Logical Reasoning Discussion

Q. |
On her walk through the park, Hansa 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. |
25 |

✖ B. |
22 |

✖ C. |
18 |

✔ D. |
17 |

**Solution:**

Option(**D**) is correct

Let the number of red but not spotted oak leaves be $x$ and number of red spotted oak leaves be $y$.

From the given conditions, we get the following tabulated table.

But, $6 + x + 22 + y+x+ 5y = 50$

$\Rightarrow 28 + 2x + 6y = 50$

$\Rightarrow x + 3y = 11$

$\because$ Red spotted oak leaves has to be positive and even.

$\Rightarrow y = 2$

$\Rightarrow x = 11- (3 \times 2) = 5$

$\Rightarrow$ Number of Oak leaves,

$= x+ y + 5y = 5 + (6 \times 2) $

$= \textbf{17}$

Hence, **option D** is the right choice.

**Rahul Porwal**

*()
*

She collected '28 + Red; Not Spotted' number of Maple leaves and not only 28 Maple leaves. As it is shown in the solution table.

Thus leaving number of Oak leaves to be less than what you have thought.

It is clear that Hansa collected $28$ leaves of maple, then the remaining $(50-28= 22)$ should be oak leaves.

So, the answer should be $22$.

Where am I wrong?