Logical Reasoning Discussion

Q. |
At a T-shirt auction, 42 Reds United T-shirts were sold and 30 Blues T-shirts were sold. No one bought more than one T-shirt of the same type and everyone bought at least one. If 60 people participated in the auction, how many bought both T-shirts? |

✖ A. |
10 |

✔ B. |
12 |

✖ C. |
14 |

✖ D. |
16 |

**Solution:**

Option(**B**) is correct

Number of people who bought Reds United T-shirts = *n*(*R*) = 42

Number of people who bought Blues T-shirts = *n*(*B*) = 30

Let the number of people who bought both

T-shirts = *n*(*R *∩ *B*) = *x*

The total number of people participating in the auction = *n*(*R *∪ *B*) = 60

As everyone bought at least one T-shirt,

*n*(*R* ∩ *B*) = *n*(*R*) + *n*(*B*) - *n*(*R* ∪ *B*)

∴ *x* = 42 + 30 – 60

∴ *x* = 12

The number of people who bought both T-shirts = *n*(*R *∩ *B*) = 12

Alternatively, the question can be easily solved by Venn diagram.

$\because$ It is given that everyone bought at least one T-shirt,

From the diagram, we can see that

42 - *x* + *x* + 30 - *x* = 60

∴ *x* = 12