Question

A survey of 60 customers of an ice-cream parlor found that:

Find the maximum possible number of customers who enjoy chocolate ice cream.

• A. 14
• B. 15
• C. 13
• D. 16

Answer 1

The correct option is C 13

Creating a Venn diagram using the given information, we get:


$C=CustomerswhoenjoybothchocolateandvanillaicecreamV=CustomerswhoenjoyonlyvanillaicecreamM=CustomerswhoenjoyvanillaandstrawberryS=Customerswhoenjoyonlystrawberryicecream$

Now, we know that 16 customers enjoy both vanilla and strawberry ice creams.

Also, no one enjoys both chocolate and strawberry flavors.

$⟹M=16$

More customers prefer single flavors over multiple flavors.

$⟹V+S>C+M⟹(V+S)=(C+M)+k$,

where k is some positive value.

Now, all 60 of the daily customers of the ice-cream parlor were surveyed.

$⟹V+S+C+M=60⟹(C+M+k)+(C+M)=60⟹2C+2M+k=60⟹2C+2\left(16\right)+k=60⟹2C+32+k=60⟹2C+k=28⟹C+\frac{k}{2}=14⟹C<14$

Now, as C denotes the number of people who enjoy chocolate ice cream, it can only be a whole number.

Hence, the maximum value of C will be the closest whole number to 14 that is less than 14.

$⟹MaximumvalueofC=13$

Therefore, the maximum possible number of customers who enjoy chocolate ice cream is 13.