Sets - GMAT Quantitative
Card 1 of 120
Let 
be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does 
have?
Let
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, which is a set of 12 elements. A set this size has 
subsets.
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Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
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Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
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Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number 
were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If 
, then 
would be placed in Region I.
Statement 2: If 
, then 
would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers - 
From Statement 1 alone, 
is a natural number; since 
, it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, 
is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
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Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
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Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
← Didn't Know|Knew It →
Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
← Didn't Know|Knew It →
Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
← Didn't Know|Knew It →
Let be the set of all perfect squares and perfect cubes between 1 and 100 inclusive. How many subsets does have?
Let
Tap to reveal answer
, which is a set of 12 elements. A set this size has subsets.
← Didn't Know|Knew It →
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number were to be placed in its correct region in the diagram, which one would it be - I, II, III, IV, or V?
Statement 1: If , then would be placed in Region I.
Statement 2: If , then would be placed in Region I.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
If real number
Statement 1: If
Statement 2: If
Tap to reveal answer
Region I comprises the natural numbers -
From Statement 1 alone, is a natural number; since , it follows that is the difference of a natural number and 7 - that is,
could be in any of three regions - I, II, or III.
Conversely, from Statement 2 alone, is the sum of a natural number and 7 - that is,
must be a natural number and it must be in Region I.
Region I comprises the natural numbers -
From Statement 1 alone,
Conversely, from Statement 2 alone,
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Given that 
and 
, is it true that positive integer 
?
Statement 1: The last digit of 
is a 0.
Statement 2: The second-to-last digit of 
is 5.
Given that
Statement 1: The last digit of
Statement 2: The second-to-last digit of
Tap to reveal answer
and 
are the sets of positive multiples of 4 and 5, respectively. For a number to be in both sets, the number must be divisible by both 4 and 5. This happens if and only if it is also divisible by 
.
The elements of 
are precisely the mulitples of 20:
All of the numbers end in 0 and have 2, 4, 6, 8,or 0 as their second-to-last digit.
Statement 1 does not, by itself, prove or disprove that 
, since there are numbers like 10 and 30 that do not fall in this set. But none of the elements of 
have 5 as their second-to-last digit, so Statement 2 proves 
to be false.
The elements of
All of the numbers end in 0 and have 2, 4, 6, 8,or 0 as their second-to-last digit.
Statement 1 does not, by itself, prove or disprove that
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Define sets 
as follows:
What is 
?
Statement 1: 
Statement 2: 
comprises ten elements, all of which are positive integers.
Define sets
What is
Statement 1:
Statement 2:
Tap to reveal answer
is the complement of 
- that is, the set of all elements in the universal set 
that are not in 
. To find 
given 
, we need to know the elements in 
. Statement 1 gives us this information; Statement 2 does not.
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Given that and , is it true that positive integer ?
Statement 1: The last digit of is a 0.
Statement 2: The second-to-last digit of is 5.
Given that
Statement 1: The last digit of
Statement 2: The second-to-last digit of
Tap to reveal answer
and are the sets of positive multiples of 4 and 5, respectively. For a number to be in both sets, the number must be divisible by both 4 and 5. This happens if and only if it is also divisible by .
The elements of are precisely the mulitples of 20:
All of the numbers end in 0 and have 2, 4, 6, 8,or 0 as their second-to-last digit.
Statement 1 does not, by itself, prove or disprove that , since there are numbers like 10 and 30 that do not fall in this set. But none of the elements of have 5 as their second-to-last digit, so Statement 2 proves to be false.
The elements of
All of the numbers end in 0 and have 2, 4, 6, 8,or 0 as their second-to-last digit.
Statement 1 does not, by itself, prove or disprove that
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Define sets as follows:
What is ?
Statement 1:
Statement 2: comprises ten elements, all of which are positive integers.
Define sets
What is
Statement 1:
Statement 2:
Tap to reveal answer
is the complement of - that is, the set of all elements in the universal set that are not in . To find given , we need to know the elements in . Statement 1 gives us this information; Statement 2 does not.
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