In a survey of 500 civil service aspirants preparing for State PSC examinations regarding … — State PSC Exam

In a survey of $500$ civil service aspirants preparing for State PSC examinations regarding their daily newspaper reading habits:
- $260$ aspirants read Newspaper A
- $220$ aspirants read Newspaper B
- $180$ aspirants read Newspaper C
- $90$ aspirants read both Newspaper A and Newspaper B
- $70$ aspirants read both Newspaper B and Newspaper C
- $80$ aspirants read both Newspaper A and Newspaper C
- $30$ aspirants read all three newspapers

How many aspirants read exactly one of these three newspapers?

A
$180$
B
$240$
$270$ Cevap
D
$420$

Cevap

The number of aspirants who read exactly one newspaper is

270

The correct answer is derived by determining the number of readers exclusive to each single newspaper set. Subtracting all overlapping regions (both the exclusive two-paper readers and three-paper readers) from each newspaper's total gives

120

for Newspaper A only,

90

for Newspaper B only, and

60

for Newspaper C only. Adding these exclusive values yields

270

Adım Adım Çözüm

Calculate the number of aspirants who read ONLY Newspaper A, ONLY Newspaper B, and ONLY Newspaper C by isolating two-set and three-set intersections.

Disjoint 2-set intersection counts (excluding all 3 newspapers):
- Reading A and B only:

90 - 30 = 60

- Reading B and C only:

70 - 30 = 40

- Reading A and C only:

80 - 30 = 50

The given two-newspaper intersection counts include the

30

aspirants who read all three newspapers.

Subtract the exclusive two-set and three-set intersection counts from each total newspaper count to find single-newspaper readers.

- Only Newspaper A:

260 - (60 + 50 + 30) = 120

- Only Newspaper B:

220 - (60 + 40 + 30) = 90

- Only Newspaper C:

180 - (50 + 40 + 30) = 60

To find readers of 'only' one paper, all overlaps must be subtracted from the total set count.

Sum the exclusive counts for Newspaper A, Newspaper B, and Newspaper C.

Total reading exactly one newspaper =

120 + 90 + 60 = 270

These three categories are mutually exclusive, so their sum gives the total count for 'exactly one'.

Anahtar Kavram

Principle of Inclusion-Exclusion for Three Sets

Soru

Cevap

Adım Adım Çözüm

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