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?
A)12
B)12.25
C)12.5
D)12.75
E)13
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j_shreyans
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Hi j_shreyans,
This question has a lot of little facts to keep track of, but the math behind it isn't too tough.
We're told that there are integer shoe sizes (from 8 to 17) and each increase (from 8 to 9, 9 to 10, 10 to 11, etc.) increases the length of the shoe by 1/4 inch. Next, we're told that the largest shoe (size 17) is 20% longer than the smallest shoe (size 8). We're asked for the size of a SIZE 15 SHOE...
From size 8 to size 17, there are 9 "increases" of 1/4 inch.
9(1/4) = 2.25 inches
This 2.25 inches represents the 20% increase in length from size 8 to size 17, so we can determine the length of a size 8 shoe.
X = length of a size 8 shoe
.2X = 2.25
X = (2.25)(5)
X = 11.25
Size 8 = 11.25 inches
Size 17 = 13.5 inches
From here, we can either "count up" from Size 8 or "count down" from Size 17. Counting down will likely be easier and faster.
Size 17 = 13.5 - 2(1/4) = 13
Size 15 = 13 inches
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This question has a lot of little facts to keep track of, but the math behind it isn't too tough.
We're told that there are integer shoe sizes (from 8 to 17) and each increase (from 8 to 9, 9 to 10, 10 to 11, etc.) increases the length of the shoe by 1/4 inch. Next, we're told that the largest shoe (size 17) is 20% longer than the smallest shoe (size 8). We're asked for the size of a SIZE 15 SHOE...
From size 8 to size 17, there are 9 "increases" of 1/4 inch.
9(1/4) = 2.25 inches
This 2.25 inches represents the 20% increase in length from size 8 to size 17, so we can determine the length of a size 8 shoe.
X = length of a size 8 shoe
.2X = 2.25
X = (2.25)(5)
X = 11.25
Size 8 = 11.25 inches
Size 17 = 13.5 inches
From here, we can either "count up" from Size 8 or "count down" from Size 17. Counting down will likely be easier and faster.
Size 17 = 13.5 - 2(1/4) = 13
Size 15 = 13 inches
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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An alternate approach is to PLUG IN THE ANSWERS, which represent a size 15 shoe.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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Matt@VeritasPrep
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I'd do this way:
Size 8 = n inches
Size 17 = 1.2n inches
Size 8 = n inches
Size 17 = n + 9/4 inches
So 1.2n = n + 9/4, or
1.2n = n + 2.25
120n = 100n + 225
20n = 225
n = 11.25
Hence a size 8 is 11.25 inches, a size 17 is 13.5 inches, and a size 15 is 13 inches.
Size 8 = n inches
Size 17 = 1.2n inches
Size 8 = n inches
Size 17 = n + 9/4 inches
So 1.2n = n + 9/4, or
1.2n = n + 2.25
120n = 100n + 225
20n = 225
n = 11.25
Hence a size 8 is 11.25 inches, a size 17 is 13.5 inches, and a size 15 is 13 inches.
