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Director  Joined: 20 Jul 2004
Posts: 529
A straight picket fence is composed of x pickets each of whi  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 36% (02:08) correct 64% (02:01) wrong based on 702 sessions

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A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?

A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

Attachments Fence.JPG [ 13.67 KiB | Viewed 14708 times ]

Originally posted by hardworker_indian on 08 Sep 2004, 01:58.
Last edited by Bunuel on 20 Sep 2013, 02:30, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert V
Joined: 02 Sep 2009
Posts: 58105
Re: A straight picket fence is composed of X pickets each of  [#permalink]

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4
7
laserglare wrote:
Can someone please explain why the answer is not D

I did it algebraically.

Basically since the 'space between pickets' is 6 inches and the pickets are 1/2 inch

why can't we just use 6 1/2 x + 1/2
Because each picket will have 6 inches of space and then you just add 1/2 inch for the extra picket. Doing this algebraically I get D

(6.5 x + .5) / 12 --> (13x - 12) / 24

A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?
A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

x pickets mean x-1 fences, each of which is 6 inches wide.

So, the length = $$6(x-1)+\frac{1}{2}*x=\frac{13x-12}{2}$$ inches, or $$\frac{13x-12}{24}$$ feet.

Hope it's clear.
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Director  Joined: 16 Jun 2004
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2
E for me too

let X = 4
the length = 3*6 + (1/2)*4 = 20 inches = 20/12 feet = 5/3 feet.

Applying 5/3 in answer choices we have for E) (13*4 - 12)/24 = 5/3feet

I had made some silly mistakes earlier. Stand corrected. Thanks to sdanquah

Originally posted by venksune on 08 Sep 2004, 11:56.
Last edited by venksune on 08 Sep 2004, 12:56, edited 3 times in total.
Manager  Joined: 21 Aug 2004
Posts: 122

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3
I think bot of you are missing something to this question,I hope I could compy the question here and digest it properly.
I think the answer shd be E

Number of pickeks = x
Size of pickets = 1/2
length of pickets = 1/2x
If there are x pickets, it implies that there are x -1 spaces between the picket
Length of space = 6

total number of length = 1/2 x + 6(x-1) in inches
total lenth in feet =( 1/2 x + 6(x-1))/12
Simplify to get (13X-12)/24
Manager  Joined: 05 Sep 2004
Posts: 85

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sdanquah wrote:
I think bot of you are missing something to this question,I hope I could compy the question here and digest it properly.
I think the answer shd be E

Number of pickeks = x
Size of pickets = 1/2
length of pickets = 1/2x
If there are x pickets, it implies that there are x -1 spaces between the picket
Length of space = 6

total number of length = 1/2 x + 6(x-1) in inches
total lenth in feet =( 1/2 x + 6(x-1))/12
Simplify to get (13X-12)/24

Alternatively, each picket and the adjacent empty space represents a length of 6.5 inches.

Thus, total length of the fence = 6.5x - (6 inches for the one fewer empty space) = (13x-12)/2 in inches = (13x-12)/24 in feet.
GMAT Club Legend  Joined: 07 Jul 2004
Posts: 4060
Location: Singapore

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2
This is crazy. I got to the point where I do not know what the conversion factor is from inches to feet. Since GMAT is taken by an international community, shouldn't they stick to SI units?
Manager  Joined: 07 Jul 2013
Posts: 94
Re: A straight picket fence is composed of X pickets each of  [#permalink]

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1
1
Can someone please explain why the answer is not D

I did it algebraically.

Basically since the 'space between pickets' is 6 inches and the pickets are 1/2 inch

why can't we just use 6 1/2 x + 1/2
Because each picket will have 6 inches of space and then you just add 1/2 inch for the extra picket. Doing this algebraically I get D

(6.5 x + .5) / 12 --> (13x - 12) / 24
Manager  Joined: 21 Aug 2014
Posts: 152
Location: United States
Concentration: Other, Operations
GMAT 1: 700 Q47 V40 GMAT 2: 690 Q44 V40 WE: Science (Pharmaceuticals and Biotech)
Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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Would the GMAT consider that the imperial unit system is general knowledge? I am asking because I come from a metric system country and have no idea about feet inches, pound ounces and all of that...

Will I have to learn it?
Math Expert V
Joined: 02 Sep 2009
Posts: 58105
Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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nachobioteck wrote:
Would the GMAT consider that the imperial unit system is general knowledge? I am asking because I come from a metric system country and have no idea about feet inches, pound ounces and all of that...

Will I have to learn it?

No. The question itself will supply the relative conversions. Though you should have a few basic ones memorized: 1 hour = 60 minutes, ...

Check other Conversion problems to practice in Special Questions Directory.
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Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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3
2
hardworker_indian wrote:
A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?

A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

Whenever you have variables in the answer choices, just plug in.
If x = 1, there is only one picket which is 1/2 inch wide. Since 1 foot has 12 inches, 1/2 inch would be 1/24 of a foot.
Look for the choice in which if you put x = 1, you get 1/24.

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Intern  Joined: 23 Sep 2015
Posts: 37
A straight picket fence is composed of x pickets each of whi  [#permalink]

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Bunuel wrote:
laserglare wrote:
Can someone please explain why the answer is not D

I did it algebraically.

Basically since the 'space between pickets' is 6 inches and the pickets are 1/2 inch

why can't we just use 6 1/2 x + 1/2
Because each picket will have 6 inches of space and then you just add 1/2 inch for the extra picket. Doing this algebraically I get D

(6.5 x + .5) / 12 --> (13x - 12) / 24

A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?
A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

x pickets mean x-1 fences, each of which is 6 inches wide.

So, the length = $$6(x-1)+\frac{1}{2}*x=\frac{13x-12}{2}$$ inches, or $$\frac{13x-12}{24}$$ feet.

Hope it's clear.

i started it with making an equation just like you did but what i did is:

$$6(x-1)+\frac{1}{2}*x=.5(x-1)+\frac{1}{24}*x$$

but by solving this equation i couldn't come to the final equation which is in the options list.

can you help me out with it...i want to understand when to convert it before hand and when to wait for it . :/

HELP
Math Expert V
Joined: 02 Aug 2009
Posts: 7824
Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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nishantdoshi wrote:
i started it with making an equation just like you did but what i did is:

$$6(x-1)+\frac{1}{2}*x=.5(x-1)+\frac{1}{24}*x$$

but by solving this equation i couldn't come to the final equation which is in the options list.

can you help me out with it...i want to understand when to convert it before hand and when to wait for it . :/

HELP

Hi,
lets start where you left..

$$6(x-1)+\frac{1}{2}*x=.5(x-1)+\frac{1}{24}*x$$...
$$.5x-.5+\frac{x}{24}$$..
$$\frac{{24(.5x-.5)+x}}{24}$$
$$\frac{{(12x-12)+x}}{24}$$...
$$\frac{{13x-12}}{24}$$...
this is the answer required..

But I can advice you that do the change in inches to feets in the final step rather than in initial steps..
It will be less complicated..
$$6(x-1)+\frac{1}{2}*x=6x-6+\frac{1}{2}*x$$...
=$$\frac{{(12x-12)+x}}{2}=\frac{{13x-12}}{2}$$..
now change to feet by dividing by 12..
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Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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nishantdoshi wrote:

i started it with making an equation just like you did but what i did is:

$$6(x-1)+\frac{1}{2}*x=.5(x-1)+\frac{1}{24}*x$$

but by solving this equation i couldn't come to the final equation which is in the options list.

can you help me out with it...i want to understand when to convert it before hand and when to wait for it . :/

HELP

Note that all options have a single x. So this should give you a hint that you have to further simplify your expression to bring the x's together. Once you do, it will match one option.
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Intern  Joined: 27 Jun 2015
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GRE 1: Q162 V147 Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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pickets mean x-1 fences, each of which is 6 inches wide.

So, the length = 6(x−1)+12∗x=13x−122 inches, or 13x−1224 feet.

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Joined: 16 Dec 2013
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Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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Bunuel wrote:
laserglare wrote:
Can someone please explain why the answer is not D

I did it algebraically.

Basically since the 'space between pickets' is 6 inches and the pickets are 1/2 inch

why can't we just use 6 1/2 x + 1/2
Because each picket will have 6 inches of space and then you just add 1/2 inch for the extra picket. Doing this algebraically I get D

(6.5 x + .5) / 12 --> (13x - 12) / 24

A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?
A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

x pickets mean x-1 fences, each of which is 6 inches wide.

So, the length = $$6(x-1)+\frac{1}{2}*x=\frac{13x-12}{2}$$ inches, or $$\frac{13x-12}{24}$$ feet.

Hope it's clear.

Why can't I interpret the question as having 8 pickets. the Equation is [m]6(x/2-1)+\frac{1}{2}*x.

Where am I going wrong. The question says 2 pairs of picket..
Math Expert V
Joined: 02 Aug 2009
Posts: 7824
Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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Avinashs87 wrote:
Bunuel wrote:
laserglare wrote:
Can someone please explain why the answer is not D

I did it algebraically.

Basically since the 'space between pickets' is 6 inches and the pickets are 1/2 inch

why can't we just use 6 1/2 x + 1/2
Because each picket will have 6 inches of space and then you just add 1/2 inch for the extra picket. Doing this algebraically I get D

(6.5 x + .5) / 12 --> (13x - 12) / 24

A straight picket fence is composed of x pickets each of which is 1/2 inch wide. If there are 6 inches of space between each pair of pickets, which of the following represents the length of fence in feet?
A. 13x/2
B. 13x/2 - 6
C. 13x/24
D. (13x+1)/24
E. (13x-12)/24

x pickets mean x-1 fences, each of which is 6 inches wide.

So, the length = $$6(x-1)+\frac{1}{2}*x=\frac{13x-12}{2}$$ inches, or $$\frac{13x-12}{24}$$ feet.

Hope it's clear.

Why can't I interpret the question as having 8 pickets. the Equation is [m]6(x/2-1)+\frac{1}{2}*x.

Where am I going wrong. The question says 2 pairs of picket..

Hi,
If you take x as 8..
the width of pickets will be 8*1/2=4..
there is 6 in gap between each pair..
In 8 pickets, there will be 8-1=7 gaps..
so length of gaps= 7*6=42
TOTAL= 42+4=46 inches or 46/12 feet..

check all choices..
E. (13x-12)/24= (13*8-12)/24= 92/24=46/12..
this is our answer
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Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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Hi, I got it until the step prior to conversion. I am not able to find the conversion factor in the question step. I realize that I have to express the answer in feet but are we expected to know the conversion factor too?
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Posts: 7824
Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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marvas8581 wrote:
Hi, I got it until the step prior to conversion. I am not able to find the conversion factor in the question step. I realize that I have to express the answer in feet but are we expected to know the conversion factor too?

No, ACTUALs are likely to provide you the necessary info in the Q itself of all measurements, which are not universal..
as in this case many countries follow metric system ..
conversions of pound etc too should be given
yes, universal things like 1 hour = 60 min = 3600 sec etc should be known to you
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Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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2 questions: how you know 1 foot = 12 inch?
and the question says the gap between a pair of pickets, or between 2 pickets and other 2 is 6 inch, not between just 2.
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Re: A straight picket fence is composed of x pickets each of whi  [#permalink]

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inandout wrote:
2 questions: how you know 1 foot = 12 inch?
and the question says the gap between a pair of pickets, or between 2 pickets and other 2 is 6 inch, not between just 2.

GMAT will give you the relation between units such as feet and inches.

Also, the question says: "If there are 6 inches of space between each pair of pickets".
So you can pick up any two adjacent pickets - distance between them will be 6 inches.
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Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: A straight picket fence is composed of x pickets each of whi   [#permalink] 16 May 2017, 23:38

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