GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #2091 : Problem Solving Questions

Find the median of the following set of numbers:

Possible Answers:

Correct answer:

Explanation:

The median is the middle number when the numbers are sorted from smallest to largest. Since they are already sorted, the answer is .

Example Question #541 : Arithmetic

Find the median of the following data set:

Possible Answers:

Correct answer:

Explanation:

Find the median of the following data set:

 

To find median, we must first arrange our terms in ascending order.

So...

Now, our median will be the term directly in the middle of our data set. In this case, the median is 117.

Example Question #542 : Arithmetic

Give the median of the set .

Possible Answers:

Correct answer:

Explanation:

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

Example Question #85 : Descriptive Statistics

.

Give the median of the set .

Possible Answers:

 and  are both medians.

Correct answer:

Explanation:

The median of an even number of data values is the arithmetic mean of the middle two when the scores are arranged in descending order. Here, the scores are in descending order, and the middle two scores are  and , so the median is their arithmetic mean, or .

Example Question #543 : Arithmetic

Find the median of the following set of numbers:

Possible Answers:

Correct answer:

Explanation:

To find the median, order the numbers from smallest to greatest and then find the one in the middle. Thus, the answer is .

Example Question #92 : Descriptive Statistics

Given five distinct positive integers -  - which of them is the median?

Statement 1: 

Statement 2: 

Possible Answers:

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

Explanation:

The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. 

Assume both statements. The orderings 

,

, and

are all consistent with both statements. But in the first scenario,  is the median; in the other two,  is the median. Therefore, it cannot be determined which is the median.

Example Question #545 : Arithmetic

What do you need to know in order to determine the median of a data set with one hundred elements?

Possible Answers:

The fiftieth-highest element

Both the highest and lowest elements

Both the fiftieth-highest and fiftieth-lowest elements

The fiftieth-lowest element

All one hundred elements

Correct answer:

Both the fiftieth-highest and fiftieth-lowest elements

Explanation:

The median of a dataset with an even number of elements is the arithmetic mean of the two elements that fall in the middle when the elements are arranged in ascending order. Since there are 100 elements and , this means the fiftieth-highest and fiftieth-lowest elements.

Example Question #1 : Mode

Rita keeps track of the number of times she goes to the gym each week for 1260 weeks.  She goes 1 day a week for 119 weeks, 2 days a week for 254 weeks, 3 days a week for 376 weeks, and 4 days a week for 511 weeks.  What is the mode of the number of days she goes to the gym each week?

Possible Answers:

511 weeks

2.5 days/week

4 days/week

119 weeks

1 day/week

Correct answer:

4 days/week

Explanation:

The mode is the number that comes up most frequently in a set.  Rita goes to the gym 4 times a week for 511 weeks.  She clearly goes 4 times per week far more often than she goes 1, 2, or 3 times per week.  Therefore the mode is 4 days/week.  It is NOT 511 weeks.  That is the frequency with which 4 days/week occurs, but not the mode.

Example Question #2 : Calculating Mode

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

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:

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.

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

Example Question #1 : Calculating Mode

Consider the data set . It is known that . How many modes does this data set have, and what are they?

Possible Answers:

The set has two modes, 6 and .

The set has one mode, 6.

The set has three modes, 6, 8, and .

The set has two modes, 6 and 8.

The set has one mode, .

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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