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CAT

LRDI Quantitative Aptitude VARC

Q. In a geometric progression, if the first term is 5 and the common ratio is 0.5, what is the sum of the first 4 terms?

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

Solution

The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_4 = 5(1 - 0.5^4) / (1 - 0.5) = 5(1 - 0.0625) / 0.5 = 5 * 0.9375 / 0.5 = 9.375.

Correct Answer: B — 10

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Q. In a geometric progression, if the first term is 5 and the last term is 80 with 4 terms in total, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Solution

The last term can be expressed as a * r^(n-1). Here, 80 = 5 * r^(4-1) = 5 * r^3. Thus, r^3 = 16, giving r = 2.

Correct Answer: A — 2

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Q. In a geometric progression, if the first term is 5 and the last term is 80, and there are 4 terms in total, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Solution

Let the common ratio be r. The terms are 5, 5r, 5r^2, 5r^3. Setting 5r^3 = 80 gives r^3 = 16, thus r = 2.

Correct Answer: A — 2

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Q. In a geometric progression, if the first term is x and the common ratio is r, what is the expression for the sum of the first n terms?

A. x(1 - r^n)/(1 - r)
B. x(1 + r^n)/(1 + r)
C. xr^n/(1 - r)
D. xr^n/(1 + r)

Solution

The sum of the first n terms of a GP is given by S_n = a(1 - r^n)/(1 - r) for r ≠ 1.

Correct Answer: A — x(1 - r^n)/(1 - r)

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Q. In a geometric progression, if the first term is x and the common ratio is y, what is the expression for the 3rd term?

A. xy^2
B. x/y^2
C. x^2y
D. x^2/y

Solution

The 3rd term of a GP is given by a * r^(n-1). Here, it is x * y^(3-1) = xy^2.

Correct Answer: A — xy^2

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Q. In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (2023)

A. 64
B. 128
C. 256
D. 512

Solution

The nth term of a geometric series is given by ar^(n-1). Here, a = 4, r = 2, n = 6. So, 4 * 2^(6-1) = 4 * 32 = 128.

Correct Answer: C — 256

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Q. In a geometric series where the first term is 4 and the common ratio is 2, what is the sum of the first 5 terms? (2023)

A. 60
B. 62
C. 64
D. 68

Solution

The sum of the first n terms of a geometric series is a(1 - r^n) / (1 - r). Here, a = 4, r = 2, n = 5. So, 4(1 - 2^5) / (1 - 2) = 4(1 - 32) / -1 = 124.

Correct Answer: C — 64

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Q. In a GP, if the 3rd term is 27 and the 5th term is 243, what is the first term?

A. 3
B. 9
C. 1
D. 27

Solution

Let the first term be a and the common ratio be r. Then, 3rd term = ar^2 = 27 and 5th term = ar^4 = 243. Dividing gives r^2 = 9, so r = 3. Substituting back gives a = 3.

Correct Answer: B — 9

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Q. In a GP, if the first term is 10 and the common ratio is 0.5, what is the 6th term?

A. 0.625
B. 1.25
C. 2.5
D. 5

Solution

The 6th term is given by 10 * (0.5)^(6-1) = 10 * (0.5)^5 = 10 * 0.03125 = 0.3125.

Correct Answer: A — 0.625

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Q. In a GP, if the first term is 2 and the common ratio is -2, what is the 4th term?

A. 8
B. -8
C. 32
D. -32

Solution

The 4th term is given by 2 * (-2)^(4-1) = 2 * (-8) = -16.

Correct Answer: B — -8

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Q. In a GP, if the first term is 4 and the common ratio is 1/2, what is the 6th term?

A. 0.25
B. 0.5
C. 1
D. 2

Solution

The 6th term is given by a * r^(n-1) = 4 * (1/2)^(6-1) = 4 * (1/32) = 0.125, which is 0.25.

Correct Answer: A — 0.25

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Q. In a GP, if the first term is 5 and the common ratio is 1/2, what is the sum of the first four terms?

A. 15
B. 10
C. 12.5
D. 20

Solution

The first four terms are 5, 2.5, 1.25, and 0.625. Their sum is 5 + 2.5 + 1.25 + 0.625 = 9.375.

Correct Answer: C — 12.5

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Q. In a GP, if the first term is 5 and the last term is 80, and there are 4 terms in total, what is the common ratio?

A. 2
B. 3
C. 4
D. 5

Solution

Let the common ratio be r. The terms are 5, 5r, 5r^2, 5r^3. Setting 5r^3 = 80 gives r^3 = 16, thus r = 2.

Correct Answer: A — 2

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Q. In a GP, if the first term is 7 and the common ratio is 1/2, what is the 6th term?

A. 0.4375
B. 0.5
C. 1
D. 1.75

Solution

The 6th term is given by 7 * (1/2)^(6-1) = 7 * (1/32) = 0.4375.

Correct Answer: A — 0.4375

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Q. In a GP, if the first term is x and the common ratio is y, what is the expression for the 6th term?

A. xy^5
B. xy^6
C. x^6y
D. x^5y

Solution

The nth term of a GP is given by a * r^(n-1). Thus, the 6th term = x * y^(6-1) = xy^5.

Correct Answer: A — xy^5

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Q. In a group of 150 people, 90 like basketball, 60 like soccer, and 30 like both. How many people like neither sport?

A. 30
B. 60
C. 90
D. 120

Solution

The number of people who like at least one sport is 90 + 60 - 30 = 120, so those who like neither is 150 - 120 = 30.

Correct Answer: A — 30

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Q. In a group of 150 people, 90 like dogs, 60 like cats, and 30 like both. How many people like only cats?

A. 30
B. 60
C. 90
D. 120

Solution

The number of people who like only cats is 60 - 30 = 30.

Correct Answer: A — 30

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Q. In a group of 150 people, 90 like reading fiction, 60 like reading non-fiction, and 30 like both. How many like only non-fiction?

A. 30
B. 60
C. 90
D. 150

Solution

The number of people who like only non-fiction is: 60 - 30 = 30.

Correct Answer: A — 30

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Q. In a group of 150 people, 90 like tea, 60 like coffee, and 30 like both. How many people like neither tea nor coffee?

A. 30
B. 60
C. 90
D. 120

Solution

The number of people who like either tea or coffee is: 90 + 60 - 30 = 120. Therefore, those who like neither is: 150 - 120 = 30.

Correct Answer: B — 60

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Q. In a group of 200 people, 120 like action movies, 80 like drama movies, and 50 like both. How many like only action movies?

A. 70
B. 50
C. 80
D. 120

Solution

The number of people who like only action movies is 120 - 50 = 70.

Correct Answer: A — 70

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Q. In a group of 200 people, 120 like action movies, 80 like drama, and 50 like both. How many like only action movies?

A. 70
B. 50
C. 80
D. 120

Solution

The number of people who like only action movies is 120 - 50 = 70.

Correct Answer: A — 70

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Q. In a group of 200 people, 120 like basketball, 80 like football, and 50 like both. How many people like only basketball?

A. 70
B. 50
C. 80
D. 120

Solution

The number of people who like only basketball is: 120 - 50 = 70.

Correct Answer: A — 70

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Q. In a group of 200 people, 120 like basketball, 80 like football, and 50 like both. How many like only basketball?

A. 70
B. 50
C. 80
D. 120

Solution

The number of people who like only basketball is: 120 - 50 = 70.

Correct Answer: A — 70

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Q. In a group of 200 people, 120 like dogs, 80 like cats, and 50 like both. How many people like only dogs?

A. 70
B. 50
C. 80
D. 100

Solution

The number of people who like only dogs is 120 - 50 = 70.

Correct Answer: A — 70

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Q. In a group of 200 people, 120 like football, 80 like basketball, and 40 like both. How many people like only football?

A. 40
B. 80
C. 120
D. 160

Solution

The number of people who like only football is 120 - 40 = 80.

Correct Answer: B — 80

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Q. In a group of 200 people, 120 like football, 80 like basketball, and 50 like both. How many people like neither sport?

A. 30
B. 50
C. 70
D. 80

Solution

The number of people who like at least one sport is: 120 + 80 - 50 = 150. Therefore, those who like neither is: 200 - 150 = 50.

Correct Answer: C — 70

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Q. In a group of 200 people, 120 like football, 80 like basketball, and 50 like both. How many people like only football?

A. 70
B. 50
C. 80
D. 120

Solution

The number of people who like only football is 120 - 50 = 70.

Correct Answer: A — 70

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Q. In a group of 200 people, 120 like reading, 80 like writing, and 50 like both. How many people like only writing?

A. 30
B. 50
C. 80
D. 20

Solution

The number of people who like only writing is 80 - 50 = 30.

Correct Answer: A — 30

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Q. In a group of 200 people, 120 like sports, 80 like music, and 50 like both. How many people like only music?

A. 30
B. 50
C. 80
D. 100

Solution

The number of people who like only music is 80 - 50 = 30.

Correct Answer: A — 30

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Q. In a group of 300 people, 150 like rock music, 100 like pop music, and 50 like both. How many people like only rock music?

A. 50
B. 100
C. 150
D. 200

Solution

The number of people who like only rock music is 150 - 50 = 100.

Correct Answer: B — 100

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