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. 17
• B. 22
• C. 25
• D. 18

Hint:

Let the number of red spotted oak leaves be a and the number of red unspotted oak leaves be b; express every category in a and b and use the total of 50.

Answer 1

The Correct Option is A

Step 1: Define variables.
Let a = number of red oak leaves with spots (even, positive), and b = number of red oak leaves without spots.

Step 2: Fill every category.
Red oak spotted = a. Red oak unspotted = b. Non-red oak (all spotted) = 5a. Red maple unspotted = b (equal to red oak unspotted). Red maple spotted = 6. Non-red maple leaves are all unspotted: 22.

Step 3: Total of 50.
a + b + 5a + b + 6 + 22 = 50, so 6a + 2b = 22, that is 3a + b = 11.

Step 4: Use the conditions.
a is even and positive: a = 2 gives b = 5; a = 4 gives b = -1, which is impossible. So a = 2 and b = 5.

Step 5: Oak leaves.
Oak = a + b + 5a = 2 + 5 + 10 = 17.

Final Answer:
The correct option is (1): 17