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605-655 (Medium)|   Geometry|      
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Bunuel
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 20 Nov 2018, 00:39
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E
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45% (medium)

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58% (01:21) correct 42% (01:33) wrong based on 357 sessions

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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 rod for each side?

A. 6
B. 4
C. 3
D. 2
E. 1
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E
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 20 Nov 2018, 06:29
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Bunuel
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
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Triangle rule length : third side< 2nd and 1st side
in this case only 1 case is possible 5+3>7 so IMO E
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 04 Dec 2018, 07:40
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Bunuel
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
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hi

what about 7 + 1 > 3 ...?

thanks
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 04 Dec 2018, 09:03
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Archit3110
Bunuel
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
Show more

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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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 04 Dec 2018, 09:47
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Archit3110
Bunuel
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
Show more

Archit3110
hi

My bad, got it!
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 Updated on: 30 Aug 2020, 05:42
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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Bunuel
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
Show more

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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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 01 Jan 2019, 23:29
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Archit3110
Bunuel
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
Show more


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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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 02 Jan 2019, 07:05
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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
Show more

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

Cheers,
Brent
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 02 Jan 2019, 16:44
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Archit3110
Bunuel
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
Show more

hannan4644

Writing the triangle as either way doesnt make the triangle different in anyway... it would be same triangle only.
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 07 Feb 2019, 19:39
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Bunuel
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
Show more

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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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 05 May 2019, 02:59
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Bunuel
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.

Answer: E

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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 05 May 2019, 07:33
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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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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters 21 Aug 2023, 04:24
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