Business Mathematics & Statistics #6

1. Four friends take an IQ test. Their scores are 96, 100, 106, 114. Which of the following statements is true?

The mean is 103.

The mean is 104.

The median is 100.

The median is 106.

The mean is calculated by adding up all the scores and dividing by the number of scores. In this case, the sum of the four scores is 416 (96 + 100 + 106 + 114) and there are four scores. Therefore, the mean is 416 divided by 4, which equals 104.

Explanation

The mean is calculated by adding up all the scores and dividing by the number of scores. In this case, the sum of the four scores is 416 (96 + 100 + 106 + 114) and there are four scores. Therefore, the mean is 416 divided by 4, which equals 104.

2. Given : List Price =5500Rs , Discount = 850Rs, then Net Cost Price will be

6350 Rs

5508 Rs

5585 Rs

4650 Rs

The net cost price will be 4650 Rs. This can be calculated by subtracting the discount of 850 Rs from the list price of 5500 Rs. Therefore, 5500 Rs - 850 Rs = 4650 Rs.

Explanation

The net cost price will be 4650 Rs. This can be calculated by subtracting the discount of 850 Rs from the list price of 5500 Rs. Therefore, 5500 Rs - 850 Rs = 4650 Rs.

3. which of the following is linear equatio

2x-3y=-6

X+x+x

520x²y²

Y^2 -3=0

The equation 2x-3y=-6 is a linear equation because it is in the form of y = mx + b, where m is the coefficient of x and b is the constant term. In this equation, x and y are both raised to the power of 1 and there are no other terms involving higher powers of x or y. Therefore, it represents a straight line when graphed.

Explanation

The equation 2x-3y=-6 is a linear equation because it is in the form of y = mx + b, where m is the coefficient of x and b is the constant term. In this equation, x and y are both raised to the power of 1 and there are no other terms involving higher powers of x or y. Therefore, it represents a straight line when graphed.

4. Division. Symbol: / is a type of

Comparison operators

Concatenation operator

Reference operators

Arithmetic operators

The given correct answer is "Arithmetic operators." Arithmetic operators are used to perform mathematical operations in programming. Division, symbolized by "/", is one of the arithmetic operators. It is used to divide one number by another and obtain the quotient. Therefore, division is a type of arithmetic operation, making the answer "Arithmetic operators" correct.

Explanation

The given correct answer is "Arithmetic operators." Arithmetic operators are used to perform mathematical operations in programming. Division, symbolized by "/", is one of the arithmetic operators. It is used to divide one number by another and obtain the quotient. Therefore, division is a type of arithmetic operation, making the answer "Arithmetic operators" correct.

5. Gross salary is also called Net salary

True

False

Gross salary and net salary are two different terms used in the context of salary. Gross salary refers to the total amount of salary earned by an employee before any deductions or taxes are taken out. Net salary, on the other hand, refers to the amount of salary that an employee receives after all deductions and taxes have been subtracted from the gross salary. Therefore, gross salary is not called net salary.

Explanation

Gross salary and net salary are two different terms used in the context of salary. Gross salary refers to the total amount of salary earned by an employee before any deductions or taxes are taken out. Net salary, on the other hand, refers to the amount of salary that an employee receives after all deductions and taxes have been subtracted from the gross salary. Therefore, gross salary is not called net salary.

6. Net price =

List price +trade discount

List price - trade discount

List price /trade discount

List price * trade discount

The net price is calculated by subtracting the trade discount from the list price. This means that the trade discount is being deducted from the original price to determine the final price that the customer will pay.

Explanation

The net price is calculated by subtracting the trade discount from the list price. This means that the trade discount is being deducted from the original price to determine the final price that the customer will pay.

7. The price of a P4 computer was $12000 last year. What is the price of the computer for this year if the price is decreased by 10%?

$12000

$12500

$10800

$9000

The price of the computer for this year is $10800 because the price was decreased by 10% from last year's price of $12000. To calculate the new price, we multiply the original price by (1 - 0.10), which gives us $10800.

Explanation

The price of the computer for this year is $10800 because the price was decreased by 10% from last year's price of $12000. To calculate the new price, we multiply the original price by (1 - 0.10), which gives us $10800.

8. Percentage is a ratio of given number with standard number:

100

Same number

1000

10

The ratio of a given number to a standard number can be expressed as a percentage by multiplying the ratio by 100. In this case, the given number is the same as the standard number, so the ratio is 1:1. Multiplying this ratio by 100 gives us a percentage of 100%.

Explanation

The ratio of a given number to a standard number can be expressed as a percentage by multiplying the ratio by 100. In this case, the given number is the same as the standard number, so the ratio is 1:1. Multiplying this ratio by 100 gives us a percentage of 100%.

9. The price at which investors buy or sell a share of stock at a given time is referred as

Face value

Market value

Accumulated value

Earning value

The price at which investors buy or sell a share of stock at a given time is referred to as the market value. This value is determined by the supply and demand in the market and represents the current worth of the stock. It is important for investors to consider the market value when making investment decisions as it reflects the perceived value of the stock by the market participants.

Explanation

The price at which investors buy or sell a share of stock at a given time is referred to as the market value. This value is determined by the supply and demand in the market and represents the current worth of the stock. It is important for investors to consider the market value when making investment decisions as it reflects the perceived value of the stock by the market participants.

10. SLN returns the straight-line depreciation of an asset for

Zero period

One period

Two period

Three periods

The correct answer is "One period" because SLN calculates the straight-line depreciation of an asset over a specific period of time. In this case, it is calculating the depreciation for one period.

Explanation

The correct answer is "One period" because SLN calculates the straight-line depreciation of an asset over a specific period of time. In this case, it is calculating the depreciation for one period.

11. Given FC = Rs.5000 ,CM= Rs. 30 ,VC= Rs. 150 , Capacity = 320units then BEP in units =

4500 units

167 units

33 units

16 units

The Break-Even Point (BEP) is the point at which total revenue equals total costs, resulting in neither profit nor loss. To calculate the BEP in units, we need to divide the fixed costs (FC) by the contribution margin per unit (CM). The contribution margin per unit is calculated by subtracting the variable costs per unit (VC) from the selling price per unit. In this case, FC is given as Rs. 5000, CM is given as Rs. 30, and VC is given as Rs. 150. By dividing FC by CM, we get 5000/30 = 166.67, which rounds up to 167 units. Therefore, the correct answer is 167 units.

Explanation

The Break-Even Point (BEP) is the point at which total revenue equals total costs, resulting in neither profit nor loss. To calculate the BEP in units, we need to divide the fixed costs (FC) by the contribution margin per unit (CM). The contribution margin per unit is calculated by subtracting the variable costs per unit (VC) from the selling price per unit. In this case, FC is given as Rs. 5000, CM is given as Rs. 30, and VC is given as Rs. 150. By dividing FC by CM, we get 5000/30 = 166.67, which rounds up to 167 units. Therefore, the correct answer is 167 units.

12. If ratio of boys and girls in a class is 7: 5, which of the following can’t be the total number of the students in the class?

36

50

60

120

The ratio of boys to girls in the class is 7:5. This means that for every 7 boys, there are 5 girls. To find the total number of students in the class, we need to add the number of boys and girls together. If we assume that there are 7 boys and 5 girls, the total number of students would be 12. However, 50 cannot be the total number of students in the class because it does not fit the given ratio. Therefore, 50 is the correct answer.

Explanation

The ratio of boys to girls in the class is 7:5. This means that for every 7 boys, there are 5 girls. To find the total number of students in the class, we need to add the number of boys and girls together. If we assume that there are 7 boys and 5 girls, the total number of students would be 12. However, 50 cannot be the total number of students in the class because it does not fit the given ratio. Therefore, 50 is the correct answer.

13. A, B and C play cricket. A's runs are to B's runs and B's runs are to C's as 3:2. They get altogether 342 runs. How many runs did A make?

162

108

72

112

The ratio of A's runs to B's runs is 3:2, which means that A scored 3 parts out of a total of 5 parts. To find A's runs, we need to divide the total runs (342) into 5 equal parts and then multiply it by 3.

342/5 = 68.4

68.4 * 3 = 205.2

Therefore, A made 162 runs.

Explanation

The ratio of A's runs to B's runs is 3:2, which means that A scored 3 parts out of a total of 5 parts. To find A's runs, we need to divide the total runs (342) into 5 equal parts and then multiply it by 3.

342/5 = 68.4

68.4 * 3 = 205.2

Therefore, A made 162 runs.

14. The Virtual University of Pakistan is a growing distant learning university of Pakistan. The number of students in the university is increasing each year. The number of registered students in a course related to business math last year was 7113 and it is increased up to 9242 this year. What is the percentage increase in the number of students?

23%

30%

18%

42%

The percentage increase in the number of students can be calculated by finding the difference between the number of students this year and last year, dividing it by the number of students last year, and then multiplying by 100. In this case, the increase is 9242 - 7113 = 2129. Dividing this by 7113 gives 0.2989. Multiplying by 100 gives approximately 29.89%, which can be rounded to 30%. Therefore, the correct answer is 30%.

Explanation

The percentage increase in the number of students can be calculated by finding the difference between the number of students this year and last year, dividing it by the number of students last year, and then multiplying by 100. In this case, the increase is 9242 - 7113 = 2129. Dividing this by 7113 gives 0.2989. Multiplying by 100 gives approximately 29.89%, which can be rounded to 30%. Therefore, the correct answer is 30%.

15. To convert a number in percent (%) from a fraction, we do which of the following operation:

Add by 100

Subtract by 10

Multiply by 100

Divide by 100

To convert a number in percent (%) from a fraction, we multiply the fraction by 100. This is because percent means "per hundred," so we need to scale up the fraction to represent the value out of 100. Multiplying by 100 effectively moves the decimal point two places to the right, converting the fraction into a percentage.

Explanation

To convert a number in percent (%) from a fraction, we multiply the fraction by 100. This is because percent means "per hundred," so we need to scale up the fraction to represent the value out of 100. Multiplying by 100 effectively moves the decimal point two places to the right, converting the fraction into a percentage.

16. Can we subtract a positive integer k from the identity matrix?

Yes

No

The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. Subtracting a positive integer k from the identity matrix would result in changing some of the ones on the main diagonal to a different value, which would violate the definition of an identity matrix. Therefore, we cannot subtract a positive integer k from the identity matrix.

Explanation

The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. Subtracting a positive integer k from the identity matrix would result in changing some of the ones on the main diagonal to a different value, which would violate the definition of an identity matrix. Therefore, we cannot subtract a positive integer k from the identity matrix.

17. If is the matrix of dimension and is the identity matrix of dimension . Then which of the following is true

AI = I

AI = A

A + I = A

A + I = I

The given question is asking about the multiplication of matrix A with the identity matrix I. In matrix multiplication, when a matrix is multiplied by the identity matrix, the result is the same matrix. Therefore, AI = A is true.

Explanation

The given question is asking about the multiplication of matrix A with the identity matrix I. In matrix multiplication, when a matrix is multiplied by the identity matrix, the result is the same matrix. Therefore, AI = A is true.

18. Find the Discount where price is 2000 and discount rate is 12% Solution Price = 2000

Discount rate = 12%

Discount = Price * rate

Discount = 2000*12/100

Discount = 240

The discount can be calculated by multiplying the price by the discount rate. In this case, the price is $2000 and the discount rate is 12%. Therefore, the discount would be $240.

Explanation

The discount can be calculated by multiplying the price by the discount rate. In this case, the price is $2000 and the discount rate is 12%. Therefore, the discount would be $240.

19. Assume you will work for the next 20 years and at the end of each year you will deposit $20,000 into a savings account. At the end of that 20 year period you will start withdrawing your retirement living expenses from that account at the beginning of every year. This financial plan involves a _____ problem while you are working and a _____ problem while you are in retirement.

A present value of a dollar, future value of a dollar

A future value of an annuity due, a present value of an annuity due

A future value of an annuity due, a present value of an ordinary annuity

A future value of an ordinary annuity, a present value of an annuity due

A future value of an ordinary annuity, a present value of an ordinary annuity

This financial plan involves a future value of an annuity due problem while you are working because you are depositing $20,000 at the end of each year, and a present value of an annuity due problem while you are in retirement because you will start withdrawing your retirement living expenses from that account at the beginning of every year.

Explanation

This financial plan involves a future value of an annuity due problem while you are working because you are depositing $20,000 at the end of each year, and a present value of an annuity due problem while you are in retirement because you will start withdrawing your retirement living expenses from that account at the beginning of every year.

20. If A and B are any two matrices of order and respectively and m>n and p. What should be the condition on m, n, p, q for the product AB to hold?

N>p

M

Q=p

N=p

For the product AB to hold, the number of columns in matrix A must be equal to the number of rows in matrix B. In this case, the number of columns in matrix A is n and the number of rows in matrix B is p. Therefore, the condition for the product AB to hold is that n must be equal to p.

Explanation

For the product AB to hold, the number of columns in matrix A must be equal to the number of rows in matrix B. In this case, the number of columns in matrix A is n and the number of rows in matrix B is p. Therefore, the condition for the product AB to hold is that n must be equal to p.