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CAT

LRDI Quantitative Aptitude VARC

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%

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

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%

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%

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%

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 R is sitting between S and T in a circular arrangement, and U is sitting opposite S, who is sitting next to U?

A. R
B. S
C. T
D. V

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?

A. R
B. S
C. T
D. U

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

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 set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, what is the difference A - B?

A. {1, 2}
B. {3, 4}
C. {5, 6}
D. {}

Solution

The difference A - B includes elements in A that are not in B, which are {1, 2}.

Correct Answer: A — {1, 2}

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Q. If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, what is the intersection of sets A and B? (2023)

A. {1, 2}
B. {3, 4}
C. {5, 6}
D. {1, 2, 5, 6}

Solution

The intersection of sets A and B includes the elements that are common to both sets. Therefore, the intersection is {3, 4}.

Correct Answer: B — {3, 4}

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Q. If set A = {1, 2, 3} and set B = {2, 3, 4}, what is A - B? (2023)

A. {1}
B. {2, 3}
C. {3, 4}
D. {}

Solution

A - B represents the elements in A that are not in B. Thus, A - B = {1}.

Correct Answer: A — {1}

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Q. If set A = {a, b, c} and set B = {b, c, d}, what is the hybrid set formed by the intersection of A and B?

A. {a, b, c, d}
B. {b, c}
C. {a, d}
D. {}

Solution

The intersection of sets A and B includes only the elements that are present in both sets, which are {b, c}.

Correct Answer: B — {b, c}

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Q. If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?

A. {2, 4, 6, 8}
B. {2}
C. {2, 3, 5, 7}
D. {2, 3, 5, 7, 4, 6, 8}

Solution

The intersection A ∩ B includes elements that are both even and prime, which is {2}.

Correct Answer: B — {2}

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Q. If set A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?

A. 20
B. 15
C. 10
D. 25

Solution

The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 10 + 15 - 5 = 20.

Correct Answer: A — 20

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Q. If set A contains 10 elements, set B contains 15 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?

A. 20
B. 15
C. 10
D. 5

Solution

The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 10 + 15 - 5 = 20.

Correct Answer: A — 20

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Q. If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, how many elements are in the union of sets A and B?

A. 20
B. 25
C. 10
D. 15

Solution

The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.

Correct Answer: A — 20

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Q. If set A contains 15 elements, set B contains 10 elements, and the intersection of A and B contains 5 elements, what is the number of elements in the union of sets A and B?

A. 20
B. 25
C. 15
D. 10

Solution

The number of elements in the union of sets A and B is given by |A ∪ B| = |A| + |B| - |A ∩ B| = 15 + 10 - 5 = 20.

Correct Answer: B — 25

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Q. If set A contains the elements {1, 2, 3, 4} and set B contains the elements {3, 4, 5, 6}, what is the intersection of sets A and B?

A. {1, 2}
B. {3, 4}
C. {5, 6}
D. {1, 2, 3, 4, 5, 6}

Solution

The intersection of sets A and B is the set of elements that are common to both sets. Therefore, the intersection is {3, 4}.

Correct Answer: B — {3, 4}

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Q. If set A contains the numbers {1, 2, 3, 4, 5} and set B contains the numbers {4, 5, 6, 7, 8}, what is the intersection of sets A and B?

A. {1, 2, 3}
B. {4, 5}
C. {6, 7, 8}
D. {1, 2, 3, 4, 5, 6, 7, 8}

Solution

The intersection of sets A and B is the set of elements that are common to both sets, which is {4, 5}.

Correct Answer: B — {4, 5}

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Q. If set C = {x | x is a multiple of 3 and less than 30}, how many elements are in set C?

A. 8
B. 9
C. 10
D. 11

Solution

The multiples of 3 less than 30 are {3, 6, 9, 12, 15, 18, 21, 24, 27}, totaling 9 elements.

Correct Answer: B — 9

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Q. If set C is a hybrid set formed by combining set A and set B, which of the following is a possible characteristic of set C?

A. Set C cannot have any elements from set A.
B. Set C must have all elements from set B.
C. Set C may have elements that are exclusive to either set A or set B.
D. Set C will always be larger than both set A and set B.

Solution

Hybrid sets can include elements that are exclusive to either of the original sets, making them versatile in composition.

Correct Answer: C — Set C may have elements that are exclusive to either set A or set B.

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Q. If set C is a hybrid set formed by combining set A and set B, which of the following must be true?

A. All elements of set A are in set C.
B. Set C cannot have more elements than set A.
C. Set C must contain at least one element from set B.
D. Set C is identical to set A.

Solution

By definition, a hybrid set formed from set A and set B must include all elements from set A.

Correct Answer: A — All elements of set A are in set C.

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Q. If set C is defined as the set of all x such that x is a multiple of 3 and less than 15, which of the following is a member of set C?

A. 12
B. 15
C. 9
D. 16

Solution

Both 12 and 9 are multiples of 3 and less than 15, but 12 is the first option listed.

Correct Answer: A — 12

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Q. If set C is defined as {x | x is an integer and x is divisible by 3}, which of the following integers is NOT a member of set C?

A. 6
B. 9
C. 10
D. 12

Solution

The integer 10 is not divisible by 3, hence it is not a member of set C.

Correct Answer: C — 10

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Q. If set D is a hybrid set that includes elements from set E and set F, which of the following is a valid conclusion?

A. All elements of set E are in set D.
B. Set D cannot have any elements from set F.
C. Set D may contain elements that are not in either set E or set F.
D. Set D must be equal to the intersection of set E and set F.

Solution

Hybrid sets can include additional elements beyond those found in the original sets, allowing for greater flexibility.

Correct Answer: C — Set D may contain elements that are not in either set E or set F.

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Q. If set D is defined by the constraints z ≥ 2 and z ≤ 8, which of the following is the range of values for set D?

A. 2 to 8
B. 1 to 9
C. 0 to 10
D. 2 to 9

Solution

The range of values for set D is from 2 to 8, inclusive.

Correct Answer: A — 2 to 8

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Q. If set E = {x, y, z} and set F = {y, z, w}, what is the complement of set E with respect to the universal set U = {x, y, z, w, v}?

A. {v}
B. {w, v}
C. {x, y, z}
D. {y, z}

Solution

The complement of set E with respect to the universal set U includes all elements in U that are not in E, which is {v}.

Correct Answer: A — {v}

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Q. If set F contains elements {a, b, c} and set G contains elements {b, c, d}, what is the intersection of sets F and G?

A. {a, b, c, d}
B. {b, c}
C. {a, d}
D. {}

Solution

The intersection of sets F and G includes only the elements that are present in both sets, which are {b, c}.

Correct Answer: B — {b, c}

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Q. If set G = {1, 2, 3} and set H = {2, 3, 4}, what is the result of the difference G - H? (2023)

A. {1}
B. {2, 3}
C. {3, 4}
D. {}

Solution

The difference G - H includes elements in G that are not in H, which results in {1}.

Correct Answer: A — {1}

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Q. If set H contains elements {a, b, c} and set I contains elements {b, c, d}, what is the union of these two sets?

A. {a, b, c}
B. {b, c, d}
C. {a, b, c, d}
D. {a, d}

Solution

The union of sets H and I is {a, b, c, d}, which includes all unique elements from both sets.

Correct Answer: C — {a, b, c, d}

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