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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If the sides of a triangle have lengths x, y, and z,
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18 Dec 2018, 07:19
18 Dec 2018, 07:19
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If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I. 28
II. 36
III. 42
A I only
B II only
C I and II only
D I and III only
E I, II, and III
I. 28
II. 36
III. 42
A I only
B II only
C I and II only
D I and III only
E I, II, and III
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If the sides of a triangle have lengths x, y, and z,
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18 Dec 2018, 16:08
18 Dec 2018, 16:08
3
GreenlightTestPrep wrote:
If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I. 28
II. 36
III. 42
A I only
B II only
C I and II only
D I and III only
E I, II, and III
I. 28
II. 36
III. 42
A I only
B II only
C I and II only
D I and III only
E I, II, and III
First of all, the perimeter CANNOT equal 28
We know this because we're told that x + y = 30, which means the sum of two sides is 30
In order for the perimeter (x+y+z) to equal 28, side z would have to have length -2, which makes no sense.
ELIMINATE A, C, D, and E
Answer: B
On test day, I wouldn't spend any more time on this question, but for "fun", let's keep going. . .
Now that we've shown the perimeter CANNOT equal 28, let's show that the perimeter CANNOT equal 42
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
We're told that y + z = 20, which means the sum of sides y and z is 20
The above rule tells us that the third side (side x) must be LESS THAN 20
If x is less than 20, and y+z = 20, it's impossible for the perimeter (x+y+z) to equal 42
Finally, the perimeter (x+y+z) CAN equal 36
If x = 16 y = 14, and z = 6, then all of the conditions are met, AND the perimeter is 36
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Re: If the sides of a triangle have lengths x, y, and z,
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25 Apr 2024, 17:24
25 Apr 2024, 17:24
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
