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For a given triangle with sides x,3x and 24, what is the
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01 Aug 2013, 03:37
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For a given triangle with sides x,3x and 24, what is the value of the perimeter? I. (x3)(x10) = 0 II.The perimeter is a perfect square. Source: My own.
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Re: For a given triangle with sides x,3x and 24, what is the
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01 Aug 2013, 04:47
Rule for triangles: the sum of two sides must be grater than the third side. For a given triangle with sides x,3x and 24, what is the value of the perimeter?I. \((x3)(x10) = 0\)So x can be 3, and the sides would be \(3,9,24\) <== this is not a triangle as \(3+9<24\). Or x can be 10, and the sides would be \(10,30,24\) <== this is a legit triangle. Sufficient II.The perimeter is a perfect square.Applying the rule we get \(3x+x>24\) or \(x>6\) \(24+3x>x\) or \(12+2x>0\) (this is irrelevant as it's always truex must be positive) \(24+x>3x\) or \(12>x\). So \(12>x>6\) and the perimeter will range from if \(x=12\), \(P=72\)  if \(x=6\) \(P=48\). Between 48 and 72 there are the following perfect squares: \(49,64\). Thus x could have two values, and the perimeter would change. Not sufficient
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Re: For a given triangle with sides x,3x and 24, what is the
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01 Aug 2013, 04:08
mau5 wrote: For a given triangle with sides x,3x and 24, what is the value of the perimeter?
I. (x3)(x10) = 0
II.The perimeter is a perfect square.
OA after some discussion. From I X = 3 or X = 10, Plugging into stem 3 + 9 + 24 = 36 or 10 + 30 + 24 = 64...not sufficient From II...not enough info I + II both potential answers are perfect squares, not sufficient..
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Re: For a given triangle with sides x,3x and 24, what is the
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03 Aug 2013, 08:08
mau5 wrote: For a given triangle with sides x,3x and 24, what is the value of the perimeter?
I. (x3)(x10) = 0
II.The perimeter is a perfect square.
Source: My own. I is sufficient it is clear II x+3x+24=A*2 4x+24=A*2 4(X+6)=A*2 2*2 (X+6)= A*2 solution are x = 3, 10, 19, 30, 43... for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10 x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19 x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30 So from II statement x is only 10 The answer is D.



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Re: For a given triangle with sides x,3x and 24, what is the
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03 Aug 2013, 08:16
bboev wrote: mau5 wrote: For a given triangle with sides x,3x and 24, what is the value of the perimeter?
I. (x3)(x10) = 0
II.The perimeter is a perfect square.
Source: My own. I is sufficient it is clear II x+3x+24=A*2 4x+24=A*2 4(X+6)=A*2 2*2 (X+6)= A*2 solution are x = 3, 10, 19, 30, 43... for x=3 sides would be 3, 9, 24, but 3+9<24 can not be sides of triangle x=10 sides would be 10, 30, 24 and 10+24>30 , x can be 10 x=19 sides would be 19, 57, 24 but 19+24<57 , x can not be 19 x=30, sides would be 30,90, 24 but 30+24<90 , x can not be 30 So from II statement x is only 10 The answer is D. You are assuming that x can only be an integer. you get a perfect square for \(x = \frac{25}{4}\) and forms a valid triangle.
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Re: For a given triangle with sides x,3x and 24, what is the
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03 Aug 2013, 08:23
i  sufficient. i think that is easy ii  24+x > 3X So X < 12 and x+3x>24 then X > 6 24+4X perfect square x can only 10 Sufficient
So D



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Re: For a given triangle with sides x,3x and 24, what is the
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03 Aug 2013, 08:28
AMITAGARWAL2 wrote: i  sufficient. i think that is easy ii  24+x > 3X So X < 12 and x+3x>24 then X > 6 24+4X perfect square x can only 10 Sufficient
So D Nope.Please refer to the post above. Thanks.
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Re: For a given triangle with sides x,3x and 24, what is the
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05 Aug 2013, 14:21
mau5 wrote: AMITAGARWAL2 wrote: i  sufficient. i think that is easy ii  24+x > 3X So X < 12 and x+3x>24 then X > 6 24+4X perfect square x can only 10 Sufficient
So D Nope.Please refer to the post above. Thanks. it's an obvious (A). because x=3 or x=10 . for a triangle with such sides (x,3x and 24) it's not possible that x=3. because x+3x>24 have to be true always). so x=10 and we know the perimeter = 4x+24=64 st(2) is not needed at all. Answer is (A)
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Re: For a given triangle with sides x,3x and 24, what is the
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05 Jul 2018, 00:44
mau5 wrote: For a given triangle with sides x,3x and 24, what is the value of the perimeter?
I. (x3)(x10) = 0
II.The perimeter is a perfect square.
Source: My own. #From first statement we have one value satisfying triangle's properties..ie x=10 *Strike out BCE. Ans must be A or D *Now perimeter is 4x+24 #According to statement 2 it must b a perfect square...and because of traingles properties x must b greater than equals to 7 and less than 12(PROPERTY OF TRIANGLE I M TALKING ABOUT IS THAT SUM OF ANY TWO SIDES IS ALWAYS GREATER THAN THE THIRD ONE) *4x+24= 64 is only condition in which x lies b/w 7 and 12(7 inclusive) **SO ANS IS (D) I ASSUMED THAT IS AN INTEGER Sent from my Redmi Note 4 using GMAT Club Forum mobile app



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Re: For a given triangle with sides x,3x and 24, what is the
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05 Jul 2018, 01:01
mau5 wrote: For a given triangle with sides x,3x and 24, what is the value of the perimeter?
I. (x3)(x10) = 0
II.The perimeter is a perfect square.
Source: My own. sides x, 3x and 24 so x+3x > 24 4x > 24 x > 6 1.x=3,x=10 since x is > 6 , x=10 sufficient 2. x+3x+24 = a^2 4x+24=perfect square perfect squares > 24 are 36 for which 4x=12 , x =3 but x should be > 6 49 for which 4x=25 , x=6.25 64 for which 4x=30 , x=7.50 ... insufficient A it is !!




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