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

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.

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

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
­

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 ­

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.

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.

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

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.­

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