Sets - GMAT Quantitative

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

We are looking for the union of the sets. That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, , the number has to be one greater than a number that is a multiple of five, four, and three. Since , the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.

comprises the set of elements common to all three sets. However, since is the set of all even integers and comprises the set of all odd integers, no element can be common to all three sets. The correct response is 0.

are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, , the number has to be one greater than a number that is a multiple of five, four, and three. Since , the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.

There are three choices for (1, 2, and 3), and similarly there are three choices for (also 1, 2, and 3). Together there are possible functions from to . Remember to multiply, NOT add.

comprises the set of elements common to all three sets. However, since is the set of all even integers and comprises the set of all odd integers, no element can be common to all three sets. The correct response is 0.

comprises the set of elements common to all three sets. However, since is the set of all even integers and comprises the set of all odd integers, no element can be common to all three sets. The correct response is 0.

are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, , the number has to be one greater than a number that is a multiple of five, four, and three. Since , the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.

Add each element of to each element of .

= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

Add each element of to each element of .

= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

Add each element of to each element of .

= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

Add each element of to each element of .

= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

There are three choices for (1, 2, and 3), and similarly there are three choices for (also 1, 2, and 3). Together there are possible functions from to . Remember to multiply, NOT add.

comprises the set of all odd integers except 1; comprises the set of all integers of the form , a natural number. Therefore, any number that is not in the union of these two sets must be in neither one.

, so is even or 1 (although 1 is not a choice). We can eliminate odd choices 147, 149, and 151 immediately.

, so we determine which number cannot be expressed as , a natural number.

148 is elminated, since it is two less than a multiple of 3. 150 is the correct choice.