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An irregular plot of land is surrounded by four straight segments of fence of meter lengths

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by BTGmoderatorDC » Thu Apr 16, 2020 5:55 pm

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Difficulty—

An irregular plot of land is surrounded by four straight segments of fence of meter lengths (5x + 5), (5x + 5), (3x + 10) and 2x. Is the total length of fence greater than 70 meters?

(1) The average (arithmetic mean) fence segment length is less than 25 meters.

(2) The largest fence segment is three times the length of the smallest fence segment.


OA B

Source: Princeton Review
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Re: An irregular plot of land is surrounded by four straight segments of fence of meter lengths

by Jay@ManhattanReview » Thu Apr 16, 2020 10:27 pm
BTGmoderatorDC wrote: ↑
Thu Apr 16, 2020 5:55 pm
 An irregular plot of land is surrounded by four straight segments of fence of meter lengths (5x + 5), (5x + 5), (3x + 10) and 2x. Is the total length of fence greater than 70 meters?

(1) The average (arithmetic mean) fence segment length is less than 25 meters.

(2) The largest fence segment is three times the length of the smallest fence segment.

OA B

Source: Princeton Review
From the information, we know that the total length of the fence

= (5x + 5) + (5x + 5) + (3x + 10) + 2x = 17x + 20

So, we have to ascertain whether 17x = 20 > 70 => x > 2.9...

Question rephrased; Is x > 2.9...?

Let's take each statement one by one.

(1) The average (arithmetic mean) fence segment length is less than 25 meters.

[(5x + 5) + (5x + 5) + (3x + 10) + 2x]/5 < 25

x < 4.7...

Case 1: If 4,7.. > x > 2.99, the answer is yes.
Case 2: If 2.9.. > x, the answer is no.

No unique answer. Insufficient.

(2) The largest fence segment is three times the length of the smallest fence segment.

We can be certain that the length of the smallest fence is 2x meters; however, the length of the largest fence can be (3x + 10) or (5x + 5).

Case 1: Say the length of the largest fence is (3x + 10).

=> 3x + 10 = 3*2x => x = 3.33 > 2.99. The answer is yes.

Case 2: Say the length of the largest fence is (5x + 5).

=> 5x + 5 = 3*2x => x = 5 > 2.99. The answer is yes.

unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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