GMAT Math : Arithmetic

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Example Questions

Example Question #2051 : Problem Solving Questions

If is a negative number, what is the difference between the mean and the median of the following numbers:

n, n+7, n-8, n-3, n+9

Possible Answers:

Correct answer:

Explanation:

To find the median, write the numbers in ascending orders.

n-8, n-3, n, n+7, n+9

Remember the median is the midpoint value with half of the values below it and the other half of the values above it.

The median is the third number which is n.

The mean is:

$\frac{(n-8)+(n-3)+n+(n+7)+(n+9)}{5}=\frac{5n-11+16}{5}$

$=\frac{5n+5}{5}$

=n+1

mean - median = n+1-n=1

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Example Question #31 : Calculating Arithmetic Mean

The arithmetic mean of the set $\left \{ a, b, c, d\right \}$ is 100.

Which of these expressions is equal to the arithmetic mean of the set $\left \{ a, b, c \right \}$ ?

Possible Answers:

$100 - \frac{1}{4}d$

$75 - \frac{1}{3}d$

$133\frac{1}{3} - \frac{1}{3}d$

$75 - \frac{1}{4}d$

$100 - \frac{1}{3}d$

Correct answer:

$133\frac{1}{3} - \frac{1}{3}d$

Explanation:

$\frac{a+b+c+d}{4} = 100$

a+b+c+d = 400

a+b+c = 400 - d

$\frac{a+b+c }{3}= \frac{400 - d}{3} = \frac{400}{3} - \frac{d}{3} = 133\frac{1}{3} - \frac{1}{3}d$

The arithmetic mean of $\left \{ a, b, c \right \}$ is equal to $133\frac{1}{3} - \frac{1}{3}d$

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Example Question #42 : Descriptive Statistics

The arithmetic mean of the set $\left \{ a, b, c, d, e, f, 100\right \}$ is 250 .

Give the arithmetic mean of the set $\left \{ a, b, c, d, e, f\right \}$ .

Possible Answers:

$308\frac{1}{3}$

225

$235 \frac{5}{7}$

$191\frac{2}{3}$

275

Correct answer:

275

Explanation:

We are told that:

$\frac{a+b+c+d+e+f+100 }{7} = 250$

Multiplying each side by :

$\frac{a+b+c+d+e+f+100 }{7} \cdot 7 = 250 \cdot 7$

a+b+c+d+e+f+100 =1,750

Subtracting 100 from each side:

a+b+c+d+e+f =1,650

At this point, we can solve for the arithmetic mean of the set $\left \{ a, b, c, d, e, f\right \}$ :

$\frac{a+b+c+d+e+f }{6}=\frac{1,650}{6} = 275$ , the arithmetic mean of the set $\left \{ a, b, c, d, e, f\right \}$ .

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Example Question #45 : Descriptive Statistics

A bakery sold a daily average of 25 croissants last week. The table above shows the number of croissants sold each day except Sunday. Find the number of croissants sold on Sunday.

Possible Answers:

Correct answer:

Explanation:

Let be the number of croissants sold on Sunday. The daily average of croissants sold in the past week is:

$\frac{29+15+12+10+34+38+x}{7}=25$

Solve for :

29+15+12+10+34+38+x=175

138+x=175

x=175-138=37

The number of croissants sold on Sunday is .

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Example Question #2051 : Problem Solving Questions

Five friends go out to a restaurant to celebrate the birthday of one of them. The cost of the meal for all of them including tax is $\$280.00$ . They decide to leave a $15\%$ tip and to split the total amount equally. If the person celebrating his or her birthday does not pay, how much do each of the other four friends pay?

Possible Answers:

$\$64.40$

$\$88.50$

$\$74.50$

$\$80.50$

$\$59.50$

Correct answer:

$\$80.50$

Explanation:

The total cost of the meal including tax and the $15\%$ tip is:

$280\times(1+0.15)=322$

They split the total amount equally between four of them, so each of those four people then pays:

$\frac{322}{4}=80.5$

Each of the four friends pays $\$80.50$ .

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Example Question #2052 : Problem Solving Questions

Calculate the arithmetic mean for the following set of data:

(13, 7, 5, 6, 8, 9)

Possible Answers:

Correct answer:

Explanation:

To calculate the mean of a set of data, we sum the values and then divide by the number of values present. In this case we have 6 values, so we add them all together and then divide by 6 to find the arithmetic mean for this set of data:

$\mu=\frac{\sum_{i=1}^{6}x_i}{6}=\frac{13+7+5+6+8+9}{6}=\frac{48}{6}=8$

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Example Question #2053 : Problem Solving Questions

Calculate the mean of the following set of data:

$\begin{Bmatrix} 7, 11, 8, 13, 14, 9, 8 \end{Bmatrix}$

Possible Answers:

Correct answer:

Explanation:

To calculate the mean of a set of a data, we add up all the entries and then divide the result by the number of entries in the data set. There are seven entries in the given set, so we'll add them up and then divide by seven to find the mean:

$\mu=\frac{7+11+8+13+14+9+8}{7}=\frac{70}{7}=10$

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Example Question #2052 : Problem Solving Questions

The arithmetic mean of and is 35. Also, x - y = 30 . What is ?

Possible Answers:

y = 20

y = 30

y = 25

y = 40

y = 35

Correct answer:

y = 20

Explanation:

If the arithmetic mean of and is 35, then

$\frac{x+ y}{2} = 35$ .

This, along with the statement

x - y = 30 ,

form a system of equations that can be solved as follows:

x - y + y = 30 + y

x = 30 + y

Substitute:

$\frac{ 30 + y+ y}{2} = 35$

$\frac{ 30 +2y}{2} = 35$

$\frac{ 30 +2y}{2} \cdot 2 = 35\cdot 2$

30 +2y = 70

30 +2y - 30 = 70 - 30

2y = 40

$2y \div 2 = 40 \div 2$

y = 20

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Example Question #2061 : Problem Solving Questions

The arithmetic mean of and is 66. The arithmetic mean of and is 60. The arithmetic mean of and is 72. Give the arithmetic mean of , , and .

Possible Answers:

Insufficient information is given to determine the mean.

Correct answer:

Explanation:

The arithmetic mean of and is 64, so

$\frac{x+ y}{2}= 66$

Similarly,

$\frac{x+ z}{2}= 60$

$\frac{y+ z}{2}= 72$

Add the expressions:

$\frac{x+ y}{2} + \frac{x+ z}{2}+ \frac{y+ z}{2}= 66+ 60 +72$

$\frac{2x+2 y+ 2z}{2} = 198$

x+y+z= 198

The arithmetic mean of , , and is

$\frac{x+y+z}{3}= \frac{198}{3} = 66$

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Example Question #55 : Descriptive Statistics

The arithmetic mean of and is 76. The arithmetic mean of and is 63. The arithmetic mean of and is 84.

Order , , and from least to greatest.

Possible Answers:

y, z, x

z, x, y

x, y, z

x, z, y

z, y, x

Correct answer:

x, z, y

Explanation:

The arithmetic mean of and is 76, so

$\frac{x+ y}{2}= 76$

Similarly,

$\frac{x+ z}{2}= 63$

Subtract:

$\frac{x+ y}{2}- \frac{x+ z}{2}= 76-63$

$\frac{ y-z}{2}}= 13$

$\frac{ y-z}{2}}\cdot 2= 13 \cdot 2$

y-z = 26

y = z + 26 ,

so y > z

By similar reasoning:

$\frac{x+ y}{2}= 76$

$\frac{y+ z}{2}= 84$

$\frac{y+ z}{2}- \frac{x+ y}{2}= 84 - 76$

$\frac{ z-x}{2}}= 8$

$\frac{ z-x}{2}}\cdot 2 = 8 \cdot 2$

z-x = 16

z= x+16

so z > x

Therefore, x< z< y .

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2051 : Problem Solving Questions

Example Question #31 : Calculating Arithmetic Mean

Example Question #42 : Descriptive Statistics

Example Question #45 : Descriptive Statistics

Example Question #2051 : Problem Solving Questions

Example Question #2052 : Problem Solving Questions

Example Question #2053 : Problem Solving Questions

Example Question #2052 : Problem Solving Questions

Example Question #2061 : Problem Solving Questions

Example Question #55 : Descriptive Statistics

All GMAT Math Resources

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