Six pairs of shoes are arranged in a shoe rack from left to right based on their length. Shoe A is shorter than only Shoe K and Shoe L. Shoe S is longer than Shoe B but shorter than Shoe Z. The length of Shoe K is $52 ext{ cm}$, Shoe Z is $46 ext{ cm}$, and Shoe L is $55 ext{ cm}$. What is the possible length of Shoe A?

Question

Six pairs of shoes are arranged in a shoe rack from left to right based on their length. Shoe A is shorter than only Shoe K and Shoe L. Shoe S is longer than Shoe B but shorter than Shoe Z. The length of Shoe K is $52 		ext{ cm}$, Shoe Z is $46 		ext{ cm}$, and Shoe L is $55 		ext{ cm}$. What is the possible length of Shoe A?

Accepted Answer

**Solution:**

1. The given order based on length is: Shoe L > Shoe K > Shoe A > Shoe Z > Shoe S > Shoe B.

2. From the problem, Shoe L is the longest with length $55 	ext{ cm}$, followed by Shoe K with $52 	ext{ cm}$.

3. Shoe A is shorter than only Shoe K and Shoe L, so Shoe A must be shorter than $52 	ext{ cm}$ but longer than Shoe Z.

4. Shoe Z has a length of $46 	ext{ cm}$, so Shoe A's length must be between $46 	ext{ cm}$ and $52 	ext{ cm}$.

5. Among the options, $50 	ext{ cm}$ fits this range.

**Answer:** $50 	ext{ cm}$

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