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Manager  Joined: 11 Feb 2011
Posts: 108
triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 53% (01:18) correct 47% (01:25) wrong based on 342 sessions

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triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.

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The answer is E.

S1 says that the sides are consecutive integers and one of the side is 4. There can be three possibilities
3,4,5
2,3,4
1,2,3
Clearly insufficient

S2 says that triangle A is not a right angle. I still have two cases i.e. 2,3,4 and 1,2,3. Clearly insufficient

Combining 1) and 2) two cases are left. Answer E

PS : I think the question is not making any sense. It something like - the values of a,b,c are given and suddenly the question is asking x+y+z

AnkitK wrote:
triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654

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Damn missed the checks ! Thanks fluke !

fluke wrote:
gmat1220 wrote:
The answer is E.

S1 says that the sides are consecutive integers and one of the side is 4. There can be three possibilities
3,4,5(It is a pythagorean triplet and must be a right angle triangle)
2,3,4(It is a NOT pythagorean triplet 2^2+3^2 != 4^2 and must NOT be a right angle triangle)
1,2,3(Not possible because sum of two sides is equal to the third)
Clearly insufficient

S2 says that triangle A is not a right angle. I still have two cases i.e. 2,3,4 and 1,2,3. Clearly insufficient

Combining 1) and 2) two cases are left(Just one case: 2,3,4). Answer E(C)

PS : I think the question is not making any sense. It something like - the values of a,b,c are given and suddenly the question is asking x+y+z

AnkitK wrote:
triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1252
Location: United States (IN)
Concentration: Strategy, Technology

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1
x = 3

(1)

So 2 possible triplets

3,4,5

2,3,4

1,2,3 is not possible as 2 = 3-1

Insufficient

(2)

Insufficient

(1) + (2)

It's not a pythagorean triplet from (2)

so 2,3,4

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Joined: 08 May 2009
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Concept: If a,b,c are the measurements of 3 sides of a triangle. Then measurement of b will be considering a<b<c

c-a < b < c+b .

Since x = 3

a gives 2,3,4 and 3,4,5. Not sufficient.

b still the sides can be 3,5,7 or 2,3,4 etc. Not sufficient.

a+b means 3,4,5 is not the measurements.It is 2,3,4.

Hence C.
Director  Joined: 01 Feb 2011
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1. Not sufficient

as the sides could be anyone of this combination 3,4,5 or 2,3,4

2. Not sufficient
not a right angled triangle

together we can eliminate the 2,3,4

Sufficient

Senior Manager  Joined: 02 Mar 2012
Posts: 271
Schools: Schulich '16
Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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C

x=3(given)
1) three possibilities:
1,2,3(this is not a possible triangle as 1+2=3 not >3)
2,3,4
3,4,5(right angled)

2)not a right angled.insuff ok its not right angled..but we ddont know other 2 sides

1+2

only one case 2,3,4

so ans is C
Manager  Joined: 13 Jun 2016
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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so if it i s 2-3-4 pair, what is the area? 2*3/ 2 ? Bunuel can you help?
Intern  Joined: 29 Jun 2016
Posts: 41
Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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alpham wrote:
so if it i s 2-3-4 pair, what is the area? 2*3/ 2 ? Bunuel can you help?

It is not a right angled triangle so we cannot use it directly
Instead when three sides of a triangle are known
the area of a triangle whose sides have lengths a, b, and c is

the area pf a trainagle A = sqrt{s(s-a)(s-b)(s-c)},
where s is the semiperimeter of the triangle; that is,
s=(a+b+c)/2
Intern  Joined: 29 Jun 2016
Posts: 41
Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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in this case as s=9/2
Area=sqrt(9/2*5*2*3/2*1/2)
=3/4*sqrt(15)
Current Student S
Joined: 23 Jul 2015
Posts: 143
Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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AnkitK wrote:
triangle A has one side of lenght x. if x^4=81 what is the perimeter of triangle A?
1.Triangle A has sides whose lengths are consecutive integers
2.Triangle A is not a right triangle.

What i want to know is what exactly does it mean to say Triangle A is not a Rt triangle in context to question above,It is not making sense to me.

$$x^4$$ = 81 --> x=3

stmt 1 - two possibilities {2,3,4} or {3,4,5} --> Insuff.
stmt 2 - Many possibilities --> Insuff

1 &2 only {2,3,4} possible --> Suff --> Ans is C
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Re: triangle A has one side of lenght x. if x^4=81 what is the  [#permalink]

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_________________ Re: triangle A has one side of lenght x. if x^4=81 what is the   [#permalink] 22 Oct 2018, 07:15
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