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Manager  Joined: 22 Mar 2012
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A manufacturer produces a certain men's athletic shoe in  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 65% (02:52) correct 35% (02:53) wrong based on 431 sessions

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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

What's the fastest way to solve this? Thanks!
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Joined: 16 Oct 2010
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Location: Pune, India
Re: A manufacturer produces a certain men's athletic shoes...  [#permalink]

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10
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KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

From size 8 to size 17, there are 9 increments of .25 each making the size 17 shoe 9*.25 = 2.25 inches more than the size 8 shoe.
This 2.25 accounts for 20% of the length of size 8 shoe so length of size 8 shoe is 2.25*5 = 11.25 inches
Length of size 15 shoe must be 11.25 + .25*7 = 13 inches
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Re: A manufacturer produces a certain men's athletic shoes...  [#permalink]

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5
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KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

8 - k inches
9 - k + 0.25 inches

17 = ?

17 = k + 9 * 0.25 = K + 2.25

k + 2.25 = 1.2k

k = 2.25/0.2 = 11.25

Size of 15 = k + 7 * 0.25

= 11.25 + 1.75 = 13

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Re: A manufacturer produces a certain men's athletic shoes...  [#permalink]

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3
Let the length of the smallest shoe size(8) be x. Thus the length for size 17 is 1.2x. Now, we know that

x+9*(1/4) =1.2x

Thus, 0.2x = 9/4.

Multiply on both sides by 6,

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

E.
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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4
1
8-----9-----10-----11-----12-----13-----14-------15-------16--------17
x----------------------------x+1-------------------x+1.75----x+2------x+2.25

Condition 17 is 20% greater than 8 --------> x+2.25 = x+(20/100)x --------->100x + 225 = 120x --------> x=11.25 --------> x+1.75 = 13 simple enough
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Intern  Joined: 06 May 2014
Posts: 11
Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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subhashghosh wrote:
KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

8 - k inches
9 - k + 0.25 inches

17 = ?

17 = k + 9 * 0.25 = K + 2.25

k + 2.25 = 1.2k

k = 2.25/0.2 = 11.25

Size of 15 = k + 7 * 0.25

= 11.25 + 1.75 = 13

where did you get 1.2k ?
CEO  S
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Schools: Kellogg '18 (M)
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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anik1989 wrote:
subhashghosh wrote:
KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

8 - k inches
9 - k + 0.25 inches

17 = ?

17 = k + 9 * 0.25 = K + 2.25

k + 2.25 = 1.2k

k = 2.25/0.2 = 11.25

Size of 15 = k + 7 * 0.25

= 11.25 + 1.75 = 13

where did you get 1.2k ?

It is from the statement that the largest length = 20% MORE than the smallest size (=k).

20% more = k + k *0.2 = 1.2k

Hope this helps.
Intern  Joined: 06 May 2014
Posts: 11
Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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VeritasPrepKarishma wrote:
KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

From size 8 to size 17, there are 9 increments of .25 each making the size 17 shoe 9*.25 = 2.25 inches more than the size 8 shoe.
This 2.25 accounts for 20% of the length of size 8 shoe so length of size 8 shoe is 2.25*5 = 11.25 inches
Length of size 15 shoe must be 11.25 + .25*7 = 13 inches

can not understand this part size 8 shoe is 2.25*5 = 11.25 inches
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Joined: 20 Mar 2014
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Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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2 p
anik1989 wrote:
VeritasPrepKarishma wrote:
KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

From size 8 to size 17, there are 9 increments of .25 each making the size 17 shoe 9*.25 = 2.25 inches more than the size 8 shoe.
This 2.25 accounts for 20% of the length of size 8 shoe so length of size 8 shoe is 2.25*5 = 11.25 inches
Length of size 15 shoe must be 11.25 + .25*7 = 13 inches

can not understand this part size 8 shoe is 2.25*5 = 11.25 inches

look at it this way.

Let x be the smallest size corresponding to size 8

The largest size (for size 17) will thus become 9*.25+x

Given that the largest size is 20% more than the smallest size , thus 9*.25+x = 1.2x giving you x=11.25 and thus size 15 will be 7*.25+11.25=13

Hope this helps.
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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subhashghosh wrote:
KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

8 - k inches
9 - k + 0.25 inches

17 = ?

17 = k + 9 * 0.25 = K + 2.25

k + 2.25 = 1.2k

k = 2.25/0.2 = 11.25

Size of 15 = k + 7 * 0.25

= 11.25 + 1.75 = 13

How did you get k = 2.25/0.2 = 11.25??
CEO  S
Joined: 20 Mar 2014
Posts: 2550
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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WE: Engineering (Aerospace and Defense)
Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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subhashghosh wrote:
KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

8 - k inches
9 - k + 0.25 inches

17 = ?

17 = k + 9 * 0.25 = K + 2.25

k + 2.25 = 1.2k

k = 2.25/0.2 = 11.25

Size of 15 = k + 7 * 0.25

= 11.25 + 1.75 = 13

How did you get k = 2.25/0.2 = 11.25??

That is exactly what you will get from the equation, 9*0.25+x=1.2x , where x=smallest size, 1.2x=largest size = 9*0.25+x.

Thus from 9*0.25+x=1.2x ---> 9*0.25=1.2x-x=0.2x --> 2.25=0.2x ---> x=2.25/0.2 = 11.25. Thus size 15 = 7*0.25+11.25 = 11.25+1.75 = 13. E is the correct answer.
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

first identify this is an arithmetic progression, then minus 7, coz you want to start from 1, or you're very likely to be trapped

s=a1......a17-7=a10

from here things get simple:

for all the arithmetic progressions, you have an=a1+(n-1)*the difference: the question gives it is 1/4

so: a17-7=10=a8-7=1+(10-1)*1/4=1.2a1

simplify it you get 1.2a1=a1+9/4, so a1=45/4

then a15-7=a8=45/4+(8-1)/4=52/4=13
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A manufacturer produces a certain men's athletic shoe in  [#permalink]

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9*(1/4)=9/4 inches is a difference between smallest and largest size

(9/4)*(100/20)=45/4 inches is the smallest size

7*(1/4)=7/4 is the difference between smallest size and size 15

So, 45/4+7/4=52/4=13

E
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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8 - x
9 = x+0.25
10=x+0.5
11=x+0.75
12=x+1
13=x+1.25
14=x+1.5
15=x+1.75
16=x+2
17=x+2.25

we know that length of 17 - length of 8 is equal to 0.2 of length of 8. From this, we can see that 2.25 = 0.2x => x=2.25*5 = 11.25
now we need to know the length of 15. 15 = x+1.75 and is equal to 13.
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

L(8) = Length of size 8
L(17) = length of size 17

L(17) = 1.2 * L(8)

L(17) = L(8) + 0.25 *(17 - 8)
L(17) = L(8) + 0.25 * 9
L(17) = L(8) + 2.25

IF L(8) + 2.25 = 1.2 * L(8)
THEN 0.2 * L(8) = 2.25
L(8) = 2.25 / 0.2
L(8) = 11.25
L(15) = 11.25 + (15 - 8) * 0.25
L(15) = 11.25 + 7 * 0.25
L(15) = 11.25 + 1.75
L(8) = 13.00
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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le'ts do it! try equations:
1,2 small=large
small+9/4 (means 17-8)=large
s+9/4=1,2
s=0,2*9/4=90/8
now we need to find size 15: 90/8+7/4=104/8=13

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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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KAS1 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?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13

What's the fastest way to solve this? Thanks!

The fastest way to solve this problem is by creating a table and setting up simple algebra.

List the sizes in ascending order

Size | Length
8 | x
9 | x + 1/4
10 | x + 1/2
11 | x + 3/4
12 | x + 1
13 | x + 5/4
14 | x + 6/4
15 | x + 7/4
16 | x + 2
17 | x + 9/4

x + 9/4 = 6/5*x from the info provided (the largest size is 20% greater than the smallest size).

x = 13.
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A manufacturer produces a certain men's athletic shoe in  [#permalink]

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Differences in length between size 8 (smallest) to size 17 (largest): L - S= 9*(1/4)= 2.25 inches. (1)
The largest size of this shoe is 20% longer than the smallest size: 1.2 S = L or 5S=6L (2)

From (1) and (2) => L = 2.25*6 =13.5 inches

Size 15= Size 17 - 2*(1/4) = 13.5 - 0.5 = 13 inches => Answer is E
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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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Let L= largest shoe, S smallest shoe.

L-S = 9/4 ( difference in size / corresponding increase)

L= 1.2S

Solve for L. L would come out to be 13.5. Substract 0.5 for 15 size.

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Re: A manufacturer produces a certain men's athletic shoe in  [#permalink]

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Hi All,

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

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