Directions (88-90) :Study the following information carefully and answer the questions given below:

Six pairs of shoes are arranged in a shoe rack according to their length from left to right. Shoe A is shorter than only Shoe K and Shoe L. Shoe S is longer than Shoe B and shorter than Shoe Z. The Length of Shoe K is 52cm and the length of Shoe Z is 46cm. The length of shoe L is 55cm.

What will the possible Length of Shoe A?

The correct option is 50cm.

Step-by-step Explanation:

Let us analyze the given information step-by-step to arrange the six pairs of shoes in ascending/descending order according to their length from left to right (or from shortest to longest / longest to shortest):

1. There are 6 shoes in total. Let's arrange them in order from longest (position 1) to shortest (position 6):

2. "Shoe A is shorter than only Shoe K and Shoe L."
This statement means that only two shoes are longer than Shoe A. Therefore, Shoe A must be the 3rd longest shoe.
So, the order from longest to shortest starts with Shoe K/L in the 1st and 2nd positions, followed by Shoe A in the 3rd position.

3. We are given the exact lengths of Shoe L and Shoe K:
• Length of Shoe L = 55 cm
• Length of Shoe K = 52 cm

Since both Shoe L (55 cm) and Shoe K (52 cm) are longer than Shoe A, Shoe A must be shorter than 52 cm.

4. "Shoe S is longer than Shoe B and shorter than Shoe Z."
This gives the relative ordering: Shoe Z > Shoe S > Shoe B.
Since Shoe A is at position 3, these remaining three shoes (Z, S, B) must occupy positions 4, 5, and 6 respectively.

5. We are also given:
• Length of Shoe Z = 46 cm

So, the arrangement of shoes from longest to shortest is:
Position 1: Shoe L (55 cm)
Position 2: Shoe K (52 cm)
Position 3: Shoe A
Position 4: Shoe Z (46 cm)
Position 5: Shoe S
Position 6: Shoe B

6. Finding the possible length of Shoe A:
From our arrangement, Shoe A lies between Shoe K and Shoe Z in length.

$\text{Length of Shoe Z}<\text{Length of Shoe A}<\text{Length of Shoe K}$

Substituting the known values:

$46\text{ cm}<\text{Length of Shoe A}<52\text{ cm}$

Now, let us evaluate the given options to see which value falls strictly between 46 cm and 52 cm:

• 44cm (Less than 46cm - Incorrect)
• 40cm (Less than 46cm - Incorrect)
• 50cm (Between 46cm and 52cm - Correct)
• 59cm (Greater than 52cm - Incorrect)

Therefore, the possible length of Shoe A is 50cm.