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# A manufacturer produces a certain men's athletic shoe in

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

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13 Feb 2013, 16:42
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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!
[Reveal] Spoiler: OA

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

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13 Feb 2013, 20:07
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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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13 Feb 2013, 17:08
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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 shoe in [#permalink]

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14 Feb 2013, 07:44
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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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Re: A manufacturer produces a certain men's athletic shoe in [#permalink]

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17 Sep 2015, 06:40
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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 shoes... [#permalink]

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14 Feb 2013, 01:55
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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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17 Sep 2015, 06:03
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 ?

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

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17 Sep 2015, 06:11
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.

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

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17 Sep 2015, 06:22
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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Re: A manufacturer produces a certain men's athletic shoe in [#permalink]

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21 Oct 2015, 03:40
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??

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

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21 Oct 2015, 04:14
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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21 Oct 2015, 16:40
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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22 Oct 2015, 01:04
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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24 Oct 2015, 12:14
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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12 Nov 2015, 04:50
this question by default is computationally intensive. the question forces you to back-solve and even with starting with C and understanding that C is a bit small, it took me 5 mins overall to rule out further whether E is the answer

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

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09 Feb 2017, 15:34
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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21 Mar 2017, 14:15
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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28 May 2017, 20:16
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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20 Nov 2017, 12:20
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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22 Nov 2017, 23:46
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] 22 Nov 2017, 23:46
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