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 answer is 50cm.

Step-by-Step Explanation:

1. Understand the given data:

There are six pairs of shoes arranged in a shoe rack according to their length from left to right (or ordered from shortest to longest / longest to shortest). Let's arrange them from longest to shortest (Rank 1 being the longest and Rank 6 being the shortest):

• Total shoes = 6 (A, K, L, S, B, Z)

• "Shoe A is shorter than only Shoe K and Shoe L" - This means only two shoes (K and L) are longer than Shoe A. Therefore, Shoe A must be the 3rd longest shoe.

• "Shoe S is longer than Shoe B and shorter than Shoe Z" - This gives the relative order: Z > S > B.

• Since Shoe A is 3rd longest, the remaining three shoes (Z, S, B) must occupy the 4th, 5th, and 6th positions respectively: Z (4th) > S (5th) > B (6th).

2. Summary of the arrangement from longest to shortest:

(L / K) > (K / L) > A > Z > S > B

3. Given lengths of specific shoes:

• Length of Shoe L = 55 cm

• Length of Shoe K = 52 cm

• Length of Shoe Z = 46 cm

4. Determine the possible length of Shoe A:

From our arrangement, Shoe A lies between Shoe K and Shoe Z in length.

Therefore, the length of Shoe A must be strictly greater than the length of Shoe Z (46 cm) and strictly less than the length of Shoe K (52 cm):

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

5. Check the options:

• 44cm (Less than 46cm - Incorrect)

• 40cm (Less than 46cm - Incorrect)

• 50cm (Between 46cm and 52cm - Correct)

• 59cm (Greater than 52cm - Incorrect)

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