Question

Vijay buys some eggs. After bringing the eggs home, he finds two to be rotten and throws them away. Of the remaining eggs, he puts five-ninth in his fridge, and brings the rest to his mother, Rashmi's house. She cooks two eggs and puts the rest in her fridge. If her fridge cannot hold more than five eggs, what is the maximum possible number of eggs bought by Vijay?

• A. 11
• B. 17
• C. 16
• D. 23
• E. 20

Hint:

In fraction-based real-world word problems, the intermediate quantities must be integers. Always look for the divisibility constraints (e.g., $(x-2)$ must be a multiple of the denominator 9) to eliminate invalid algebraic bounds.

Answer 1

The Correct Option is A

Step 1: Formulate the algebraic inequality.
Let the initial number of eggs be $x$. Remaining eggs after throwing 2 away = $x - 2$.
He puts $\frac{5}{9}(x - 2)$ in his fridge.
He brings the rest, which is $\frac{4}{9}(x - 2)$, to his mother.

Step 2: Apply the mother's constraint.
Mother cooks 2 eggs. Remaining for her fridge = $\frac{4}{9}(x - 2) - 2$.
Her fridge holds maximum 5 eggs, so: $\frac{4}{9}(x - 2) - 2 \le 5$.
$\frac{4}{9}(x - 2) \le 7 \Rightarrow x - 2 \le \frac{63}{4} = 15.75 \Rightarrow x \le 17.75$.

Step 3: Find the maximum valid integer.
The number of remaining eggs $(x - 2)$ must be exactly divisible by 9 (so that $\frac{5}{9}$ yields a whole number of eggs).
Possible values for $(x - 2)$ that are multiples of 9 and less than 15.75 are 9.
If $x - 2 = 9$, then $x = 11$.