Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. What is the total amount after 5 years if $1000 is invested at a compound interest rate of 3% per annum?

A. $1159.27
B. $1200.00
C. $1100.00
D. $1050.00

Solution

Amount = P(1 + r/n)^(nt) = 1000(1 + 0.03/1)^(1*5) = 1000(1.159274) = 1159.27

Correct Answer: A — $1159.27

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Q. What is the total number of days from January 1, 2020 to December 31, 2020?

A. 365
B. 366
C. 364
D. 367

Solution

2020 is a leap year, so there are 366 days from January 1, 2020 to December 31, 2020.

Correct Answer: B — 366

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Q. What is the total surface area of a cube with a side length of 6 cm?

A. 72 cm²
B. 144 cm²
C. 36 cm²
D. 48 cm²

Solution

Surface Area = 6 * side² = 6 * 6² = 6 * 36 = 216 cm².

Correct Answer: B — 144 cm²

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Q. What is the total surface area of a sphere with a radius of 7 cm? (Use π = 3.14)

A. 615.44 cm²
B. 153.86 cm²
C. 308 cm²
D. 154 cm²

Solution

Surface Area = 4πr² = 4 * 3.14 * 7² = 615.44 cm²

Correct Answer: A — 615.44 cm²

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Q. What is the true discount on a bill of Rs. 10000 due in 1 year if the Banker's Discount is Rs. 1000?

A. Rs. 900
B. Rs. 1000
C. Rs. 1100
D. Rs. 800

Solution

True Discount = Banker's Discount × (Time / (Time + 1)) = 1000 × (1 / (1 + 1)) = Rs. 500.

Correct Answer: A — Rs. 900

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Q. What is the true discount on a bill of Rs. 30000 due in 2 years if the Banker's Discount is Rs. 3000?

A. Rs. 2500
B. Rs. 3000
C. Rs. 3500
D. Rs. 2000

Solution

True Discount = Banker's Discount × (Time / (Time + 1)) = 3000 × (2 / (2 + 1)) = Rs. 2000.

Correct Answer: A — Rs. 2500

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Q. What is the true discount on a bill of Rs. 5000 due in 3 months if the Banker's Discount is Rs. 125?

A. Rs. 100
B. Rs. 125
C. Rs. 150
D. Rs. 200

Solution

True Discount = Banker's Discount * (Time / (Time + 1)) = 125 * (3/12) = Rs. 31.25.

Correct Answer: A — Rs. 100

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Q. What is the true discount on a sum of $10000 due in 10 years at 5% per annum?

A. $2000
B. $2500
C. $3000
D. $3500

Solution

Present Worth = 10000 / (1 + 0.05*10) = 10000 / 1.5 = $6666.67. True Discount = 10000 - 6666.67 = $3333.33.

Correct Answer: B — $2500

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Q. What is the true discount on a sum of $8000 due in 5 years at 7% per annum?

A. $500
B. $600
C. $700
D. $800

Solution

Present Worth = 8000 / (1 + 0.07*5) = 8000 / 1.35 = $5925.93. True Discount = 8000 - 5925.93 = $2074.07.

Correct Answer: C — $700

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Q. What is the value of (10^3) * (10^-1)?

A. 10^2
B. 10^1
C. 10^0
D. 10^-1

Solution

Using the property of indices, a^m * a^n = a^(m+n). Here, 10^3 * 10^-1 = 10^(3-1) = 10^2.

Correct Answer: A — 10^2

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Q. What is the value of (10^3) / (10^2)?

A. 10^1
B. 10^0
C. 10^2
D. 10^3

Solution

Using the property of indices, a^m / a^n = a^(m-n). Here, 10^3 / 10^2 = 10^(3-2) = 10^1.

Correct Answer: A — 10^1

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Q. What is the value of (3^4) / (3^2)?

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

Solution

Using the property of indices, a^m / a^n = a^(m-n), we have (3^4) / (3^2) = 3^(4-2) = 3^2.

Correct Answer: A — 3^2

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Q. What is the value of (4^3) * (4^-1)?

A. 4^2
B. 4^3
C. 4^1
D. 4^0

Solution

Using the property of indices, a^m * a^n = a^(m+n), we have (4^3) * (4^-1) = 4^(3-1) = 4^2.

Correct Answer: A — 4^2

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Q. What is the value of (4^3) * (4^2)?

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

Solution

Using the property of indices, a^m * a^n = a^(m+n), we have (4^3) * (4^2) = 4^(3+2) = 4^5.

Correct Answer: A — 4^5

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Q. What is the value of (7^0) + (7^1)?

A. 0
B. 1
C. 7
D. 8

Solution

Using the property that any number raised to the power of 0 is 1, we have 7^0 = 1 and 7^1 = 7, thus 1 + 7 = 8.

Correct Answer: D — 8

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Q. What is the value of (7^3) * (7^-2)?

A. 7^1
B. 7^0
C. 7^2
D. 7^3

Solution

Using the property of indices, a^m * a^n = a^(m+n). Here, 7^3 * 7^-2 = 7^(3-2) = 7^1.

Correct Answer: A — 7^1

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Q. What is the value of (x^2) * (x^3) / (x^4)?

A. x^1
B. x^0
C. x^2
D. x^3

Solution

Using the property of indices, we have (x^2 * x^3) / x^4 = x^(2+3-4) = x^1.

Correct Answer: A — x^1

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Q. What is the value of (x^3 * x^2)?

A. x^5
B. x^6
C. x^7
D. x^8

Solution

Using the property of indices, a^m * a^n = a^(m+n). Here, x^3 * x^2 = x^(3+2) = x^5.

Correct Answer: A — x^5

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Q. What is the value of (x^3) / (x^2) when x = 2?

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

Solution

Using the property of indices, (x^3) / (x^2) = x^(3-2) = x^1. When x = 2, it equals 2.

Correct Answer: A — 2

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Q. What is the value of 7^2 + 3^2?

A. 58
B. 62
C. 70
D. 74

Solution

Calculating 7^2 = 49 and 3^2 = 9. Therefore, 49 + 9 = 58.

Correct Answer: A — 58

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Q. What is the value of log10(0.01)?

A. -1
B. -2
C. 0
D. 1

Solution

log10(0.01) = log10(10^-2) = -2.

Correct Answer: B — -2

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Q. What is the value of log10(0.1)?

A. -1
B. 0
C. 1
D. 2

Solution

log10(0.1) = -1 because 10^-1 = 0.1.

Correct Answer: A — -1

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Q. What is the value of log10(1)?

A. 0
B. 1
C. -1
D. undefined

Solution

log10(1) = 0 because 10^0 = 1.

Correct Answer: A — 0

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Q. What is the value of log10(100)?

A. 1
B. 2
C. 3
D. 0

Solution

log10(100) = 2 because 10^2 = 100.

Correct Answer: B — 2

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Q. What is the value of log10(1000)?

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

Solution

log10(1000) = log10(10^3) = 3.

Correct Answer: C — 3

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Q. What is the value of log10(50) approximately?

A. 1.5
B. 1.7
C. 1.9
D. 2.0

Solution

log10(50) is approximately 1.7.

Correct Answer: B — 1.7

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Q. What is the value of log2(1)?

A. 0
B. 1
C. 2
D. 3

Solution

log2(1) = 0, since any number to the power of 0 is 1.

Correct Answer: A — 0

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Q. What is the value of log2(1/8)?

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

Solution

1/8 = 2^-3, so log2(1/8) = -3.

Correct Answer: B — -3

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Q. What is the value of log2(16)?

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

Solution

log2(16) = 4, since 2^4 = 16.

Correct Answer: C — 4

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Q. What is the value of log2(32)?

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

Solution

log2(32) = log2(2^5) = 5.

Correct Answer: B — 5

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Arithmetic Aptitude

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