Question

On her walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following:
The number of red oak leaves with spots is even and positive.
The number of red oak leaves without any spot equals the number of red maple leaves without spots.
All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves.
There are no spotted maple leaves that are not red.
There are exactly 6 red spotted maple leaves.
There are exactly 22 maple leaves that are neither spotted nor red.
How many oak leaves did she collect?

• A. 22
• B. 17
• C. 25
• D. 18

Hint:

Translate conditions into equations and use parity constraints to quickly narrow possibilities.

Answer 1

The Correct Option is A

Let red spotted oak = $x$. Non-red oak (all spotted) = $5x$.
Red unspotted oak = $y$, red unspotted maple = $y$.
Given: red spotted maple = 6, unspotted non-red maple = 22.
Total leaves = $x + 5x + y + y + 6 + 22 = 50$.
$\Rightarrow 6x + 2y + 28 = 50 \Rightarrow 6x + 2y = 22 \Rightarrow 3x + y = 11$.
Test even positive $x$: $x=2, y=5 \Rightarrow$ oaks = $2+5x+ y + y = 2+10+5+5=22$.