GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #547 : Arithmetic

For which of the following values of would the median and the mode of the data set be equal?

$\left \{ 13, 11, 19, 17, 13, 15, 13, 17, N \right \}$

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

If the known values are ordered from least to greatest, the set looks like this:

$\left \{11, 13, 13, 13, 15, 17, 17, 19 \right \}$

Below are each of the choices, followed by the set that results if it is added to the above set, followed by the median - the middle element - and the mode - the most frequently occurring element.

$11: \left \{11, 11, 13, 13, 13, 15, 17, 17, 19 \right \}; median \; 13, mode\; 13$

$15: \left \{11, 13, 13, 13, 15, 15, 17, 17, 19 \right \}; median \; 15, mode\; 13$

$17: \left \{11, 13, 13, 13, 15, 17, 17, 17, 19 \right \}; median \; 15, modes\; 13, 17\; (bimodal)$

$19: \left \{11, 13, 13, 13, 15, 17, 17, 19, 19 \right \}; median \; 15, mode\; 13$

Only the addition of 11 yields a set with median and mode equal to each other.

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Example Question #1 : Calculating Mode

Consider the data set $\left \{ 2, 4,5, 6, 6, 6, 7, 8, 8, 10, N, N\right \}$ . It is known that N > 10 . How many modes does this data set have, and what are they?

Possible Answers:

The set has two modes, 6 and .

The set has two modes, 6 and 8.

The set has one mode, .

The set has one mode, 6.

The set has three modes, 6, 8, and .

Correct answer:

The set has one mode, 6.

Explanation:

Of the known elements, 6 occurs the most frequently - three times. Since the unknown occurs only twice, and it cannot be equal to any of the other elements, its value does not affect the status of 6 as the most frequent element. Therefore, regardless of , 6 is the only mode.

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Example Question #1 : Calculating Mode

What is the mode for the following set:

{1,2,8,9,7,4,1,1,3,2,3}

Possible Answers:

Correct answer:

Explanation:

The mode is the number that appears most frequently:

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Example Question #94 : Descriptive Statistics

Determine the mode of the following set of data:

(9, 6, 7, 9, 7, 5, 10, 7, 6, 8, 4, 5, 13)

Possible Answers:

Correct answer:

Explanation:

The mode of a set of data is the entry that appears most often within the set. One easy way to determine the mode is by arranging the set in increasing order:

(9, 6, 7, 9, 7, 5, 10, 7, 6, 8, 4, 5, 13) $\rightarrow$ (4, 5, 5, 6, 6, 7, 7, 7, 8, 9, 9, 10, 13)

Now that the set is arranged in increasing order, we can see how often each value appears in the set. The value 7 appears three times, which is more than any other entry is repeated, so this is the mode of the set.

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Example Question #4 : Calculating Mode

Determine the mode of the following set of data:

$\begin{Bmatrix} 31, 29, 27, 30, 29, 31, 32, 28, 29 \end{Bmatrix}$

Possible Answers:

Correct answer:

Explanation:

The mode of a set of data is the entry that occurs most often within the set. An easy way to determine which entry occurs the most often is by arranging the set in increasing order:

$\begin{Bmatrix} 31, 29, 27, 30, 29, 31, 32, 28, 29 \end{Bmatrix}\rightarrow \begin{Bmatrix} 27, 28, 29, 29, 29, 30, 31, 31, 32\end{Bmatrix}$

Now we can see that 29 is repeated more often than any other number in the set, so this is the mode.

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Example Question #95 : Descriptive Statistics

Determine the mode of the following set of data:

(12, 6, 7, 12, 6, 1, 3, 6, 7, 17, 6)

Possible Answers:

Correct answer:

Explanation:

The mode of a set of data is the entry that appears most frequently within the set. An easy way to determine the mode is by arranging the set in increasing order:

$(12, 6, 7, 12, 6, 1, 3, 6, 7, 17, 6) \rightarrow (1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17)$

Now we can see that the value of is repeated more times than any other value, so this is the mode of the set of data.

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Example Question #2 : Calculating Mode

Determine the mode for the following set of numbers.

{6,2,5,5,8,4}

Possible Answers:

$\textup{All of the numerical answers provided are correct.}$

$\textup{None of the other answers is correct.}$

Correct answer:

Explanation:

The mode is the most frequent number, thus our answer is .

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Example Question #3 : Calculating Mode

Find the mode of the following set of numbers:

$\textup{4,6,7,7,8,10,28}$

Possible Answers:

Correct answer:

Explanation:

The mode is the most frequent number, thus the answer is .

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Example Question #10 : Calculating Mode

A = B > C > D > E

Give the mode of the set $\left \{ A, B, C, D, E \right \}$ .

Possible Answers:

$\frac{A + E }{2}$

$\frac{A +B+ C+D+E }{5}$

The set has no mode.

Correct answer:

Explanation:

The mode of a set, if it exists, is the value that occurs most frequently. The inequality

A = B > C > D > E

means that the set

$\left \{ A, B, C, D, E \right \}$

can be rewritten as

$\left \{ A,A, C, D, E \right \}$ .

The most frequently occurring value is , making this the mode.

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Example Question #11 : Calculating Mode

Find the mode of the following set of numbers.

$\textup{1,1,2,7,8,10,11}$

Possible Answers:

Correct answer:

Explanation:

The mode is the most frequent number. Thus, our answer is .

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #547 : Arithmetic

Example Question #1 : Calculating Mode

Example Question #1 : Calculating Mode

Example Question #94 : Descriptive Statistics

Example Question #4 : Calculating Mode

Example Question #95 : Descriptive Statistics

Example Question #2 : Calculating Mode

Example Question #3 : Calculating Mode

Example Question #10 : Calculating Mode

Example Question #11 : Calculating Mode

All GMAT Math Resources

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