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# If each of the sides of a triangle satisfies the equation x2+18=9x ,

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Manager
Joined: 10 Feb 2015
Posts: 107
GMAT 1: 710 Q48 V38
If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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09 Apr 2016, 05:27
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Difficulty:

85% (hard)

Question Stats:

43% (01:40) correct 57% (01:49) wrong based on 353 sessions

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If each of the sides of a triangle satisfies the equation x^2+18=9x, the perimeter of the triangle CANNOT be:

(A) 9
(B) 12
(C) 15
(D) 18
(E) Any of the four values above is possible.
Math Expert
Joined: 02 Aug 2009
Posts: 7044
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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09 Apr 2016, 06:45
4
4
rukna wrote:
If each of the sides of a triangle satisfies the equation :-
x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9
B. 12
C. 15
D. 18
E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI,
each side satisfies$$x^2+18=9x$$
$$x^2-9x+18=0$$..
$$(x-3)(x-6)=0$$..
so x=3 or x=6..
so sides can be 3 or 6...
If all 3, P= 9
if all 6, P = 18
If two sides 6 and third side 3= 2*6+3=15
If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?..
NO,the sum of two sides which are 3 is EQUAL to third side..
so TRIANGLE is not possible, it will be just a straight line measuring 6..
so 12 is not possible

ans B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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##### General Discussion
Manager
Joined: 10 Feb 2015
Posts: 107
GMAT 1: 710 Q48 V38
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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09 Apr 2016, 21:57
Thanks. I can't believe what silly mistake I did.
if you practice only 700 level question, your mind sometimes get screwed and you start finding something strange even in basic questions

Thanks for explaining.
Intern
Joined: 25 Apr 2016
Posts: 25
Concentration: Entrepreneurship, Marketing
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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09 May 2017, 18:55
chetan2u wrote:
rukna wrote:
If each of the sides of a triangle satisfies the equation :-
x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9
B. 12
C. 15
D. 18
E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI,
each side satisfies$$x^2+18=9x$$
$$x^2-9x+18=0$$..
$$(x-3)(x-6)=0$$..
so x=3 or x=6..
so sides can be 3 or 6...
If all 3, P= 9
if all 6, P = 18
If two sides 6 and third side 3= 2*6+3=15
If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?..
NO,the sum of two sides which are 3 is EQUAL to third side..
so TRIANGLE is not possible, it will be just a straight line measuring 6..
so 12 is not possible

ans B

Could you plz explain the part highlighted in blue?
As to why if the sum of 2 sides is equal to the 3rd,then it cannot be a triangle?
Math Expert
Joined: 02 Aug 2009
Posts: 7044
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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09 May 2017, 19:11
ishitam wrote:
chetan2u wrote:
rukna wrote:
If each of the sides of a triangle satisfies the equation :-
x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9
B. 12
C. 15
D. 18
E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI,
each side satisfies$$x^2+18=9x$$
$$x^2-9x+18=0$$..
$$(x-3)(x-6)=0$$..
so x=3 or x=6..
so sides can be 3 or 6...
If all 3, P= 9
if all 6, P = 18
If two sides 6 and third side 3= 2*6+3=15
If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?..
NO,the sum of two sides which are 3 is EQUAL to third side..
so TRIANGLE is not possible, it will be just a straight line measuring 6..
so 12 is not possible

ans B

Could you plz explain the part highlighted in blue?
As to why if the sum of 2 sides is equal to the 3rd,then it cannot be a triangle?

Hi,
If two sides are 3 and third side is 6....AB =BC=3...
So the third side AC has to be less than AB+BC or 6 because than only Point B will make an angle.
When it is 6, it means AC is a straight line and B is the midpoint of the line.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 05 Mar 2017
Posts: 156
Location: India
Concentration: Operations, General Management
GMAT 1: 640 Q48 V29
GPA: 3.9
WE: Operations (Transportation)
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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04 Jul 2017, 08:52
ishitam wrote:
chetan2u wrote:
rukna wrote:
If each of the sides of a triangle satisfies the equation :-
x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9
B. 12
C. 15
D. 18
E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI,
each side satisfies$$x^2+18=9x$$
$$x^2-9x+18=0$$..
$$(x-3)(x-6)=0$$..
so x=3 or x=6..
so sides can be 3 or 6...
If all 3, P= 9
if all 6, P = 18
If two sides 6 and third side 3= 2*6+3=15
If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?..
NO,the sum of two sides which are 3 is EQUAL to third side..
so TRIANGLE is not possible, it will be just a straight line measuring 6..
so 12 is not possible

ans B

Could you plz explain the part highlighted in blue?
As to why if the sum of 2 sides is equal to the 3rd,then it cannot be a triangle?

Learn a basic and very important rule:

For a triangle,
Difference of other two sides < third side < sum of other two sides
Intern
Joined: 20 Aug 2017
Posts: 39
Location: United States (FL)
Schools: Stanford '20 (D)
GMAT 1: 750 Q49 V42
GPA: 3.4
If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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Updated on: 18 Sep 2017, 03:18
1
rukna wrote:
If each of the sides of a triangle satisfies the equation:-
x^2+18=9x.

Could this be reworded better? I don't think that a "side" satisfies an equation. The length of a side can satisfy an equation. How about

"If the length x of any side of a triangle satisfies..."?

Originally posted by alainca on 01 Sep 2017, 04:03.
Last edited by alainca on 18 Sep 2017, 03:18, edited 2 times in total.
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Joined: 14 Nov 2016
Posts: 1319
Location: Malaysia
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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10 Sep 2017, 02:08
rukna wrote:
If each of the sides of a triangle satisfies the equation x^2+18=9x, the perimeter of the triangle CANNOT be:

(A) 9
(B) 12
(C) 15
(D) 18
(E) Any of the four values above is possible.

If x² - 9x + 18 = 0, then (x - 3)(x - 6) = 0 and x = 3 or x = 6, so each side of the triangle is 3 or 6. A 3-3-6 triangle violates our law of triangles, however: remember that the two shorter sides must have a sum greater than the length of the longest side!
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Intern
Joined: 10 Sep 2017
Posts: 5
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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17 Sep 2017, 19:19
alainca Agreed! The wording is super ambiguous. Are real GMAT questions like this? or is it just veritas prep questions that are frequently ambiguous??

alainca wrote:
rukna wrote:
If each of the sides of a triangle satisfies the equation:-
x^2+18=9x.

Could this be reworded better? I don't think that a "side" satisfies an equation. The length of a side can satisfy an equation. How about

"If the length x of each side of a triangle satisfies..."?
Senior Manager
Joined: 03 Apr 2013
Posts: 278
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: If each of the sides of a triangle satisfies the equation x2+18=9x ,  [#permalink]

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14 Nov 2017, 01:51
chetan2u wrote:
rukna wrote:
If each of the sides of a triangle satisfies the equation :-
x^2+18=9x

then the perimeter of the triangle CANNOT be:

A. 9
B. 12
C. 15
D. 18
E. Any of the four values above is possible.

For some reason, I find the fault in question. Can someone please explain. Posted official answer.

HI,
each side satisfies$$x^2+18=9x$$
$$x^2-9x+18=0$$..
$$(x-3)(x-6)=0$$..
so x=3 or x=6..
so sides can be 3 or 6...
If all 3, P= 9
if all 6, P = 18
If two sides 6 and third side 3= 2*6+3=15
If two sides 3 and third side 6, P= 2*3+6=12.. BUT is this possible?..
NO,the sum of two sides which are 3 is EQUAL to third side..
so TRIANGLE is not possible, it will be just a straight line measuring 6..
so 12 is not possible

ans B

And I thought that here "x" represents the x-coordinate of the vertices! Damn I don't know wat I was thinking. But it should be specified that x represents the length of each sides.
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Re: If each of the sides of a triangle satisfies the equation x2+18=9x , &nbs [#permalink] 14 Nov 2017, 01:51
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