A straight picket fence is composed of x pickets each of whi

Question

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

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

Bunuel · Accepted Answer

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 .

Answer: E.

Hope it's clear.

KarishmaB · Answer

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.

Answer (E)

venksune · Answer

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

sdanquah · Answer

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

intr3pid · Answer

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.

ywilfred · Answer

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?

laserglare · Answer

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

nachobioteck · Answer

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?

Bunuel · Answer

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 .

nishantdoshi · Answer

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

chetan2u · Answer

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..

KarishmaB · Answer

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.

vaibhavpanchal · Answer

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.

Answer: E.

Avinashs87 · Answer

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

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

chetan2u · Answer

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

marvas8581 · Answer

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?

chetan2u · Answer

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

inandout · Answer

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.

KarishmaB · Answer

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.

A straight picket fence is composed of x pickets each of whi

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