Question

A mother was asked how many gifts she had in the bag. She replied that there were dolls but six, cars but six, and all books but six. How many gifts had she in all?

• A. 9
• B. 18
• C. 27
• D. 36

Hint:

Translate “all but six” as “the other types together are six”. Set up simple equations to solve.

Answer 1

The Correct Option is C

Let the number of dolls = D, cars = C, books = B
The mother said:
- There were dolls but six ⇒ gifts that are not dolls = 6 ⇒ C + B = 6
- There were cars but six ⇒ gifts that are not cars = 6 ⇒ D + B = 6
- All books but six ⇒ gifts that are not books = 6 ⇒ D + C = 6
Now add the three equations: \[ (C + B) + (D + B) + (D + C) = 6 + 6 + 6 = 18 \\ 2D + 2C + 2B = 18 \Rightarrow D + C + B = 9 \] So each of D, C, B = 9 Total gifts = 9 dolls + 9 cars + 9 books = 27