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?
12
12.25
12.5
12.75
13
Shoe size
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- sahilchaudhary
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Good question josh80.
Let the length of size 8 shoe = x.
So, the length of size 17 shoe = x + 20% of x = x + x/5. (1)
Since, it is given that each unit increase in size corresponds to a 1/4 inch increase in size.
So, the length of size 9 shoe = x + 1/4.
Similarly, the length of size 10 shoe = x + 2/4.
Similarly, the length of size 15 shoe = x + 7/4.
Similarly, the length of size 17 shoe = x + 9/4. (2)
Equating (1) and (2), since they both represent length of size 17 shoe.
x + x/5 = x + 9/4
x = 45/4.
So, the length of size 15 shoe = x + 7/4 = 45/4 + 7/4 = 52/4 = 13.
The correct answer is E.
Let the length of size 8 shoe = x.
So, the length of size 17 shoe = x + 20% of x = x + x/5. (1)
Since, it is given that each unit increase in size corresponds to a 1/4 inch increase in size.
So, the length of size 9 shoe = x + 1/4.
Similarly, the length of size 10 shoe = x + 2/4.
Similarly, the length of size 15 shoe = x + 7/4.
Similarly, the length of size 17 shoe = x + 9/4. (2)
Equating (1) and (2), since they both represent length of size 17 shoe.
x + x/5 = x + 9/4
x = 45/4.
So, the length of size 15 shoe = x + 7/4 = 45/4 + 7/4 = 52/4 = 13.
The correct answer is E.
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An alternate approach is to PLUG IN THE ANSWERS, which represent a size 15 shoe.josh80 wrote: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?
12
12.25
12.5
12.75
13
Answer choices A and E -- both integer values -- are the easiest to plug in.
Every shoe size is 1/4-inch greater than the next smallest shoe size.
The average test-taker will be more attracted to A than to E, since an increase of 1/4 seems more relevant to a length of 12.
Don't be an average test-taker: start with E.
Since a size 17 shoe is 20% greater than a size 8 shoe, the correct answer choice must yield the following ratio:
(size 17)/(size 8) = 120/100 = 6/5.
Answer choice E: size 15 = 13 inches = 52/4 inches
Size 17 shoe = 52/4 + (2)(1/4) = 54/4.
Size 8 shoe = 52/4 - (7)(1/4) = 45/4.
(size 17)/(size 8) = (54/4) / (45/4) = 54/45 = 6/5.
Success!
The correct answer is E.
Algebraic approach:
Let x = a size 8 shoe.
Each increase in shoe size is equal to 1/4 inch.
Thus, an increase of 9 shoe sizes -- from size 8 to size 17 -- is equal to 9/4 inches.
Since these 9/4 inches represent a 20% increase from a size 8, we get:
9/4 = 0.2x
9/4 = (1/5)x
x = 45/4.
A size 15 shoe -- an increase of 7 sizes from a size 8 shoe -- must be 7/4 inches longer than a size 8 shoe:
45/4 + 7/4 = 52/4 = 13.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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