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SAT Math : How to find the intersection of a Venn Diagram

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Example Question #11 : How To Find The Intersection Of A Venn Diagram

What is the intersection of the Venn Diagram shown below?

Screen shot 2015 10 27 at 3.45.31 pm

Possible Answers:

6,20,8,4,16,3,100,14,10,9

15,43,1,19,6,17,12,11,35,7,31,22,21,25

3,5,1,3,9

6,20,8,4,16,3,100,14,10,9,15,43,1,19,6,17,12,11,35,7,31,22,21,25

2,5,6,13,24

Correct answer:

2,5,6,13,24

Explanation:

The intersection of the Venn Diagram is only the numbers in both circles.

The section in the middle contains the answer set.

Thus the intersection is, 2,5,6,13,24 .

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Example Question #21 : Venn Diagrams

Find $A\bigcap B$

A = $\{{1, 4, 5, 22, 55, 154}\}$

B = $\{{0, 2, 4, 5, 12, 23, 56, 133, 154, 201}\}$

Possible Answers:

$\{{200}\}$

$\{{4, 5, 154}\}$

$\{{0, 1, 2, 4, 5, 12, 22, 23, 55, 56, 133, 154, 201}\}$

$\{{0}\}$

$\{{0, 2, 4, 5, 23, 55, 154}\}$

Correct answer:

$\{{4, 5, 154}\}$

Explanation:

$A\bigcap B$ represents the intersection of the two sets A and B. The intersection of A and B is the set of elements that are contained in both A and B.

The elements that appear in A and B are 4, 5, and 154.

Therefore, the intersection of A and B is $\{{4, 5, 154}\}$ .

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Example Question #12 : How To Find The Intersection Of A Venn Diagram

Farmer John has one hundred plots of land. Sixty plots grow corn. Forty plots grow carrots. These numbers take into account that some of the plots grow both corn and carrots.

How many plots grow both corn and carrots?

Possible Answers:

Correct answer:

Explanation:

To find how many plots grow both carrots and corn, we subtract 60-40 = 20 .

That means that fifty plots grow corn only, while thirty plots grow carrots only.

Screen shot 2015 11 17 at 5.07.20 pm

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Example Question #21 : Venn Diagrams

What is the intersection of the sets A and B?

A = $\{{1, 4, 5, 12, 35, 67, 101}\}$

B = $\{{0, 4, 17, 35, 66, 69, 70, 99}\}$

Possible Answers:

$\{{0, 1, 4, 5, 12, 17, 35, 66, 67, 69, 70, 99, 101}\}$

$\{{4, 35, 67}\}$

$\{{4, 35}\}$

$\{{0, 1, 5, 12, 17, 66, 67, 69, 70, 99, 101}\}$

$\{{1}\}$

Correct answer:

$\{{4, 35}\}$

Explanation:

The intersection of 2 sets A and B is the set of the items that are included in both sets. The items that appear in both A and B are 4 and 35.

Therefore, the intersection of A and B is $\{{4, 35}\}$ .

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Example Question #22 : Venn Diagrams

Venn 1

In the above Venn diagram, let the universal set be

$U =\left \{ 1, 2, 3, ...40 \right \}$

$A = \left \{ x | x$ yields a remainder of 1 when divided by 4 $\left \right \}$

$B = \left \{ x | x$ yields a remainder of 1 when divided by 3 $\left \right \}$

How many elements of would be placed in the shaded portion of the above diagram?

Possible Answers:

Six

Seven

Nine

Five

Eight

Correct answer:

Six

Explanation:

The shaded portion of the Venn diagram is $A \cap B'$ - the set of all elements in but not .

The following elements of yield a remainder of 1 when divided by 4, and therefore comprise set :

$A = \left \{ 1, 5, 9, 13, 17, 21, 25, 29, 33, 37 \right \}$

If 3 is subtracted from each, what results are the elements whose division by 4 yields a remainder of 1, and thus, elements of .

The following elements of yield a remainder of 1 when divided by 4, and therefore comprise set :

$B = \left \{ 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40 \right \}$

The elements in that are also elements in are 1, 13, 25, and 37 - four elements out of ten. Therefore, the set $A \cap B'$ comprises six elements.

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SAT Math : How to find the intersection of a Venn Diagram

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : How To Find The Intersection Of A Venn Diagram

Example Question #21 : Venn Diagrams

Example Question #12 : How To Find The Intersection Of A Venn Diagram

Example Question #21 : Venn Diagrams

Example Question #22 : Venn Diagrams

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