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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one

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by BTGModeratorVI » Thu Aug 27, 2020 12:07 pm

Timer

00:00

Answers

A

B

C

D

E

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Difficulty—

Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1

Answer: E
Source: Princeton Review
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using

by Brent@GMATPrepNow » Sun Aug 30, 2020 4:42 am
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:07 pm
 Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1

Answer: E
Source: Princeton Review
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

Let's focus on this part: length of third side < SUM of A and B
We can also say that the length of LONGEST side must be less than the SUM of the other two sides

Let's systematically go through all possible combinations of 3 sides

case a) the LONGEST side has a length of 7 meters
So, 7 must be less than the SUM of the other two sides
This means the remaining 2 sides must have lengths 3 and 5 meters
So, a triangle with lengths 3-5-7 is POSSIBLE
This is the ONLY possible configuration in which the LONGEST side has a length of 7 meters

case b) the LONGEST side has a length of 5 meters
So, 5 must be less than the SUM of the other two (shorter) sides
If 5 is the longest side, then the other 2 sides must have lengths of 1 and 3 meters
HOWEVER, this breaks our rule that says the length of LONGEST side must be less than the SUM of the other two sides
So, we CANNOT have a triangle in which the LONGEST side has a length of 5 meters

case c) the LONGEST side has a length of 3 meters
This cannot work, since there's only one rod that has a length that's less than 1

case d) the LONGEST side has a length of 1 meters
This cannot work

So, there's only 1 possible triangle that can be created.

Answer: E
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using

by gmatter2012 » Tue Sep 01, 2020 2:00 am
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:07 pm
 Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1

Answer: E
Source: Princeton Review

Dear Moderator
Please check the answer in the timer. Although in the spoiler you have written E but in the timer you must have chosen a different OA as even after selecting E , I was shown a red cross. Hope you will look into this.
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using

by Scott@TargetTestPrep » Wed Sep 02, 2020 5:40 am
BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:07 pm
 Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1

Answer: E

Solution:

Since the sum of 2 sides of a triangle must be greater than the 3rd, the only option for the three sides is {3, 5, 7}. We cannot use the rod of length 1 meter in forming any triangles; we can verify that in any choice of three sides including the rod of length 1, there are two sides where the sum of the lengths is less than the length of the third side.

Answer: E

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