If a wire 27 meters long is cut into three pieces of three : GMAT Data Sufficiency (DS)
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# If a wire 27 meters long is cut into three pieces of three

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If a wire 27 meters long is cut into three pieces of three [#permalink]

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01 Feb 2012, 07:05
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If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

(1) The length of the longest piece is twice the length of the shortest piece
(2) The sum of the length of the two shorter pieces is 15 meters
[Reveal] Spoiler: OA

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01 Feb 2012, 07:17
Let S = shortest piece, M = middle piece, and L = longest piece. The stem says that S + M + L = 27 meters.

(1) INSUFFICIENT. The statement says L = 2S. However, the statement says nothing about the length of M. As a result, more than one solution is possible. For example, if S = 6, then L = 12 and M = 9. Or, if S = 5.5, then L = 11 and M = 10.5.

(2) SUFFICIENT. This statement says S + M = 15. If you substitute this equation into the original equation provided in the stem, you have:
S + M + L = 27 (original equation)
15 + L = 27 (substitute 15 for "S + M")
L = 12 (subtract 15 from both sides)

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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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01 Feb 2012, 10:00
If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

Actually one can solve the question without any formula.

(1) The length of the longest piece is twice the length of the shortest piece --> 6+8+12=27 or 5.5+10.5+11=27. Not sufficient.

(2) The sum of the length of the two shorter pieces is 15 meters --> if the sum of the two shorter pieces is 15 meters then longest piece must be 27-15=12. Sufficient.

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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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01 Feb 2012, 15:08
Bunuel wrote:
If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

Actually one can solve the question without any formula.

(1) The length of the longest piece is twice the length of the shortest piece --> 6+8+12=27 or 5.5+10.5+11=27. Not sufficient.

(2) The sum of the length of the two shorter pieces is 15 meters --> if the sum of the two shorter pieces is 15 meters then longest piece must be 27-15=12. Sufficient.

Hi Bunnel

I too came up with same solution

But From 2

we know that all three have different lengths and we now know that one of the lengths is 12 and sum of the other two lengths is 15, but now when you consider all 3 lengths they can be

11,3,12--------->Length of longest piece is 12
14,1,12----------->Length of longest piece is 14
13,2,12----------->Length of longest piece is 13

So we do not get a unique solution, so i marked C.......Plz correct me if i am wrong

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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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01 Feb 2012, 15:15
kotela wrote:
Bunuel wrote:
If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

Actually one can solve the question without any formula.

(1) The length of the longest piece is twice the length of the shortest piece --> 6+8+12=27 or 5.5+10.5+11=27. Not sufficient.

(2) The sum of the length of the two shorter pieces is 15 meters --> if the sum of the two shorter pieces is 15 meters then longest piece must be 27-15=12. Sufficient.

Hi Bunnel

I too came up with same solution

But From 2

we know that all three have different lengths and we now know that one of the lengths is 12 and sum of the other two lengths is 15, but now when you consider all 3 lengths they can be

11,3,12--------->Length of longest piece is 12
14,1,12----------->Length of longest piece is 14
13,2,12----------->Length of longest piece is 13

So we do not get a unique solution, so i marked C.......Plz correct me if i am wrong

Look at the red part. (2) states this in a different way: The sum of the length of the two SHORTER pieces is 15 meters, so the third one left must be the longest piece.

Does that make sense?
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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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01 Feb 2012, 17:18
Bunuel wrote:
kotela wrote:
Bunuel wrote:
If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

Actually one can solve the question without any formula.

(1) The length of the longest piece is twice the length of the shortest piece --> 6+8+12=27 or 5.5+10.5+11=27. Not sufficient.

(2) The sum of the length of the two shorter pieces is 15 meters --> if the sum of the two shorter pieces is 15 meters then longest piece must be 27-15=12. Sufficient.

Hi Bunnel

I too came up with same solution

But From 2

we know that all three have different lengths and we now know that one of the lengths is 12 and sum of the other two lengths is 15, but now when you consider all 3 lengths they can be

11,3,12--------->Length of longest piece is 12
14,1,12----------->Length of longest piece is 14
13,2,12----------->Length of longest piece is 13

So we do not get a unique solution, so i marked C.......Plz correct me if i am wrong

Look at the red part. (2) states this in a different way: The sum of the length of the two SHORTER pieces is 15 meters, so the third one left must be the longest piece.

Does that make sense?

Thanks Bunnel it makes sense

I always make silly mistakes...when i review i almost crack every problem,the problem with me is i am unable to do it during the exam time......Any suggestion please
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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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01 Feb 2012, 17:22
kotela wrote:
Thanks Bunnel it makes sense

I always make silly mistakes...when i review i almost crack every problem,the problem with me is i am unable to do it during the exam time......Any suggestion please

We all do from time to time. It will pass with practice. Just keep paying attention to all the words in the stem/statements. The GMAT questions are very well written and every word has its purpose.
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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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06 Nov 2014, 07:34
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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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18 Jan 2015, 05:56
Quote:
If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

Actually one can solve the question without any formula.

(1) The length of the longest piece is twice the length of the shortest piece --> 6+8+12=27 or 5.5+10.5+11=27. Not sufficient.

Hi,

I didn't consider the decimal option of 5.5+10.5+11=27 and got the answer wrong, as I assumed 6+8+12 is the only option that fits the statement. Not sure how can I avoid this in the exam?

Thanks
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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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18 Jan 2015, 06:18
mydreammba wrote:
If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

(1) The length of the longest piece is twice the length of the shortest piece
(2) The sum of the length of the two shorter pieces is 15 meters

Statement (I)
It does not talk about the length of middle piece! Multiple solutions possible!

Statement (II)
Gives length of two shorter pieces as 15m. What is left is longest piece!
Hence 27-15= 12m
Suficient!

Ans: B
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Re: If a wire 27 meters long is cut into three pieces of three [#permalink]

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18 Jan 2015, 12:14
Hi aj0809,

When dealing with DS questions, it helps to be a little bit cynical/suspicious. Ask yourself: "What do I REALLY KNOW? What specific details did the prompt give me and what did it NOT tell me?" In real life, there are plenty of situations in which you're not dealing with integers (the bill at a restaurant, credit card/utility bills, distance traveled, etc.), so non-integers isn't a strange concept. You have to show how THOROUGH your thinking is to pick up these points - the "math work" isn't normally that difficult, but you have to be constantly thinking about the possibilities to make sure that you have the correct answer.

GMAT assassins aren't born, they're made,
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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 10 Feb 2014 Posts: 8 Followers: 0 Kudos [?]: 0 [0], given: 6 Re: If a wire 27 meters long is cut into three pieces of three [#permalink] ### Show Tags 19 Apr 2015, 02:03 short question if we know that a+b+c = 27 they are all different means a>b>c (1) a=2c --> 2c+b+c=27 3c+b=27 / 3 c+b=9 so we know that the two shortest pieces are 9. --> The Longest is 27-9 = 18 what am I doing wrong please help Bunuel Math Expert Joined: 02 Sep 2009 Posts: 35951 Followers: 6866 Kudos [?]: 90120 [0], given: 10418 Re: If a wire 27 meters long is cut into three pieces of three [#permalink] ### Show Tags 19 Apr 2015, 02:51 stilstyle wrote: short question if we know that a+b+c = 27 they are all different means a>b>c (1) a=2c --> 2c+b+c=27 3c+b=27 / 3 c+b=9 so we know that the two shortest pieces are 9. --> The Longest is 27-9 = 18 what am I doing wrong please help Bunuel If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece? How did you get c+b=9 from 3c + b = 27? That's not correct. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8019 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 363 Kudos [?]: 2377 [0], given: 163 Re: If a wire 27 meters long is cut into three pieces of three [#permalink] ### Show Tags 19 Apr 2015, 10:53 Hi stilstyle, There are a couple of problems with what you're typed out (although most of the individual 'pieces' of your work are fine). Here's what's "fine": 1) Calling the 3 segments A, B and C 2) Stating A+B+C = 27 3) A > B > C (since the three segments are DIFFERENT lengths) 4) A = 2C (from Fact 1) 5) The substituion: A+B+C = 27 A = 2C 2C+B+C = 27 3C + B = 27 Here's what's INCORRECT: 1) The algebra after the substitution...Dividing both sides by 3 will NOT get you the result that you typed: 3C+B = 27 C + (B/3) = 9 is the correct result 2) The two "short" segment CANNOT be the same length (remember, they're DIFFERENT lengths). 3) The shortest segment CANNOT be 9. If it were, then the other two pieces would be GREATER than 9 and the total would be GREATER than 27. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: If a wire 27 meters long is cut into three pieces of three   [#permalink] 19 Apr 2015, 10:53
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