A farmer plans to build a fence next to a stretch of driveway. Each fe

Question

A farmer plans to build a fence next to a stretch of driveway. Each fence post will be one foot wide and there will be three feet of space between posts. If the driveway is 65 feet long and the fence will be on just one side of the driveway, then how many posts will the farmer need to complete the fence?

A) 16

B) 17

C) 18

D) 19

E) 20

A) 16

B) 17

C) 18

D) 19

E) 20

luffy_ueki · Answer

1ft. fence 3ft. space
<--------><---------------------------> (repeat)
Stretch of roadway = 65 ft.
lets take a number which is divisible by 4 (1+3)
64/4 = 16
16 fence posts & and 16 spaces left.
Remaining 65 - 64 = 1 ft. => put one fence post in this length.

thus 16+1 = 17 fence posts required

luffy_ueki · Answer

1ft. fence 3ft. space
<--------><---------------------------> (repeat)
Stretch of roadway = 65 ft.
lets take a number which is divisible by 4 (1+3)
64/4 = 16
16 fence posts & and 16 spaces left.
Remaining 65 - 64 = 1 ft. => put one fence post in this length.

thus 16+1 = 17 fence posts required

KarishmaB · Answer

Let's visualise a fence: Each fence post and the space to its right will account for a total of 1 + 3 = 4 feet. So to cover 64 feet, we will need 64/4 = 16 posts. The last one foot will be covered by one more fence post so in all we will need 17 fence posts

Answer (B)

dhaundiyalmanan · Answer

Can you help me understand why the farmer will build another fence in the last 1 feet and not leave it since the question says that there has to be 3 feet gap between the 2 fences.

dhaundiyalmanan · Answer

Can you help me understand why the farmer will build another fence in the last 1 feet and not leave it since the question says that there has to be 3 feet gap between the 2 fences.

Mostakim94 · Answer

Lets think it like

ne fence post+gap between two posts=4 Now the highest multiple of 4 less than 65 is 64.(4*16=64) That leaves us with 1 extra foot, which is also the measurement of one post. So total number of posts(16+1)=17 Answer.B Posted from my mobile device

Basshead · Answer

65 / 4 = 16 remainder 1.

16 + 1 = 17 fences needed.

achloes · Answer

KarishmaB   EMPOWERgmatRichC

Could you please help me understand why there is a need to cover the last 1 foot by a post?

The question says "need", therefore does it not point to the minimum number of posts needed to cover the 65 feet?

We can start the fencing with a space of 3 feet, followed by the post of 1 foot. Repeat 16 times, we're then left with a post at the 64th foot, with one foot of space to the end of the driveway.

Even if we were to start with a space of 2 feet, we'd still get the same result (as 3 feet between posts is required). In this case, we'd be left with 2 feet of space to the end of the driveway. Also satisfies the constraint.

Just seems unlike the GMAT to ask for the maximum number.

Appreciate your thoughts, and thank you in advance!

KarishmaB · Answer

When you plan to fence the driveway, it means you want to cordon it off i.e. not allow access to it from that side. So you put up say a barbed wire around it. But you need to put up posts to attach the wires to. Hence you have fence and fence posts. If you leave some space unfenced, then you have not fenced that side fully. People can still come in through the gaps. If we have 1 inch fence post width and 3 inches of space between them (where the wire will be), the length to be fenced can be 5 inches (post - wire - post) but cannot be say 6 inches (then 1 inch will be unfenced) stay-tuff-greater-strength-than-other-fences.png

EMPOWERgmatRichC · Answer

Hi achloes, Fence posts are a necessary part of hanging up fencing (otherwise the fencing would just lay on the ground). In this prompt, we're told that to put up one 3-foot segment of fencing, we'll need two 1-foot posts... = 5 total feet Once we have that inital 5 feet of construction, we only need another 4 feet to put up the NEXT piece of fencing (since we already have a post to work with from the initial construction)... = 9 total feet This pattern will go on until we hit the desired total distance (in this case, a total of 65 feet - with the last 1 foot of distance taken up by a post, since we need that final post to hold up the last piece of fencing). GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

Ahmed31 · Answer

Hi  karishma   IanStewart   ScottTargetTestPrep

I solved the question correctly. 
However, I have a confusion whether we should also consider cases such as ....

Case 1. Starting with Gap of 3 m or 2m or 1m ( 3m being max because after that a fence post is needed.) 
Gap(3m) + Fence Post (1m)

...OTHER Than 
Case - Starting with the fence Post
Fence Post 1m + Gap(3m)

OR 
I am just over analysing- :/

Regards, 
Ahmed

IanStewart · Answer

In general, I wouldn't worry about the wording of unofficial questions. There are a lot of ambiguously worded prep company math and verbal questions, and you won't see that kind of wording on the real test. For what it's worth, though, I agree with you. I imagine the author of the question would say "of course you need a post at either end of the fence", but I don't see why that needs to be true. The fence is alongside a driveway, which presumably extends up to the side of a garage or building. Why can't we chain some fence to the side of the building, rather than to an initial post? At a minimum, that issue makes the solution more complicated, and if you don't need a post at either end of the fence, then the answer changes. There are two other problems with the wording of the question, but as I said earlier, that doesn't distinguish this question from those of other prep companies -- companies in general aren't nearly as careful with language as the real GMAT question writers are.

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A farmer plans to build a fence next to a stretch of driveway. Each fe

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