Question

Ajosey buys some avocados. After bringing the avocados home, she finds two to be rotten and throws them away. Of the remaining avocados, she puts five-ninth in her fridge, and brings the rest to her hostel. She eats two avocados and puts the rest in her hostel's mess fridge. If her hostel mess fridge cannot hold more than five avocados, what is the maximum possible number of avocados bought by Ajosey?

• A. 19
• B. 21
• C. 14
• D. 29
• E. 20

Hint:

In such word problems, ensure all quantities are integers and satisfy all constraints. Sometimes the intended interpretation leads to a different algebraic condition.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Let the total number of avocados be $x$.
Step 2: Key Formula or Approach:
1. After removing 2: $x - 2$.
2. Remainder after putting $5/9$ in fridge: $\frac{4}{9}(x - 2)$.
3. Final number in hostel mess fridge: $\frac{4}{9}(x - 2) - 2$.
Condition: $\frac{4}{9}(x - 2) - 2 \leq 5$.
Step 3: Detailed Explanation:
$\frac{4}{9}(x - 2) \leq 7$.
$4(x - 2) \leq 63$.
$x - 2 \leq 15.75$.
$x \leq 17.75$.
Also, since she puts $5/9$ of $(x-2)$ in the fridge, $(x-2)$ must be a multiple of 9.
Possible values for $(x-2)$: $9, 18, 27...$
If $x-2 = 9 \implies x = 11$. This is $\leq 17.75$.
If $x-2 = 18 \implies x = 20$. This is $> 17.75$ (fails the mess fridge constraint).
Step 4: Final Answer:
The maximum possible number bought is 11.