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A rectangular garden

This topic has 3 expert replies and 0 member replies
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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A rectangular garden

Post Thu Apr 28, 2016 1:25 pm
A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?

A) 120
B) 140
C) 160
D) 180
E) 200

A

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Top Reply
Post Thu Apr 28, 2016 6:40 pm
Hi boomgoesthegmat,

This question can be solved by TESTing THE ANSWERS.

We're told that we're dealing with a rectangular garden that has a perimeter of 360 yards of fencing. This means that....

2(length) + 2(width) = 360
length + width = 180

We're also told that the length is TWICE the width. We're asked for the length of the garden. Since the answer choices are all numbers, it shouldn't take too much arithmetic to figure out which one fits all of the given information.

Let's TEST Answer B: 140 yards

IF the length is 140 yards, then...
180 - 140 = 40
140 = TWICE 70
40 does NOT = 70, so this cannot be the answer.

To 'shrink' the difference in the two values, we'll need a shorter length, and there's only one answer that fits THAT description. You can prove that it's correct with just a little more work though...

Let's TEST Answer A: 120 yards

IF the length is 140 yards, then...
180 - 120 = 60
120 = TWICE 60
60 DOES = 60, so this MUST be the answer.

Final Answer: A

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

_________________
Contact Rich at Rich.C@empowergmat.com

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Top Reply
Post Thu Apr 28, 2016 2:18 pm
boomgoesthegmat wrote:
A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards?

A) 120
B) 140
C) 160
D) 180
E) 200

A
Normally, I’d use the 1-variable approach that Matt used. However, I’ll also show how we can also use 2 variables.

Let W = the width of the rectangle
Let L = the length of the rectangle

A rectangular garden is to be twice as long as it is wide.
So, we get: L = 2W

360 yards of fencing, including the gate, will completely enclose the garden
In other words, the perimeter is 360.
So, we can write: L + L + W + W = 360
Simplify to get: 2L + 2W = 360

So, we have the following system of 2 equations with 2 unknowns:
L = 2W
2L + 2W = 360

We can take 2W in the bottom equation and replace it with L to get: 2L + L = 360
Simplify: 3L = 360
Solve: L = 120
Answer: A

Related Resources
The following videos cover the concepts/strategies that are useful for answering this question:
- Assigning variables: https://www.gmatprepnow.com/module/gmat-word-problems/video/902
- Writing equations: https://www.gmatprepnow.com/module/gmat-word-problems/video/903
- How many variables to assign?: https://www.gmatprepnow.com/module/gmat-word-problems/video/906

Cheers,
Brent

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Post Thu Apr 28, 2016 6:40 pm
Hi boomgoesthegmat,

This question can be solved by TESTing THE ANSWERS.

We're told that we're dealing with a rectangular garden that has a perimeter of 360 yards of fencing. This means that....

2(length) + 2(width) = 360
length + width = 180

We're also told that the length is TWICE the width. We're asked for the length of the garden. Since the answer choices are all numbers, it shouldn't take too much arithmetic to figure out which one fits all of the given information.

Let's TEST Answer B: 140 yards

IF the length is 140 yards, then...
180 - 140 = 40
140 = TWICE 70
40 does NOT = 70, so this cannot be the answer.

To 'shrink' the difference in the two values, we'll need a shorter length, and there's only one answer that fits THAT description. You can prove that it's correct with just a little more work though...

Let's TEST Answer A: 120 yards

IF the length is 140 yards, then...
180 - 120 = 60
120 = TWICE 60
60 DOES = 60, so this MUST be the answer.

Final Answer: A

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

_________________
Contact Rich at Rich.C@empowergmat.com

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