GMAT Fences

by on July 18th, 2013

In my years of teaching, I’ve seen all kinds of clever solutions to GMAT math problems. I’ve also seen all kinds of errors. Some are utterly bizarre—and fortunately, seldom repeated, because the students who make those mistakes usually face-palm when they review their tests and go on to learn from their missteps. But some errors are so common and so often repeated that they earned their own names. One such example is the “fencepost error.”

Here’s a simple example: Say we are setting up a straight fence that’s exactly 100 ft long, with posts every 10 feet. How many posts do we need?

Did you say 10? Tempting, but that’s the right answer to the wrong question. There are 10 sections of fence, each 10 feet long.  But there are actually 11 fenceposts, because you start with a fencepost, at 0 feet!

See?

This error can trap the unwary GMAT student in a few different ways. The most common is in finding sums of series consecutive integers.  The formula for the total of an evenly spaced list is to multiply the average value of that list by the number of items. So, you need to know exactly how many numbers you’re adding. So if a question asks for the sum of numbers between, say, 37 and 59, some students might just say there are 59 – 37 = 22 numbers on that list—but that doesn’t count 37, the first number. To ensure you solve for the correct value, you need to add the first “fencepost” and count all 23 numbers (write them out and count if you want to confirm!)

Also, rather oddly, this error shows up on the verbal section in sentence correction too. Clauses are the “fenceposts” in sentences, in a sense, and connecting words (therefore, however, so) are the fence sections. You can tell a sentence is improperly constructed if you don’t have exactly one more clause than you have connecting words.

Keep this error in mind as you solve your practice problems—and today’s question of the day. It’s a common mistake, but also an easy one to avoid once you’re aware of it. Practice will make sure you’re not fooled on Test Day.

Question of the Day:

In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 166 feet long?

(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

Solution:

Step 1: Analyze the Question

Though this is not a Geometry question, a quick sketch of the situation will help illustrate how to solve it.

So we know that the unit of one tree and one space is 1 * 1 + 14 feet = 15 feet.

Step 2: State the Task

To find how many trees can be planted, determine the feet required for a tree and the space between trees. Divide the total length of the street by the unit of one tree and the space between trees.

Step 3: Approach Strategically

Each tree takes up 1 foot, and each space takes up 14 feet. Together they take up 15 feet. Now find how many times 15 goes into the total number of feet on one side of the street:

166/15= 11, with a remainder of 1 foot.

We can plant one last tree in the remaining foot, bringing the total number of trees to 12. This means along the street, we can plant 12 trees with 11 spaces between them, as long as we start and end with a tree. (E) is correct.

Step 4: Confirm Your Answer

Make sure your answer makes sense in the context of the question. Did you take into account the remainder of the division? Will an entire tree fit in the remaining space? You can use these questions to confirm your work.

3 comments

  • Question of the day - GMAT Fences. My question concerns step 3. When I did my calculation of 166/15 I got 11.06. I am assuming you rounded up the 6 to make it 11.1. I am having a hard time wrapping my brain around the remainer being a foot. What unit is the 11 in? How do I know that each .1 is a foot? Is the general rule to round up on the GMAT? Thanks for the help in advance.

  • I don't think the author rounded up anything and neither should you. When you divide 166/15 you will get 11 as the quotient and 1 as the remainder, we don't want any decimals here. (Use a simple long division).
    The remainder is not a "foot long". The remainder is 1 unit and each tree takes up one square foot. Thus it follows that we can accommodate one more tree. Had the remainder been 2, we could have accommodated 2 more trees. Makes sense?

  • Tree------------------Tree------------------------Tree

    Lets says number of trees = n.

    Hence, number of gaps = n-1 (as seen by figure above

    Total length = 14 (number of gaps) + 1(number of trees)

    Total length = 14(n-1) + n = 15n - 14 = 166

    Hence n = 12.

    No fractions , no decimals.

    Issue with question, just the fact that trees take area of 1 square meter , doesnot mean length trees occupies is 1 meter. This needs to be specified.

    Maybe Kaplan should consider hiring me as  a tutor :)

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