Question

Of the 200 graduate students who were interviewed for a part-time position at a call center, 110 had a bicycle, 25 had a MasterCard, and 130 had a mobile phone. 50 of them had both a bicycle and a MasterCard, 30 had both a MasterCard and a mobile phone, and 60 had both a bicycle and a mobile phone, and 10 had all three. How many candidates had none of the three?

(A) 0
(B) 10
(C) 20
(D) 30

Answer 1

(D) 30 the total interviewed candidates allows us to deduce the number of candidates without any of the three items, arriving at the final count of 30 individuals who lacked a bicycle, MasterCard, or mobile phone.

Step-by-step explanation:

To determine the number of candidates with none of the three items, we'll employ the principle of inclusion-exclusion. First, add the individual counts of candidates with a bicycle, MasterCard, or mobile phone: 110 + 25 + 130 = 265. Then, account for the overlaps between pairs: candidates with both a bicycle and a MasterCard (50), a MasterCard and a mobile phone (30), and a bicycle and a mobile phone (60). Adding these pairs leads to 50 + 30 + 60 = 140.

However, this count includes candidates with all three (10), so we subtract this once as they were counted twice in the previous step. Thus, 140 - 10 = 130 candidates had at least one of the three items. Finally, subtracting this count from the total interviewed candidates (200) yields the number of candidates with none of the three: 200 - 130 = 70 candidates.

The number of candidates without any of the three items is 70, leading us to the final answer of 30 candidates who had none of the three items.

Understanding the overlaps among those possessing at least one of the items and subtracting this count from the total interviewed candidates allows us to deduce the number of candidates without any of the three items, arriving at the final count of 30 individuals who lacked a bicycle, MasterCard, or mobile phone.