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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters : Problem Solving (PS)
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# Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters

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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
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testcracker wrote:
Archit3110 wrote:
Bunuel wrote:
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

Triangle rule length : third side< 2nd and 1st side
in this case only 1 case is possible 5+3>7 so IMO E

hi

what about 7 + 1 > 3 ...?

thanks

Triangle rule states sum of two sides> third side ...

Could you please identify which is third side and other two side below as per ?
7 + 1 > 3

You have taken sum of largest and smallest side ... Which isn't correct... Hope this helps.

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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
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testcracker wrote:
Archit3110 wrote:
Bunuel wrote:
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

Triangle rule length : third side< 2nd and 1st side
in this case only 1 case is possible 5+3>7 so IMO E

hi

what about 7 + 1 > 3 ...?

thanks

Archit3110
hi

thanks a lot +1

actually I think you wanted to mean, the sum of ANY 2 sides of a triangle is greater than the third side

thanks again, take care
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
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Bunuel wrote:
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

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.

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Originally posted by BrentGMATPrepNow on 31 Dec 2018, 11:24.
Last edited by BrentGMATPrepNow on 30 Aug 2020, 05:42, edited 1 time in total.
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
Archit3110 wrote:
Bunuel wrote:
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

Triangle rule length : third side< 2nd and 1st side
in this case only 1 case is possible 5+3>7 so IMO E

We can have two triangles in the configuration 5-3-7.
1) 5-3-7
2) 3-5-7
So, I think the answer should be D
Correct me if I am wrong
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
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hannan4644 wrote:

We can have two triangles in the configuration 5-3-7.
1) 5-3-7
2) 3-5-7
So, I think the answer should be D
Correct me if I am wrong

Those 2 triangles are considered the same. So, we can only counted them once.

Cheers,
Brent
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
hannan4644 wrote:
Archit3110 wrote:
Bunuel wrote:
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

Triangle rule length : third side< 2nd and 1st side
in this case only 1 case is possible 5+3>7 so IMO E

We can have two triangles in the configuration 5-3-7.
1) 5-3-7
2) 3-5-7
So, I think the answer should be D
Correct me if I am wrong

hannan4644

Writing the triangle as either way doesnt make the triangle different in anyway... it would be same triangle only.
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
Bunuel wrote:
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

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.

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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
GMATPrepNow wrote:
Bunuel wrote:
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

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

Hi Brent,

Just a quick question . Is it sum of any two sides should be greater than third side. or is it the longest side only that needs to be considered?
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.

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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
1 3 5 — not following property of sum of two sides should be greater than third

1 3 7 — same issue as above

1 5 7 — same issue as above

3 5 7 — follows the property

One triangle possible

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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
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Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters [#permalink]
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