Median - GMAT Quantitative
Card 1 of 91
What is the mean of this set?
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What is the mean of this set?
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If 
, then 
.
If 
, then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
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What is the mean of this set?
-
-
What is the mean of this set?
Tap to reveal answer
If , then .
If , then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
← Didn't Know|Knew It →
What is the mean of this set?
-
-
What is the mean of this set?
Tap to reveal answer
If , then .
If , then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
← Didn't Know|Knew It →
What is the mean of this set?
-
-
What is the mean of this set?
Tap to reveal answer
If , then .
If , then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
← Didn't Know|Knew It →
What is the mean of this set?
-
-
What is the mean of this set?
Tap to reveal answer
If , then .
If , then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
← Didn't Know|Knew It →
What is the mean of this set?
-
-
What is the mean of this set?
Tap to reveal answer
If , then .
If , then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
← Didn't Know|Knew It →
What is the mean of this set?
-
-
What is the mean of this set?
Tap to reveal answer
If , then .
If , then
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
If
If
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
Tap to reveal answer
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
,
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
Tap to reveal answer
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
,
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
Tap to reveal answer
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
,
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
Tap to reveal answer
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
,
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
Tap to reveal answer
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
,
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
Tap to reveal answer
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
,
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
← Didn't Know|Knew It →
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
A data set comprises eleven elements, the median of which is 60. Two new elements are added to the data set.
Does the median change?
Statement 1: One of the elements added to the set is 50.
Statement 2: One of the elements added to the set is 70.
Tap to reveal answer
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
If we only assume Statement 1, then by examining these two cases, we show that we do not know whether the median changes.
Suppose the original set is
If we only know that one of the elements added is 50, then it is possible that the median does not change - this happens if the other element added is 70:
has median 60.
It is also possible that the median does change - this happens if the other element added is 50.
has median 55.
A similar argument can be used to demonstrate that Statement 2 is insufficient.
However, suppose we know both. 60 is the sixth-highest element of the old data set, and, since one element greater than 60 and one less than 60 are added, 60 is the seventh-highest element of the new thirteen-element set. We therefore know the median did not change.
← Didn't Know|Knew It →