If a rope is cut into three pieces of unequal length, what is the leng

Question

If a rope is cut into three pieces of unequal length, what is the length of these pieces of rope?

(1) The combined length of the two longer pieces is 12 meters.

(2) The combined of the two shorter pieces is 11 meters.

nageshbvrch · Accepted Answer

If a rope is cut into three pieces of unequal length, what is the length of the shortest of these pieces of rope?
(1) The combined length of the longer two pieces of rope is 12 meters.
(2) The combined length of the shorter two pieces of rope is 11 meters.

Explanation:

I think the question is little ambiguity,

It is understood the question can not be solved by individual statements.

Let us combine both the statements and see....

According to the date S + M + L = Total length (T), shortest (S), largest (L), Middle (M)

(1) The combined length of the longer two pieces of rope is 12 meters. i.e., M + L = 12
(2) The combined length of the shorter two pieces of rope is 11 meters. i.e., S + M = 11

If we subtract both we get L - S = 1, that is the longest of the three is 1 greater than the shortest of the three ( L = S + 1 )

Now if S + M = 11 and M + L = 12, then 5.1 + 5.9 = 11 and 5.9 + 6.1 = 12 , and 5.1 + 5.9 + 6.1 = T ( 17.1) , here the greatest number is 1 greater than the least number, and the total value is 17.1

But 5.2 + 5.8 = 11 and 5.8 + 6.2 = 12 , and 5.2 + 5.8 + 6.2 = T ( 17.2) , here the greatest number is 1 greater than the least number, and the total value is 17.2

We can also check few more decimal values 5.01 + 5.99 = 11 and 5.99 + 6.01 = 12 , and 5.01 + 5.99 + 6.01 = T ( 17.01) , here the greatest number is 1 greater than the least number, and the total value is 17.01.

In the above three cases the lease value could be 5.2, 5.1, 5.01,..... and many more, 
so we can not determine the least value as the total is not defined.

The correct answer is E.

camel · Answer

I got E. I don't see how you could know from the info provided and considering the fact that the peices are not perfect integer lengths.

What is the answer?

wonder_gmat · Answer

Just a correction. I think it asks to find the length of  shortest  piece. It's problem 7 of section 2, right?

LakerFan24 · Answer

can't you just take a look here and notice: i have 3 variables, but only 2 (different) equations. therefore, automatically "E"?

Gladiator59 · Answer

Three pieces are of unequal length. We need to find the sum of lengths of all the pieces.

(1)  Insufficient   as length of third piece is unknown.

(2)  Insufficient  for same reason as above.

(1) + (2) together:   At first glance looks like two equations and two unknowns but on solving...  
Lets say L, M , S are the three pieces,

L + M = 12
M + S = 11

L - S = 1
L = S + 1
 If we substitute either L or S above, we just get the other equation.

Again, we cannot solve this as no further info is available.

Hence  Option (E)  is correct.

Best,
Gladi

dave13 · Answer

statement one: the length of the two longer pieces could be 5 and 7 or 4 and 8 INSUFFICIENT statement two: the length of the two shorter pieces could be 3 and 8 INSUFFICIENT COMBINING BOTH STILL INSUFFICIENT E

Gmatprep550 · Answer

Hi  LakerFan24

I thought the same and selected option E, but sometime in GMAT they make options with such twist that we can find answer in same kind situations we had in this question. Like ans might would have been possible if question would have said length of all 3 pieces were in sequence.

Eduardo86 · Answer

Think of the 3 lengths as AX XY and YB and AB is the total length, which we do not know the value.

1) AX + XY= 12 not sufficient because we do not the value of YB

2) XY + YB= 11 not sufficient because we do not know the value of AX

1+2) AX+XB=12
 XY+YB=11

as a result, we have AX-YB=1 we still do not know the value of AX and YB so not sufficient.

Pranavb1302 · Answer

i have 3 variables, but only 2 (different) equations
let 3 pieces be of length a,b,c
let length a>b>c
therefor a+b = 12
b+c = 11

solving it will give a-c = 1
hence E both are not sufficient

kungfury42 · Answer

Let the pieces be of lengths  a, b,  and  c  respectively where  a \geq b \geq c

(A)  a+b=12 . Insufficient as we don't know how small the third piece would be. One possible combination is  8+4+2=14  and other possible combination is  8+4+1=13 . Insufficient.

(B)  b+c=11 . Insufficient as we don't know how large the first piece would be. One possible combination is  20+8+3=31  and other possible combination is  40+8+3=51 . Insufficient.

Combining the two we get,
 a+b=12  and  b+c=11 
Upon simplification we get  a=c+1 
Now we know that  c  cannot be  >  than  5.5 
So let's build two cases and test

Case1:  
 c=5.5  Therefore,  a=6.5  Therefore,  b=5.5 
Therefore,  Total=6.5+5.5+5.5=17.5

Case2:  
 c=5  Therefore,  a=6  Therefore,  b=6 
Therefore,  Total=6+6+5=17

Clearly as we are arriving at two different answers even on combining the statements, we can safely say that the two statements are even together insufficient.

Hence, E.

bumpbot · Answer

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If a rope is cut into three pieces of unequal length, what is the leng

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