If a wire 27 meters long is cut into three pieces of three

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)

Answer: B

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.

Answer: B.
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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

Thanks in advance

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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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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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

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

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,
Rich
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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.
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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
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OFFICIAL GMAT EXPLANATION

If x, y, and z represent the lengths of the pieces of wire, where x < y < z, then x + y + z = 27.

From (1), z = 2x and so x + y + 2x = 3x + y = 27. Both x and y can vary in this equation. For example, if x = 5, then y = 12 and z = 10, but if x = 5.5, then y = 10.5 and z = 11. Therefore, (1) alone is not sufficient to determine the length of the longest piece of wire.

From (2), x + y = 15 so z = 27 – 15. Therefore, (2) alone is sufficient to determine the length of the longest piece of wire.

The correct answer is the second answer choice.

A + B +C = 27 given
15 + C = 27
C = 12

12 will be the longest because we will rule out the possiblity of 14, 1 and 13 ,2 or 12,3 becasue sum of two shorter side is 12

Answer: B

excellent question

2) is pretty obvious; here's my way of solving 1)

Assume longest is 2X, shortest is X, than the middle one is going to be 27-3X;

since 2X>27-3X>X so 5.4<X<6.75 -- insufficient

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