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If x>0, and two sides of a certain triangle [#permalink]
30 Aug 2016, 02:20
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29% (01:38) correct
70% (01:16) wrong based on 75 sessions
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle? Indicate all possible lengths. A) 4x+5 B) x+2 C) 6x+1 D) 5x+6 E) 2x+17




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Re: If x>0, and two sides of a certain triangle [#permalink]
30 Aug 2016, 04:35
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Hi, I think B should be one of the solutions too Let the triangle have side named A, B and C A= 2x+1 and B= 3x+4 A+B= 5x+5 Now we know from triangle inequality C < A +B Option A4x+5 < 5x+5 =>x > 0 Option B x +2 < 5x+5 => 4x < 3 => x > \(\frac{3}{4}\). There is also possible as long as x >0 it is also x > \(\frac{3}{4}\) Option C6x+1 < 5x+5 x < 4 Also a possible solution exits such that 0 < x < 4. Option D is not possible. Option E is also similarly possible.
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Re: If x>0, and two sides of a certain triangle [#permalink]
30 Aug 2016, 05:10
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Let the third side be y then (3x + 4) – (2x + 1) < y < (3x + 4) + (2x + 1) => x + 3 < y < 5x + 5
As with option B, x+2 is always less than x+3, therefore B is not possible.
And with option E, if we choose x=5, then 2x+17= 27 => from inequality, 8<27<30 Hope, the solution is clear!



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Re: If x>0, and two sides of a certain triangle [#permalink]
11 Nov 2018, 08:19
Hey I got the answer as A, C ,E..I took x as 1,3 and 8... But my workbook still shows the answer as incorrect. Can somebody help me with this question.



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Re: If x>0, and two sides of a certain triangle [#permalink]
11 Nov 2018, 09:24
Reetika1990 wrote: Hey I got the answer as A, C ,E..I took x as 1,3 and 8... But my workbook still shows the answer as incorrect. Can somebody help me with this question. The answer is correct as A, C and E. the equations can be formed in following way.. (I) the third side is less than the sum of the other two sides... so third side < (2x+1) + (3x+4) or third side < 5x+5 (II) the third side is greater than the difference of the other two sides... so third side > (2x+1)  (3x+4) or > x+3 Therefore, equation becomes \(x+3 < third side < 5x+5\)
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html



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Re: If x>0, and two sides of a certain triangle [#permalink]
12 Sep 2019, 11:49
Hi All , While 4x+5 , 6x+1 , and 2x +17 are mentioned as correct answers for x>0 there might e challenge
X tending to 0 e.g. 0.01 2x+1 = 1.02 3x+4 = 4.03
here 6x+1 as third side will become 1.06 thus three sides as 1.02,1.06, 4.03 which is not possible here 2x+17 = 17.02 which again is not possible
Again if x is big as x=1000 2x+1 =2001 3x+4 =3004 6x+1 becomes 6001 Not so sure about the answers now ?



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Re: If x>0, and two sides of a certain triangle [#permalink]
15 Oct 2019, 06:57
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x+3<3rd side length<5x+5 let's say x=1000 1003<3rd side<5005 option E: 2(1000)+17= 2017 which falls right into the region. N.B if you consider small values for x, ie 2/3 then option E is invalid. but the ques asks for which of the following could be** the length. not which of the following must be**. you have to go for every possible way out there.



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Re: If x>0, and two sides of a certain triangle [#permalink]
04 Jun 2020, 18:31
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phoenixio wrote: If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?
Indicate all possible lengths.
A) 4x+5 B) x+2 C) 6x+1 D) 5x+6 E) 2x+17 solution: of course 3x+4 > 2x+1 so, third side of the triangle is 3X+4(2x+1)<third_side<3x+4+2x+1. which gives x+3<third_side<5x+5. note: question asked which "could be" the length of third side. x>0: A) x+3<4x+5<5x+5 which is true. B) x+3<x+2<5x+5 never true. C) x+3<6X+1<5x+5 which is not true for all value of x, but is true for x<4. so, could be true. D) x+3<5x+6<5x+5 never true. E) x+3<2x+17<5x+5 which is not true for all value of x, but is true for x>=5. A,C,E




Re: If x>0, and two sides of a certain triangle
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04 Jun 2020, 18:31





