Word Problems - GMAT Quantitative
Card 1 of 920
True or false: 
Statement 1: 
is a perfect square.
Statement 2: 
is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; 
includes all multiples of 3. 
comprises all multiples of either 2 or 3.
Knowing 
is a perfect square is neither necessary nor helpful, as, for example, 
, but 
(as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that 
is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means 
Knowing
If you know that
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
Define two sets as follows:
where 
and 
are distinct positive odd integers and 
and 
are distinct positive even integers.
How many elements are contained in the set 
?
-
-
Define two sets as follows:
where
How many elements are contained in the set
Tap to reveal answer
Suppose we know 
, but we do not assume the second statement.
If 
and 
, then 
, a four-element set. If If 
and 
, then 
, a three-element set. Therefore, we cannot make a conclusion about the size of 
. A similar argument can be used to show that assuming only the second statement also does not allow a conclusion.
If we know both statements, however, 
, and we can prove that 
has four elements.
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
Suppose we know
If
If we know both statements, however,
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
← Didn't Know|Knew It →
True or false:
Statement 1: is a perfect square.
Statement 2: is a multiple of 99.
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
includes all multiples of 2; includes all multiples of 3. comprises all multiples of either 2 or 3.
Knowing is a perfect square is neither necessary nor helpful, as, for example, , but (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means
Knowing
If you know that
← Didn't Know|Knew It →
Define two sets as follows:
where and are distinct positive odd integers and and are distinct positive even integers.
How many elements are contained in the set ?
-
-
Define two sets as follows:
where
How many elements are contained in the set
Tap to reveal answer
Suppose we know , but we do not assume the second statement.
If and , then , a four-element set. If If and , then , a three-element set. Therefore, we cannot make a conclusion about the size of . A similar argument can be used to show that assuming only the second statement also does not allow a conclusion.
If we know both statements, however, , and we can prove that has four elements.
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
Suppose we know
If
If we know both statements, however,
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
← Didn't Know|Knew It →
How many elements are in the set 
?
Statement 1: 
has three more elements than 
.
Statement 2: 
includes exactly four elements not in 
.
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: 
and 
Case 2: 
and 
In both situations, 
has three more elements than 
and 
includes exactly four elements not in 
(1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, 
, and in the second case, 
.
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
Define two sets as follows:
where and are distinct positive odd integers and and are distinct positive even integers.
How many elements are contained in the set ?
-
-
Define two sets as follows:
where
How many elements are contained in the set
Tap to reveal answer
Suppose we know , but we do not assume the second statement.
If and , then , a four-element set. If If and , then , a three-element set. Therefore, we cannot make a conclusion about the size of . A similar argument can be used to show that assuming only the second statement also does not allow a conclusion.
If we know both statements, however, , and we can prove that has four elements.
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
Suppose we know
If
If we know both statements, however,
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
← Didn't Know|Knew It →
How many elements are in the set ?
Statement 1: has three more elements than .
Statement 2: includes exactly four elements not in .
How many elements are in the set
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements are true.
Consider these two cases:
Case1: and
Case 2: and
In both situations, has three more elements than and includes exactly four elements not in (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, , and in the second case, .
The two statements together do not yield an answer to the question.
Assume both statements are true.
Consider these two cases:
Case1:
Case 2:
In both situations,
The two statements together do not yield an answer to the question.
← Didn't Know|Knew It →
Define two sets as follows:
where and are distinct positive odd integers and and are distinct positive even integers.
How many elements are contained in the set ?
-
-
Define two sets as follows:
where
How many elements are contained in the set
Tap to reveal answer
Suppose we know , but we do not assume the second statement.
If and , then , a four-element set. If If and , then , a three-element set. Therefore, we cannot make a conclusion about the size of . A similar argument can be used to show that assuming only the second statement also does not allow a conclusion.
If we know both statements, however, , and we can prove that has four elements.
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
Suppose we know
If
If we know both statements, however,
The answer is that both statements together are sufficient to answer this question, but neither statement alone is sufficient.
← Didn't Know|Knew It →