DSQ: Calculating mode - GMAT Quantitative
Card 1 of 77
Give the median of the data set
,
where 
and 
are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose 
but 
is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of 
, the two middle elements must both be 84, making the median 84.
Now, suppose 
but 
is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if 
, as stated before, the median is 84. But if 
, the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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Give the median of the data set
,
where and are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose but is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of , the two middle elements must both be 84, making the median 84.
Now, suppose but is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if , as stated before, the median is 84. But if , the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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Give the median of the data set
,
where and are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose but is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of , the two middle elements must both be 84, making the median 84.
Now, suppose but is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if , as stated before, the median is 84. But if , the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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Give the median of the data set
,
where and are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose but is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of , the two middle elements must both be 84, making the median 84.
Now, suppose but is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if , as stated before, the median is 84. But if , the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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Give the median of the data set
,
where and are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose but is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of , the two middle elements must both be 84, making the median 84.
Now, suppose but is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if , as stated before, the median is 84. But if , the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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Give the median of the data set
,
where and are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose but is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of , the two middle elements must both be 84, making the median 84.
Now, suppose but is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if , as stated before, the median is 84. But if , the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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Give the median of the data set
,
where and are integers.
-
-
Give the median of the data set
where
Tap to reveal answer
Suppose but is unknown. The above set, with known elements ordered, is
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of , the two middle elements must both be 84, making the median 84.
Now, suppose but is unknown. The above set, with known elements ordered, is
The median cannot be determined with certainty. For example, if , as stated before, the median is 84. But if , the middle elements are 84 and 87, making the median 85.5.
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
Suppose
The median is the arithmetic mean of the two middle elements, when the elements are ordered.
Regardless of the value of
Now, suppose
The median cannot be determined with certainty. For example, if
The answer is that Statement 1 alone is sufficent to answer the question, but Statement 2 alone is not.
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What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
Tap to reveal answer
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
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What is the value of 
in the list above?
(1) 
(2) The mode of the numbers in the list is 
.
What is the value of
(1)
(2) The mode of the numbers in the list is
Tap to reveal answer
The mode is the value that appears most often in a set of data. In our list the value that appears most often is n. Therefore n is the mode of the numbers in the list.
Only statement (2) is useful in finding the value of n as it states that the mode of the numbers in the list is 16.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is n. Therefore n is the mode of the numbers in the list.
Only statement (2) is useful in finding the value of n as it states that the mode of the numbers in the list is 16.
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What is the value of 
in the list of numbers above?
(1) 
.
(2) The mode of the numbers in the list is 
.
What is the value of
(1)
(2) The mode of the numbers in the list is
Tap to reveal answer
The mode is the value that appears most often in a set of numbers. In the list given, the value that appears the most is m. Therefore, m is the mode in the list of numbers given.
(1) 
Therefore, 
.
Statement (1) is sufficient
(2) The mode of the numbers in the list is 6.
Therefore, 
.
Statement (2) is sufficient
Each Statement ALONE is SUFFICIENT
The mode is the value that appears most often in a set of numbers. In the list given, the value that appears the most is m. Therefore, m is the mode in the list of numbers given.
(1)
Therefore,
Statement (1) is sufficient
(2) The mode of the numbers in the list is 6.
Therefore,
Statement (2) is sufficient
Each Statement ALONE is SUFFICIENT
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What is the value of 
in the list of numbers above?
(1) The mode of the numbers in the list is 
.
(2) 
.
What is the value of
(1) The mode of the numbers in the list is
(2)
Tap to reveal answer
The mode is the value that appears most often in a set of data. In our list the value that appears most often is m+1. Therefore m+1 is the mode of the numbers in the list.
Only statement (1) is useful in finding the value of m as it states that the mode of the numbers in the list is 14.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is m+1. Therefore m+1 is the mode of the numbers in the list.
Only statement (1) is useful in finding the value of m as it states that the mode of the numbers in the list is 14.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
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What is the sum of 
and 
?
(1) The mode of the numbers in the list is 
.
(2) The product of 
and 
is 
.
What is the sum of
(1) The mode of the numbers in the list is
(2) The product of
Tap to reveal answer
The mode is the value that appears most often in a set of data. In our list the value that appears most often is 2y. Therefore 2y is the mode of the numbers in the list.
(1) The mode of the numbers in the list is 20.
We still don't know the value of x. Statement (1) ALONE is not sufficient.
(2) The product of x and y is 150.
Statement (2) ALONE is not sufficient.
Using both statements, we can write
Therefore, 
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is 2y. Therefore 2y is the mode of the numbers in the list.
(1) The mode of the numbers in the list is 20.
We still don't know the value of x. Statement (1) ALONE is not sufficient.
(2) The product of x and y is 150.
Statement (2) ALONE is not sufficient.
Using both statements, we can write
Therefore,
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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Find the mode of the following set of numbers:
Find the mode of the following set of numbers:
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The mode is the number that occurs most frequently. Therefore, our answer is 
.
The mode is the number that occurs most frequently. Therefore, our answer is
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What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
Tap to reveal answer
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
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What is the value of in the list above?
(1)
(2) The mode of the numbers in the list is .
What is the value of
(1)
(2) The mode of the numbers in the list is
Tap to reveal answer
The mode is the value that appears most often in a set of data. In our list the value that appears most often is n. Therefore n is the mode of the numbers in the list.
Only statement (2) is useful in finding the value of n as it states that the mode of the numbers in the list is 16.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is n. Therefore n is the mode of the numbers in the list.
Only statement (2) is useful in finding the value of n as it states that the mode of the numbers in the list is 16.
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What is the value of in the list of numbers above?
(1) .
(2) The mode of the numbers in the list is .
What is the value of
(1)
(2) The mode of the numbers in the list is
Tap to reveal answer
The mode is the value that appears most often in a set of numbers. In the list given, the value that appears the most is m. Therefore, m is the mode in the list of numbers given.
(1)
Therefore, .
Statement (1) is sufficient
(2) The mode of the numbers in the list is 6.
Therefore, .
Statement (2) is sufficient
Each Statement ALONE is SUFFICIENT
The mode is the value that appears most often in a set of numbers. In the list given, the value that appears the most is m. Therefore, m is the mode in the list of numbers given.
(1)
Therefore,
Statement (1) is sufficient
(2) The mode of the numbers in the list is 6.
Therefore,
Statement (2) is sufficient
Each Statement ALONE is SUFFICIENT
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What is the value of in the list of numbers above?
(1) The mode of the numbers in the list is .
(2) .
What is the value of
(1) The mode of the numbers in the list is
(2)
Tap to reveal answer
The mode is the value that appears most often in a set of data. In our list the value that appears most often is m+1. Therefore m+1 is the mode of the numbers in the list.
Only statement (1) is useful in finding the value of m as it states that the mode of the numbers in the list is 14.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is m+1. Therefore m+1 is the mode of the numbers in the list.
Only statement (1) is useful in finding the value of m as it states that the mode of the numbers in the list is 14.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
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What is the sum of and ?
(1) The mode of the numbers in the list is .
(2) The product of and is .
What is the sum of
(1) The mode of the numbers in the list is
(2) The product of
Tap to reveal answer
The mode is the value that appears most often in a set of data. In our list the value that appears most often is 2y. Therefore 2y is the mode of the numbers in the list.
(1) The mode of the numbers in the list is 20.
We still don't know the value of x. Statement (1) ALONE is not sufficient.
(2) The product of x and y is 150.
Statement (2) ALONE is not sufficient.
Using both statements, we can write
Therefore,
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is 2y. Therefore 2y is the mode of the numbers in the list.
(1) The mode of the numbers in the list is 20.
We still don't know the value of x. Statement (1) ALONE is not sufficient.
(2) The product of x and y is 150.
Statement (2) ALONE is not sufficient.
Using both statements, we can write
Therefore,
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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Find the mode of the following set of numbers:
Find the mode of the following set of numbers:
Tap to reveal answer
The mode is the number that occurs most frequently. Therefore, our answer is .
The mode is the number that occurs most frequently. Therefore, our answer is
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What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
What is the mode of a data set with ten data values?
-
The value 15 occurs four times in the data set.
-
The value 16 occurs three times in the data set.
Tap to reveal answer
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
If we are given only that 15 occurs four times in the data set, it is possible that another number can occur up to six times; similarly, if we are given only that 16 occurs three times, it is possible that another number can occur up to seven times. Either way, the mode - the most frequently occurring data value - cannot be determined.
However, if we know both facts, then no other data value can occur more than three times, so 15 must be the mode.
Therefore, the answer is that both statements are sufficient, but not one alone.
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