Question: A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 20% longer than the smallest size, how long, in inches, is the shoe in size 15?

1. 12
2. 12.25
3. 12.5
4. 12.75
5. 13

Correct Answer: (E)

Solution and Explanation:
Approach Solution 1:

The problem statement informs that:

Given:

• A manufacturer produces an athletic shoe in integer sizes from 8 to 17.
• Each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe.
• The largest size of this shoe is 20% longer than the smallest size

Find Out:

• The length of the shoe size 15 in inches

Let shoe 8 = k inches
Then shoe 9 = k + 0.25 inches

Therefore we need to find the length of shoe 17
17 = k + 9 * 0.25 = K + 2.25
k + 2.25 = 1.2k
k = 2.25/0.2 = 11.25

Therefore, the size of 15 = k + 7 * 0.25 = 11.25 + 1.75 = 13 inches

Approach Solution 2:

The problem statement states that:

Given:

• A manufacturer produces an athletic shoe in integer sizes from 8 to 17.
• Each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe.
• The largest size of this shoe is 20% longer than the smallest size

Find Out:

• The length of the shoe size 15 in inches

Let’s assume the length of the smallest shoe size(8) is x.
Therefore, the length of shoe size 17 is 1.2x.

As per the conditions of the question, we can say,
x+9*(1/4) =1.2x

Thus, 0.2x = 9/4.

By multiplying 6 on both sides,

1.2x = 9*6/4.
Therefore, the length of shoe size 15 is=1.2x-2*(1/4) = 9*6/4 - 1/2 = 26/2 = 13.

Approach Solution 3:

The problem statement says that:

Given:

• A manufacturer produces an athletic shoe in integer sizes from 8 to 17.
• Each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe.
• The largest size of this shoe is 20% longer than the smallest size

Find Out:

• The length of the shoe size 15 in inches

This question can be solved in a quicker and smarter way such as follows:
As per the condition given in the question, we can write:
8-----9-----10-----11-----12-----13-----14-------15-------16--------17
x----------------------------x+1-------------------x+1.75----x+2------x+2.25

Shoe 17 is 20% greater than 8
Therefore, x+2.25 = x+(20/100)x
=>100x + 225 = 120x
=> x=11.25

Therefore, x+1.75 = 13

Hence, the length of shoe size 15 is 13 inches.

“A manufacturer produces a certain men's athletic shoe in''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions measure the scope and skills of the candidates in order to solve mathematical problems. GMAT Quant practice papers represent several questions that will help to improve the mathematical knowledge of the candidates.

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