Question

A group of 62 students were surveyed, and it was found that each of the students surveyed liked at least one of the following three fruits: apricots, bananas, and cantaloupes. 34 liked apricots. 30 liked bananas. 33 liked cantaloupes. 11 liked apricots and bananas. 15 liked bananas and cantaloupes. 17 liked apricots and cantaloupes. 19 liked exactly two of the following fruits: apricots, bananas, and cantaloupes a. How many students liked apricots, but not bananas or cantaloupes? b. How many students liked cantaloupes, but not bananas or apricots? c. How many students liked all of the following three fruits: apricots, bananas, and cantaloupes? d. How many students liked apricots and cantaloupes, but not bananas?

Answer 1

The number of students in a group were surveyed =62 students.

The three fruits served to students =Apricots, Banana's, Cantaloupes.

The number of Students liked Apricots =34 students.

The number of students liked Bananas=30 students.

The number of students liked Cantaloupes =33 students.

Number of students liked Apricots and Bananas=11 students.

Number of students liked Bananas and Cantaloupes =15 students.

Number of students liked Apricots and Cantaloupes =17 students.

Exactly number of students liked Apricots,Bananas and Cantaloupes =19 students.

a) Number of students liked Apricots, but not bananas and cantaloupes =30 students.

b) The number of students liked cantaloupes, but not apricots and bananas=33 students.

c) The number of students liked all of the three fruits = 19 students.

d) The number of students liked Apricots and Cantaloupes, but not Banana's =17 students.

If it's wrong please forgive me.

Answer 2

Note: there is some mistake in the question statement as instead of " 19 liked exactly two of the following fruits: apricots, bananas, and cantaloupes" its should be  "19 liked apricots, bananas, and cantaloupes."  

Given:

Total number of students in a group$=62$  

The number of Students that liked Apricots $=34$  

The number of students that liked Bananas$=30$  

The number of students that liked Cantaloupes $=33$  

Number of students that liked both Apricots and Bananas$=11$  

Number of students that liked both Bananas and Cantaloupes $=15$  

Number of students that liked both Apricots and Cantaloupes $=17$  

Number of students that liked Apricots, Bananas, and Cantaloupes$=19$

Solution:

Draw the required Venn diagram.

Part- a)

Observe the given Venn diagram,

Number of students that liked Apricots, but not bananas and cantaloupes$=30$

Part- b)

Observe the given Venn diagram,

The number of students liked cantaloupes, but not apricots and bananas$=33$

Part- c)

Observe the given Venn diagram,

The number of students liked all of the three fruits $= 19$

Part- d)

Observe the given Venn diagram,

The number of students liked Apricots and Cantaloupes, but not Banana's $=17$