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705-805 (Hard)|   Geometry|      
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rukna
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If each of the sides of a triangle satisfies the equation x2+18=9x , 09 Apr 2016, 06:27
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B
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Question Stats:

44% (01:41) correct 56% (01:50) wrong based on 426 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.
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B
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If each of the sides of a triangle satisfies the equation x2+18=9x , 09 Apr 2016, 07:45
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rukna
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.
Show more


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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rukna
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If each of the sides of a triangle satisfies the equation x2+18=9x , 09 Apr 2016, 22:57
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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.
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If each of the sides of a triangle satisfies the equation x2+18=9x , 09 May 2017, 19:55
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chetan2u
rukna
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
Show more

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?
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If each of the sides of a triangle satisfies the equation x2+18=9x , 09 May 2017, 20:11
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ishitam
chetan2u
rukna
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?
Show more

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.
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If each of the sides of a triangle satisfies the equation x2+18=9x , 04 Jul 2017, 09:52
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ishitam
chetan2u
rukna
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?
Show more

Learn a basic and very important rule:

For a triangle,
Difference of other two sides < third side < sum of other two sides
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If each of the sides of a triangle satisfies the equation x2+18=9x , Updated on: 18 Sep 2017, 04:18
Originally posted by alainca on 01 Sep 2017, 05:03.
Last edited by alainca on 18 Sep 2017, 04:18, edited 2 times in total.
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rukna
If each of the sides of a triangle satisfies the equation:-
x^2+18=9x.
Show more

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..."?
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If each of the sides of a triangle satisfies the equation x2+18=9x , 10 Sep 2017, 03:08
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rukna
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.
Show more

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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If each of the sides of a triangle satisfies the equation x2+18=9x , 17 Sep 2017, 20:19
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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
rukna
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..."?
Show more
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If each of the sides of a triangle satisfies the equation x2+18=9x , 14 Nov 2017, 02:51
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chetan2u
rukna
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
Show more

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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If each of the sides of a triangle satisfies the equation x2+18=9x , 01 Aug 2020, 06:55
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rukna
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.
Show more

Solution:

Let’s solve the given equation:

x^2 - 9x + 18 = 0

(x - 6)(x - 3) = 0

x = 6 or x = 3

If all the sides are 3, then the perimeter is 9. If all the sides are 6, then the perimeter is 18. If two sides are 6 and the third side is 3, then the perimeter is 15. However, it’s not possible that two sides are 3 and the third side is 6 since the sum of any two sides of a triangle must be greater than the third side, but 3 + 3 is not greater than 6. Therefore, the perimeter can’t be 12.

Answer: B
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If each of the sides of a triangle satisfies the equation x2+18=9x , 30 Jan 2022, 07:32
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Official Explanation:

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. Consider each answer choice to see if it is possible given that restriction on the sides:

(A) POSSIBLE - the triangle could be 3-3-3 (B) NOT POSSIBLE - the triangle cannot be 3-3-6 as this violates the third side rule - remember that the two shorter sides must have a sum greater than the length of the longest side! (C) POSSIBLE - the triangle could be 6-6-3 (D) POSSIBLE - the triangle could be 6-6-6 (E) INCORRECT

Since you need the one answer that is not possible, (B) is correct.
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If each of the sides of a triangle satisfies the equation x2+18=9x , 18 Nov 2023, 00:55
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