Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If log10(10x) = 2, what is the value of x?

A. 10
B. 100
C. 1000
D. 10000

Solution

10x = 10^2, so x = 10.

Correct Answer: B — 100

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Q. If log10(10^5) = x, what is the value of x?

A. 1
B. 2
C. 5
D. 10

Solution

log10(10^5) = 5.

Correct Answer: C — 5

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Q. If log10(5) = a, what is log10(25) in terms of a?

A. 2a
B. a
C. a/2
D. 4a

Solution

log10(25) = log10(5^2) = 2 * log10(5) = 2a.

Correct Answer: A — 2a

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Q. If log10(x) + log10(10) = 2, what is the value of x?

A. 10
B. 100
C. 1000
D. 10000

Solution

log10(x) = 2 - 1 = 1, so x = 10^1 = 10.

Correct Answer: B — 100

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Q. If log10(x) = -1, what is the value of x?

A. 0.1
B. 1
C. 10
D. 100

Solution

x = 10^-1 = 0.1.

Correct Answer: A — 0.1

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Q. If log10(x) = 2, what is the value of x?

A. 10
B. 100
C. 1000
D. 10000

Solution

x = 10^2 = 100.

Correct Answer: B — 100

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Q. If log2(8) = y, what is the value of y?

A. 1
B. 2
C. 3
D. 4

Solution

log2(8) = 3, so y = 3.

Correct Answer: C — 3

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Q. If log2(x) + log2(8) = 7, what is the value of x?

A. 32
B. 64
C. 128
D. 256

Solution

log2(x) = 7 - log2(8) = 7 - 3 = 4, so x = 2^4 = 16.

Correct Answer: B — 64

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Q. If log2(x) = 5, what is the value of x?

A. 16
B. 32
C. 64
D. 128

Solution

x = 2^5 = 32.

Correct Answer: C — 64

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Q. If log3(27) = a, what is the value of a?

A. 1
B. 2
C. 3
D. 4

Solution

log3(27) = 3, since 3^3 = 27.

Correct Answer: C — 3

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Q. If log3(27) = z, what is the value of z?

A. 1
B. 2
C. 3
D. 4

Solution

log3(27) = 3, since 3^3 = 27.

Correct Answer: C — 3

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Q. If log3(81) = x, what is the value of x?

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

Solution

81 = 3^4, so x = 4.

Correct Answer: C — 4

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Q. If log4(16) = a, what is the value of a?

A. 1
B. 2
C. 3
D. 4

Solution

log4(16) = 2, since 4^2 = 16.

Correct Answer: B — 2

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Q. If log4(64) = x, what is the value of x?

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

Solution

64 = 4^3, so x = 3.

Correct Answer: B — 3

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Q. If log5(125) = x, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

log5(125) = log5(5^3) = 3.

Correct Answer: C — 3

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Q. If log7(343) = x, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

343 = 7^3, so x = 3.

Correct Answer: A — 3

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Q. If log7(49) = c, what is the value of c?

A. 1
B. 2
C. 3
D. 4

Solution

log7(49) = 2, since 7^2 = 49.

Correct Answer: B — 2

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Q. If log7(49) = x, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

49 = 7^2, so x = 2.

Correct Answer: B — 2

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Q. If log7(x) = 2, what is the value of x?

A. 14
B. 28
C. 49
D. 56

Solution

x = 7^2 = 49.

Correct Answer: C — 49

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Q. If log7(x) = 3, what is the value of x?

A. 49
B. 21
C. 7
D. 14

Solution

x = 7^3 = 343.

Correct Answer: A — 49

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Q. If logb(27) = 3, what is the value of b?

A. 3
B. 9
C. 27
D. 81

Solution

b^3 = 27, so b = 3.

Correct Answer: A — 3

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Q. If logb(64) = 6, what is the value of b?

A. 2
B. 4
C. 8
D. 16

Solution

64 = b^6, so b = 64^(1/6) = 2.

Correct Answer: C — 8

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Q. If logx(100) = 2, what is the value of x?

A. 10
B. 20
C. 30
D. 40

Solution

x^2 = 100, so x = 10.

Correct Answer: A — 10

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Q. If logx(27) = 3, what is the value of x?

A. 3
B. 9
C. 27
D. 81

Solution

x = 27^(1/3) = 3.

Correct Answer: C — 27

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Q. If logx(49) = 2, what is the value of x?

A. 5
B. 7
C. 14
D. 49

Solution

x^2 = 49, so x = 7.

Correct Answer: B — 7

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Q. If logx(64) = 6, what is the value of x?

A. 2
B. 4
C. 8
D. 16

Solution

x = 64^(1/6) = 2.

Correct Answer: C — 8

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Q. If logx(81) = 4, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

x = 81^(1/4) = 3.

Correct Answer: A — 3

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Q. If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.

Correct Answer: B — 5 hours

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Q. If the age of a woman is 3 times the age of her daughter and the sum of their ages is 48, how old is the daughter?

A. 8
B. 12
C. 16
D. 20

Solution

Let the daughter's age be x. Then the woman's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

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Q. If the age of a woman is 3 times the age of her daughter and the sum of their ages is 48, what is the age of the daughter?

A. 8
B. 12
C. 16
D. 20

Solution

Let the daughter's age be x. Then the woman's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

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Arithmetic Aptitude

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