DSQ: Understanding functions - GMAT Quantitative
Card 1 of 512
True or false: 
. 
is an arithmetic sequence.
Statement 1: 
Statement 2: 
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
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Define 
True or false: 
.
Statement 1: 
is a positive number
Statement 2: 
is a negative number
Define
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements. Then 
and 
. But this does not answer the question. For example,
If 
, then
making 
true.
But if 
, then
making 
false.
Assume both statements. Then
If
making
But if
making
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A relation comprises ten ordered pairs. Is it a function?
Statement 1: The domain of the relation is 
.
Statement 2: The range of the relation is 
.
A relation comprises ten ordered pairs. Is it a function?
Statement 1: The domain of the relation is
Statement 2: The range of the relation is
Tap to reveal answer
The relation comprises ten ordered pairs. If Statement 1 alone is known, then the domain comprises ten elements, each of which must appear in exactly one ordered pair. Therefore, no domain element is matched with more than one range element, and the relation is a function.
If Statement 2 alone is known, then the range comprises ten elements, each of which must appear in exactly one ordered pair. But nothing is known about the domain. If no domain element is repeated among the ordered pairs, the relation is a function; otherwise, the relation is not a function.
The relation comprises ten ordered pairs. If Statement 1 alone is known, then the domain comprises ten elements, each of which must appear in exactly one ordered pair. Therefore, no domain element is matched with more than one range element, and the relation is a function.
If Statement 2 alone is known, then the range comprises ten elements, each of which must appear in exactly one ordered pair. But nothing is known about the domain. If no domain element is repeated among the ordered pairs, the relation is a function; otherwise, the relation is not a function.
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True or false: 
, 
is an arithmetic sequence.
Statement 1: 
Statement 2: 
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
,
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
← Didn't Know|Knew It →
True or false: . is an arithmetic sequence.
Statement 1:
Statement 2:
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
← Didn't Know|Knew It →
Define
True or false: .
Statement 1: is a positive number
Statement 2: is a negative number
Define
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements. Then and . But this does not answer the question. For example,
If , then
making true.
But if , then
making false.
Assume both statements. Then
If
making
But if
making
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Define 
Is 
greater than, less than, or equal to 
?
Statement 1: is a positive number.
Statement 2: is a negative number.
Define
Is
Statement 1:
Statement 2:
Tap to reveal answer
One must have information about both 
and 
to answer the question, so neither statement is sufficient by itself.
Now assume both statements to be true. Then, being positive and being negative, 
.
One must have information about both
Now assume both statements to be true. Then,
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A relation comprises ten ordered pairs. Is it a function?
Statement 1: Its domain is 
.
Statement 2: The line 
passes through its graph twice.
A relation comprises ten ordered pairs. Is it a function?
Statement 1: Its domain is
Statement 2: The line
Tap to reveal answer
If Statement 1 alone is assumed, then, since there are only six domain elements and ten points in the relation, at least one of the domain elements must match with more than one range element. This forces the relation to not be a function.
If Statement 2 alone is assumed, then, since 
is a vertical line that passes through the graph twice, the relation fails the vertical line test and is therefore not a function.
If Statement 1 alone is assumed, then, since there are only six domain elements and ten points in the relation, at least one of the domain elements must match with more than one range element. This forces the relation to not be a function.
If Statement 2 alone is assumed, then, since
← Didn't Know|Knew It →
Define
Is greater than, less than, or equal to ?
Statement 1: is a positive number.
Statement 2: is a negative number.
Define
Is
Statement 1:
Statement 2:
Tap to reveal answer
One must have information about both and to answer the question, so neither statement is sufficient by itself.
Now assume both statements to be true. Then, being positive and being negative, .
One must have information about both
Now assume both statements to be true. Then,
← Didn't Know|Knew It →
True or false: , is an arithmetic sequence.
Statement 1:
Statement 2:
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
,
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
← Didn't Know|Knew It →
True or false: . is an arithmetic sequence.
Statement 1:
Statement 2:
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
← Didn't Know|Knew It →
Define
True or false: .
Statement 1: is a positive number
Statement 2: is a negative number
Define
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
Assume both statements. Then and . But this does not answer the question. For example,
If , then
making true.
But if , then
making false.
Assume both statements. Then
If
making
But if
making
← Didn't Know|Knew It →
Define
Is greater than, less than, or equal to ?
Statement 1: is a positive number.
Statement 2: is a negative number.
Define
Is
Statement 1:
Statement 2:
Tap to reveal answer
One must have information about both and to answer the question, so neither statement is sufficient by itself.
Now assume both statements to be true. Then, being positive and being negative, .
One must have information about both
Now assume both statements to be true. Then,
← Didn't Know|Knew It →
A relation comprises ten ordered pairs. Is it a function?
Statement 1: Its domain is .
Statement 2: The line passes through its graph twice.
A relation comprises ten ordered pairs. Is it a function?
Statement 1: Its domain is
Statement 2: The line
Tap to reveal answer
If Statement 1 alone is assumed, then, since there are only six domain elements and ten points in the relation, at least one of the domain elements must match with more than one range element. This forces the relation to not be a function.
If Statement 2 alone is assumed, then, since is a vertical line that passes through the graph twice, the relation fails the vertical line test and is therefore not a function.
If Statement 1 alone is assumed, then, since there are only six domain elements and ten points in the relation, at least one of the domain elements must match with more than one range element. This forces the relation to not be a function.
If Statement 2 alone is assumed, then, since
← Didn't Know|Knew It →
Define
Is greater than, less than, or equal to ?
Statement 1: is a positive number.
Statement 2: is a negative number.
Define
Is
Statement 1:
Statement 2:
Tap to reveal answer
One must have information about both and to answer the question, so neither statement is sufficient by itself.
Now assume both statements to be true. Then, being positive and being negative, .
One must have information about both
Now assume both statements to be true. Then,
← Didn't Know|Knew It →
True or false: , is an arithmetic sequence.
Statement 1:
Statement 2:
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
,
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
← Didn't Know|Knew It →
True or false: . is an arithmetic sequence.
Statement 1:
Statement 2:
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
The two statements together demonstrate that two such differences are equal to each other, and that two other such differences are equal to each other. No information, however, is given about any other differences, of which there are infinitely many. Therefore, the question of whether the sequence is arithmetic or not is unresolved.
← Didn't Know|Knew It →
Define
Is greater than, less than, or equal to ?
Statement 1: is a positive number.
Statement 2: is a negative number.
Define
Is
Statement 1:
Statement 2:
Tap to reveal answer
One must have information about both and to answer the question, so neither statement is sufficient by itself.
Now assume both statements to be true. Then, being positive and being negative, .
One must have information about both
Now assume both statements to be true. Then,
← Didn't Know|Knew It →
True or false: , is an arithmetic sequence.
Statement 1:
Statement 2:
True or false:
Statement 1:
Statement 2:
Tap to reveal answer
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
,
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
An arithmetic sequence is one in which the difference of each term in the sequence and the one preceding is constant.
Assume Statement 1 alone.
meaning that at least two such differences are unequal, and proving the sequence is not arithmetic.
Statement 2 alone only proves that two such differences are equal, but says nothing about any of the other (infinitely many) such differences. Therefore, it leaves the question unresolved.
← Didn't Know|Knew It →
A relation comprises ten ordered pairs. Is it a function?
Statement 1: Its domain is .
Statement 2: The line passes through its graph twice.
A relation comprises ten ordered pairs. Is it a function?
Statement 1: Its domain is
Statement 2: The line
Tap to reveal answer
If Statement 1 alone is assumed, then, since there are only six domain elements and ten points in the relation, at least one of the domain elements must match with more than one range element. This forces the relation to not be a function.
If Statement 2 alone is assumed, then, since is a vertical line that passes through the graph twice, the relation fails the vertical line test and is therefore not a function.
If Statement 1 alone is assumed, then, since there are only six domain elements and ten points in the relation, at least one of the domain elements must match with more than one range element. This forces the relation to not be a function.
If Statement 2 alone is assumed, then, since
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