If there are 1000 students, how many teachers are there?

A. 50
B. 40
C. 60
D. 30

Solution

If the ratio of teachers to students is 1:20, then for 1000 students, the number of teachers is 1000 / 20 = 50 teachers.

Correct Answer: A — 50

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Q. In a sequence defined by a_n = 3n + 1, what is the value of a_7? (2023)

A. 22
B. 21
C. 20
D. 19

Solution

a_7 = 3(7) + 1 = 21 + 1 = 22.

Correct Answer: A — 22

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Q. In a sequence defined by a_n = 3n + 2, what is the value of a_7? (2023)

A. 23
B. 20
C. 19
D. 21

Solution

Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.

Correct Answer: A — 23

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Q. In a sequence defined by a_n = n^2 + n, what is the value of a_5? (2023)

A. 30
B. 25
C. 20
D. 15

Solution

Substituting n = 5 gives a_5 = 5^2 + 5 = 25 + 5 = 30.

Correct Answer: A — 30

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Q. In a sequence defined by the formula a_n = 3n + 2, what is the value of a_7? (2023)

A. 23
B. 20
C. 19
D. 21

Solution

Substituting n = 7 into the formula gives a_7 = 3(7) + 2 = 21 + 2 = 23.

Correct Answer: A — 23

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Q. In a sequence of numbers where each number is a multiple of 3, which of the following cannot be a member of this sequence?

A. 9
B. 15
C. 22
D. 27

Solution

22 is not a multiple of 3, while 9, 15, and 27 are.

Correct Answer: C — 22

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Q. In a sequence of numbers where each number is a multiple of 7, which of the following could be the 5th number in the sequence?

A. 28
B. 35
C. 42
D. 49

Solution

The 5th number in the sequence of multiples of 7 is 7 * 5 = 35, so 42 is the next multiple after 35.

Correct Answer: C — 42

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Q. In a sequence of numbers where each number is a multiple of 8, which of the following could be the 5th number in the sequence?

A. 32
B. 40
C. 56
D. 72

Solution

The 5th number in a sequence of multiples of 8 could be 32 (8 x 4), while the others are not multiples of 8.

Correct Answer: A — 32

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Q. In a sequence of numbers where each number is a multiple of 9, which of the following numbers cannot be in the sequence?

A. 27
B. 45
C. 81
D. 50

Solution

50 is not a multiple of 9, while 27, 45, and 81 are all multiples of 9.

Correct Answer: D — 50

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Q. In a sequence of numbers where each term increases by a constant value, if the first term is 5 and the common difference is 3, what is the 10th term?

A. 32
B. 35
C. 30
D. 28

Solution

The nth term of an AP is given by the formula a + (n-1)d. Here, a = 5, d = 3, and n = 10. Thus, the 10th term = 5 + (10-1) * 3 = 5 + 27 = 32.

Correct Answer: B — 35

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Q. In a sequence of numbers where each term is the sum of the two preceding ones, which of the following terms is the 6th term if the first two terms are 1 and 1?

A. 5
B. 8
C. 13
D. 21

Solution

The sequence is the Fibonacci sequence: 1, 1, 2, 3, 5, 8. Thus, the 6th term is 8.

Correct Answer: B — 8

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Q. In a sequence of numbers, if the first number is 5 and each subsequent number is double the previous one, what is the fifth number in the sequence?

A. 20
B. 40
C. 80
D. 160

Solution

The sequence is 5, 10, 20, 40, 80, so the fifth number is 80.

Correct Answer: D — 160

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Q. In a sequence of numbers, if the first number is 5 and each subsequent number is double the previous one, what is the 4th number in the sequence?

A. 20
B. 40
C. 10
D. 80

Solution

The sequence is 5, 10, 20, 40. Therefore, the 4th number is 40.

Correct Answer: D — 80

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