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Sets: Overview & Practice Questions

Hi everyone!

To give you some relief from the constant cribbing of new words in your vocabulary and practicing their usage, let's crack some numbers.

Our focus for today is the topic of "Sets". You won't find as many questions of this topic in the GRE but it's always better to be prepared than getting surprised on the exam day.

This post contains the theory as well as practice questions with answers posted respectively.

So, get cracking!


OVERVIEW

A set is a collection of well-defined objects called elements. The set is represented by the elements surrounded by curly braces ({ }).

For two sets A and B, if the elements of A are present in B, then A is said to be the subset of B.

Sets can be represented in the form of VENN DIAGRAM.

A Venn Diagram for two sets can be drawn as:


 

(A U B) represents the number of elements present in one of the sets A or B.

(A ⋂ B) represents the number of elements present in both the sets A & B.

(A U B) = (A) + (B) – (A ⋂ B)

Similarly, for three sets A, B, and C, the Venn Diagram can be drawn as:

 

(A U B U C) = (A) + (B) + (C) – (A ⋂ B) – (B ⋂ C) – (C ⋂ A) + (A ⋂ B ⋂ C)


PRACTICE PROBLEMS:

(1.) In the set of positive, distinct integers [a,b,c,d,e], the median is 9. What is the minimum value of a+b+c+d+e?

🔘40

🔘51

🔘28

🔘33

🔘35


Answer: 33


(2.) Set A comprises all 3-digit numbers that are multiples of 6. Set B comprises all 3-digit numbers that are multiples of 4 but are not multiples of 8. How many elements does (A ∪ B) comprise?

🔘224

🔘225

🔘263

🔘265

🔘300


Answer : 225


(3.) The product of two integers is 14.

Which of the following could be the average of the two numbers?  

🔘-4.5

🔘-5.5

🔘-6.5

🔘3.5

🔘5.5


Answer: -4.5


(4.) In a class of 25 students, every student takes either Spanish, Latin, or French, or two of the three, but no students take all three languages. 9 take Spanish, 7 take Latin and 5 take exactly two languages.

QUANTITY A

QUANTITY B

The number of students who take French

14

🔘Quantity A is greater

🔘Quantity B is greater

🔘The two quantities are equal

🔘The relationship cannot be determined


Answer: The two quantities are equal


(5.) A baby has x total toys. If 9 of the toys are stuffed animals, 7 of the toys were given to the baby by its grandmother, 5 of the toys are stuffed animals given to the baby by its grandmother, and 6 of the toys are neither stuffed animals nor given to the baby by its grandmother, what is the value of x? (Numeric Entry)


Answer: 17


(6.) An office supply store carries an inventory of 1,345 different products, all of which it categorizes as “business use,” “personal use,” or both. 740 products are categorized as “business use” ONLY and 520 products are categorized as both “business use” and “personal use.”

QUANTITY A

QUANTITY B

The number of products characterized as “personal use”.

600

🔘Quantity A is greater

🔘Quantity B is greater

🔘The two quantities are equal

🔘The relationship cannot be determined


Answer: Quantity A is greater


(7.) At a High School, everyone takes at least one language — Spanish, German, or Russian — but no one takes all three languages. If 120 students take Spanish, 50 take German, 60 take Russian, and 18 take exactly two languages, how many students are there?

🔘220

🔘212

🔘286

🔘264

🔘198 


Answer: 212


(8.) Of 60 birds found in a certain location, 20 are songbirds and 23 are migratory. (It is possible for a songbird to be migratory, or not.)

QUANTITY  A

QUANTITY B

The number of the 60 birds that are neither migratory nor songbirds

16

🔘Quantity A is greater

🔘Quantity B is greater

🔘The two quantities are equal

🔘The relationship cannot be determined


Answer: Quantity A is greater


(9.) In a school of 150 students, 75 take Latin, 110 take Spanish, and 11 take neither.

Quantity A

Quantity B

The number of students who take only Latin

46

🔘Quantity A is greater

🔘Quantity B is greater

🔘The two quantities are equal

🔘The relationship cannot be determined


Answer: Quantity B is greater


(10.) Set A comprises all 3-digit numbers that are multiples of 6. Set B comprises all 3-digit numbers that are multiples of 4 but are not multiples of 8. How many elements does (A ∪ B) comprise?

🔘225

🔘263

🔘265

🔘300

🔘224


Answer: 225


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