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# If the perimeter of a triangle is 18, then the length of one of the

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Math Expert
Joined: 02 Sep 2009
Posts: 46305
If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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24 Aug 2017, 23:48
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Difficulty:

25% (medium)

Question Stats:

74% (00:41) correct 26% (00:43) wrong based on 76 sessions

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If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

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Joined: 18 Aug 2016
Posts: 634
GMAT 1: 630 Q47 V29
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Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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25 Aug 2017, 00:31
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

one side should always be less than the sum of other two sides
if one side is 9 then the sum of other two sides will be 9..not possible

E
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Luckisnoexcuse

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Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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25 Aug 2017, 02:57
1
We know that sum of any two sides of a triangle is greater than the side

hence if the length of a side is 9 then sum of the other two sides will 9 considering the perimeter as 18
under given condition the above scenario is not possible hence the answer is E
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Joined: 11 Apr 2017
Posts: 38
Schools: Kelley '20
Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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26 Aug 2017, 13:45
one side should always be less than the sum of other two sides
if one side is 9 then the sum of other two sides will be 9..not possible

E
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Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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26 Aug 2017, 14:02
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

I understand why E is the answer. But why not option A ? if one side is 1, the other two sides will be 8 and 9. These cannot be the sides of the triangle.
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Joined: 23 Apr 2014
Posts: 4
Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 01:55
hwgmat2015 wrote:
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

I understand why E is the answer. But why not option A ? if one side is 1, the other two sides will be 8 and 9. These cannot be the sides of the triangle.

Yes, why not A?the other two sides can be 10 and 7 as well.
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Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 02:26
it can not be A
let us take the case of an equilateral triangle
perimeter is given to be 18 mm
So each side would be 6 mm
Now we have property of the triangle = a-b<c<a+b
Since each side is equal a-b=0
a+b=12
so 0<c<12 but we know that perimeter is 18 so C<=6
I hope it is clear
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Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 03:49
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

I need help

A) 1 should be greater than SUM OF OTHER 2 SIDES and Less than SUBTRACTION OF 2 SIDES

So if one side is 1 other 2 will be x+y = 17 (well it satisfies that 3rd side should be less than addition of rest 2 so 1 is valid)
But for subtraction? Lets take x= 9 , y =8 , SO 9-8 = 1 , HENCE IT SHOULD BE GREATER THAN 1 to satisfy second condition but its equal to 1 then

IT MEANS 1 CANT BE INCLUDED

Math Expert
Joined: 02 Aug 2009
Posts: 5938
If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 04:18
1
rocko911 wrote:
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

I need help

A) 1 should be greater than SUM OF OTHER 2 SIDES and Less than SUBTRACTION OF 2 SIDES

So if one side is 1 other 2 will be x+y = 17 (well it satisfies that 3rd side should be less than addition of rest 2 so 1 is valid)
But for subtraction? Lets take x= 9 , y =8 , SO 9-8 = 1 , HENCE IT SHOULD BE GREATER THAN 1 to satisfy second condition but its equal to 1 then

IT MEANS 1 CANT BE INCLUDED

hi rocko911 and hwgmat2015..

the Q is looking for CANNOT be, which means it should not be possible..

now you are looking for a triangle with sides 1,8,9 but it can be 8.5,8.5 and 1...
it is nowhere mentioned that sides are INTEGERS

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Posts: 202
Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 04:31
chetan2u wrote:
rocko911 wrote:
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

I need help

A) 1 should be greater than SUM OF OTHER 2 SIDES and Less than SUBTRACTION OF 2 SIDES

So if one side is 1 other 2 will be x+y = 17 (well it satisfies that 3rd side should be less than addition of rest 2 so 1 is valid)
But for subtraction? Lets take x= 9 , y =8 , SO 9-8 = 1 , HENCE IT SHOULD BE GREATER THAN 1 to satisfy second condition but its equal to 1 then

IT MEANS 1 CANT BE INCLUDED

hi rocko911 and hwgmat2015..

the Q is looking for CANNOT be, which means it should not be possible..

now you are looking for a triangle with sides 1,8,9 but it can be 8.5,8.5 and 1...
it is nowhere mentioned that sides are INTEGERS

yes indeed, But its also not mentioned that it cant be integers as well , so we need to take all posibilities,

SO WHAT IF WE TAKE ONE SIDE AS 1 and other two be 9+8 , then it doesnt hold for subtraction rule
becoz 9-8 = 1 and it should be greater than 1

AND IF ITS NOT SATISFYING THEN IT MEANS IT SHOULD "NOT" BE POSSIBLE just as everyone says 9 is
Math Expert
Joined: 02 Aug 2009
Posts: 5938
If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 04:37
rocko911 wrote:
chetan2u wrote:

hi rocko911 and hwgmat2015..

the Q is looking for CANNOT be, which means it should not be possible..

now you are looking for a triangle with sides 1,8,9 but it can be 8.5,8.5 and 1...
it is nowhere mentioned that sides are INTEGERS

yes indeed, But its also not mentioned that it cant be integers as well , so we need to take all posibilities,

SO WHAT IF WE TAKE ONE SIDE AS 1 and other two be 9+8 , then it doesnt hold for subtraction rule
becoz 9-8 = 1 and it should be greater than 1

AND IF ITS NOT SATISFYING THEN IT MEANS IT SHOULD "NOT" BE POSSIBLE just as everyone says 9 is

hi..

CANNOT be means it is NOT possible under any circumstances

so for any value of other two sides if 1 is possible, then it will not come under CANNOT be.

however 9 is NOT possible under any circumstances so it is our answer

for that matter 3 will not be possible if sides are 3, 7,10..
you will always have value for which each choice will not be possible..

hope it helped
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Re: If the perimeter of a triangle is 18, then the length of one of the [#permalink]

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27 Aug 2017, 05:40
Bunuel wrote:
If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1
(B) 3
(C) 6
(D) 8
(E) 9

Here E must be the answer.
as we know the sum of two sides must be greater than the third side. so if one side is 9 so sum of other two side will also be 9 and it violates rules mentioned earlier
Hence E
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Re: If the perimeter of a triangle is 18, then the length of one of the   [#permalink] 27 Aug 2017, 05:40
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