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

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

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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

OA: E

Need explanation why E is the correct answer?

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ardz24 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
Let x=2, implying that there are only 2 pickets.
Length of the 2 pickets = 2(1/2) = 1 inch.
The space between them = 6 inches.
Total length = 1+6 = 7 inches.
Total length in feet = 7/12. This is our target.

Now plug x=2 into the answers to see which yields our target of 7/12.

Only E works:
(13x-12)/24 = (13*2 - 12)/24 = 7/12.

The correct answer is E.

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Hi ardz24,

This is an example of a 'fence post' problem; they're relatively rare on the GMAT (you might not see any on Test Day). TESTing VALUES works perfectly here (as Mitch has shown), but sometimes these types of questions are about a specific calculation. The key to these types of questions is to realize that there is a 'post' at the beginning and the end of the 'row.'

Here's a variation on that idea: if you read pages 2 through 5 (inclusive) of a book, then how many pages have you read? Many people would quickly say that the answer is 3 (since 5 - 2 = 3). However, that is NOT the correct answer. We have to include page 2 (it was one of the pages read; we read 2, 3, 4 and 5 - thus the total is 4 pages) so you have to go back and include that page after you subtract it. Thus, the answer is 5 - 2 + 1 = 4

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

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Quote:
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

OA: E

Need explanation why E is the correct answer?
Hi ardz24,
Let's take a look at your question.

Since there are x pickets in the fence and each picket is 1/2 inch wide, so width of all x pickets will be (1/2)x
Now, lets find the total gap between x pickets.
If there are only 2 pickets, the gap between them is (2-1)(6) = (1)(6) = 6 inches
If there are 3 pickets, the gap between them is (3-1)(6) = (2)(6) = 12 inches
If there are 4 pickets, the gap between them is (4-1)(6) = (3)(6) = 18 inches
.....
Similarly, If there are x pickets, the gap between them is (x-1)(6) = (6x-6) inches

Total length of the fence in inches= width of x pickets + gap between x pickets
$$=\frac{1}{2}x+\left(6x-6\right)$$
$$=\frac{1}{2}x+\frac{12}{2\ }x-6$$
$$=\frac{13}{2\ }x-6$$

We are asked to find the length of fence in feet.
We know that, 1 foot = 12 inches and 1 inch = 1/12 foot, Therefore,
Total length of the fence in feet =
$$=\frac{1}{12}\left(\frac{13}{2\ }x-6\right)$$
$$=\frac{1}{12}\left(\frac{13x-12}{2\ }\right)$$
$$\left(\frac{13x-12}{24}\right)$$

Therefore, Option E is correct.

I am available, if you'd like any follow up.

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