GMAT Math : Understanding arithmetic sets

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Understanding Arithmetic Sets

Which set is NOT equal to the other sets?

Possible Answers:

Correct answer:

Explanation:

Order and repetition do NOT change a set.  Therefore, the set we want to describe contains the numbers 1, 3, and 4.  The only set that doesn't contain all 3 of these numbers is , so it is the set that does not equal the rest of the sets.

Example Question #2 : Understanding Arithmetic Sets

Given the sets A = {2, 3, 4, 5} and B = {3, 5, 7}, what is A \bigcup B ?

Possible Answers:

Correct answer:

Explanation:

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

So A \bigcup B = {2, 3, 4, 5, 7}.

Example Question #3 : Understanding Arithmetic Sets

Given the set  = {2, 3, 4, 5}, what is the value of ?

Possible Answers:

cannot be added together

Correct answer:

Explanation:

We need to add 3 to every element in .

Then:

Example Question #4 : Understanding Arithmetic Sets

There exists two sets  and .   = {1, 4} and  = {3, 4, 6}.  What is ?

Possible Answers:

Correct answer:

Explanation:

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}

Example Question #5 : Understanding Arithmetic Sets

How many functions map from  to ?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #6 : Understanding Arithmetic Sets

How many elements are in a set from which exactly 768 unique subsets can be formed?

Possible Answers:

It is not possible to form exactly 768 unique subsets.

Correct answer:

It is not possible to form exactly 768 unique subsets.

Explanation:

The number of subsets that can be formed from a set with  elements is . However,  and , so there is no integer  for which . Therefore, a set with exactly 768 elements cannot exist.

Example Question #7 : Understanding Arithmetic Sets

Let the univeraal set  be the set of all positive integers.

Define the sets

,

,

.

If the elements in  were ordered in ascending order, what would be the fourth element?

Possible Answers:

Correct answer:

Explanation:

 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.

Example Question #8 : Understanding Arithmetic Sets

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be twice that number. What is the sample space of the experiment?

Possible Answers:

Correct answer:

Explanation:

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set .

If tails comes up on the coin, twice the number on the die is recorded. This can be twice any element of the set  - that is, any element of the set .

The sample space is the union of these two sets:

Example Question #9 : Understanding Arithmetic Sets

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be half that number, with any fraction simply thrown out. What is the sample space of the experiment?

Possible Answers:

Correct answer:

Explanation:

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set .

If tails comes up on the coin, half the number on the die is recorded, and any fraction is thrown out. Half the elements of the set  comprise the set  , but since we are throwing out the fractional parts, this becomes the set 

The sample space is the union of these two sets, which is .

Example Question #10 : Understanding Arithmetic Sets

Temperature

Refer to the above graph, which shows the peak temperature in Smithville for each of seven days in a one-week period.

Between which two consecutuve days did the peak temperature see its greatest decrease?

Possible Answers:

Wednesday to Thursday

Thursday to Friday

Tuesday to Wednesday

Friday to Saturday

Monday to Tuesday

Correct answer:

Friday to Saturday

Explanation:

You only need to look for the portion of the line with the greatest negative slope, which is that which represents Friday to Saturday.

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