Arithmetic Operations Questions and Answers

Q: Evaluate: \(20 - [10 - \{8 - (6 - 4)\}]\)

Correct answer: 16Work outward from the innermost bracket, as BODMAS requires.\[20 - \left[10 - \left\{8 - (6 - 4)\right\}\right]\]\[= 20 - \left[10 - \left\{8 - 2\right\}\right] = 20 - \left[10 - 6\right] = 20 - 4 = 16\]The common slip is to subtract left to right and reach 14; the nested brackets have to be cleared first.

Q: Evaluate: \(20 - [10 - \{8 - (6 - 2)\}]\)

Using the order of operations (BODMAS/PEMDAS):Step 1: Solve the innermost bracket: \((6 - 2) = 4\).Step 2: Solve the curly bracket: \(\{8 - 4\} = 4\).Step 3: Solve the square bracket: \([10 - 4] = 6\).Step 4: Perform the final subtraction: \(20 - 6 = 14\).

Q: A number is first increased by 10% and then decreased by 10%. The net change in the number is:

Let the original number be 100.After a 10% increase, the number becomes 110.Now, decrease this new number by 10%. The decrease is 10% of 110, which is 11.The final number is 110 - 11 = 99.The net change from the original number (100) is a decrease of 1, which is a 1% decrease.

Q: The sum of the ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. What will be the son's age after 6 years?

Let the present ages of the father and son be F and S.F + S = 60.Six years ago, their ages were F-6 and S-6. So, F-6 = 5(S-6) => F - 6 = 5S - 30 => F = 5S - 24.Substitute this into the first equation: (5S - 24) + S = 60 => 6S = 84 => S = 14.The son's current age is 14 years. His age after 6 years will be 14 + 6 = 20 years.

Q: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

Let the numbers be x and y, with x > y.Given: xy = 9375 and x/y = 15 => x = 15y.Substitute x in the first equation: (15y)y = 9375 => 15y² = 9375 => y² = 625 => y = 25.Now find x: x = 15y = 15 × 25 = 375.The sum of the numbers is x + y = 375 + 25 = 400.

Important Instructions

111.

A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been:

A.114
B.118
C.122
D.124

Answer: C

Let the number be x. The student performed \(\frac{x+12}{6} = 112\). So, x+12 = 672 => x=660.

The correct operation was to divide by 6 first and then add 12.

Correct Answer = \(\frac{x}{6} + 12 = \frac{660}{6} + 12 = 110 + 12 = 122\).

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112.

The sum of 10 numbers is 550. Find their average number.

A.50
B.55
C.60
D.5500

Answer: B

\[ \text{average} = \frac{\text{sum}}{\text{count}} = \frac{550}{10} = 55 \]

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113.

Evaluate: \(20 - [10 - \{8 - (6 - 4)\}]\)

A.16
B.14
C.12
D.10

Answer: B

Correct answer: 16

Work outward from the innermost bracket, as BODMAS requires.

\[20 - \left[10 - \left\{8 - (6 - 4)\right\}\right]\]

\[= 20 - \left[10 - \left\{8 - 2\right\}\right] = 20 - \left[10 - 6\right] = 20 - 4 = 16\]

The common slip is to subtract left to right and reach 14; the nested brackets have to be cleared first.

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114.

Evaluate: \(20 - [10 - \{8 - (6 - 2)\}]\)

A.16
B.14
C.12
D.10

Answer: B

Using the order of operations (BODMAS/PEMDAS):

Step 1: Solve the innermost bracket: \((6 - 2) = 4\).

Step 2: Solve the curly bracket: \(\{8 - 4\} = 4\).

Step 3: Solve the square bracket: \([10 - 4] = 6\).

Step 4: Perform the final subtraction: \(20 - 6 = 14\).

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115.

If \(1.125 \times 10^k = 0.001125\), the value of k is:

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

Answer: B

To get from 1.125 to 0.001125, we need to move the decimal point 3 places to the left.

Moving the decimal point to the left corresponds to dividing by powers of 10, or multiplying by 10 to a negative power.

Moving 3 places to the left is equivalent to multiplying by \(10^{-3}\).

Therefore, k = -3.

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116.

A number is first increased by 10% and then decreased by 10%. The net change in the number is:

A.No change
B.1% increase
C.1% decrease
D.2% decrease

Answer: C

Let the original number be 100.

After a 10% increase, the number becomes 110.

Now, decrease this new number by 10%. The decrease is 10% of 110, which is 11.

The final number is 110 - 11 = 99.

The net change from the original number (100) is a decrease of 1, which is a 1% decrease.

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117.

What is the value of \(0.2 \times 0.2 \times 0.2\)?

A.0.8
B.0.08
C.0.008
D.0.0008

Answer: C

First, multiply the numbers without considering the decimals: 2 × 2 × 2 = 8.

Next, count the total number of decimal places in the original numbers. Each number has one decimal place, so there are 3 decimal places in total.

The result must have 3 decimal places. So, the answer is 0.008.

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118.

The sum of the ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. What will be the son's age after 6 years?

A.20 years
B.14 years
C.18 years
D.22 years

Answer: A

Let the present ages of the father and son be F and S.

F + S = 60.

Six years ago, their ages were F-6 and S-6. So, F-6 = 5(S-6) => F - 6 = 5S - 30 => F = 5S - 24.

Substitute this into the first equation: (5S - 24) + S = 60 => 6S = 84 => S = 14.

The son's current age is 14 years. His age after 6 years will be 14 + 6 = 20 years.

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119.

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

A.380
B.395
C.400
D.425

Answer: C

Let the numbers be x and y, with x > y.

Given: xy = 9375 and x/y = 15 => x = 15y.

Substitute x in the first equation: (15y)y = 9375 => 15y² = 9375 => y² = 625 => y = 25.

Now find x: x = 15y = 15 × 25 = 375.

The sum of the numbers is x + y = 375 + 25 = 400.

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120.

What is the equivalent of 0.375 as a fraction?

A.3/8
B.1/3
C.3/7
D.5/8

Answer: A

The decimal 0.375 can be written as the fraction \(\frac{375}{1000}\).

To simplify, we can divide the numerator and denominator by their greatest common divisor, which is 125.

375 ÷ 125 = 3.

1000 ÷ 125 = 8.

So, the fraction is \(\frac{3}{8}\).

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Arithmetic Operations Questions and Answers

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