The answer is E.
Let the pieces of rope in the order of length are a,b,c(the longest).
We are given
c+b = 12
a+b = 11
we can derive c-a =1

Since we can't find a unique combination of values that satisfy the above equations, they cannot be solved.

Thank you Stuart and Ian. The posts are indeed useful.

@Stuart
Sometimes by plugging in values we can arrive at a unique solution, especially when a range in which values lie is given. Can we add this to the exception to the rule which Ian has given?

E is correct

IMO:E as well!!

Even if we did not know the length explicitly we could find it implicitly. But that is not the question.

I would steer clear of all rules in equations. GMAT can be tricky as Ian rightly pointed out.
The best approach IMO is try your best to solve with the given information. First using either statements alone and then by combing both. Choose E if you fail to solve or get multiple answers.

The equations in this question are dangerously close to getting solved. Anything like integer values in the stem can give a valid solution.

An expansion of this problem could be what are the range of values for the three variables.

Answer a<b<c

5 < a < 5.5
6 < b < 5.5
6 < c

E!

selected E in 30 seconds

3 variables 2 equations, no solution=> (E) is answer

yes u r ryt.The answer is E

prinit wrote:x+y+z =?

lets assume x is the shortest x<y<z

y+z=12 --eq 1
x+y=11 -- eq 2
------------
z-x=1
=>z=1+x

now put in 1
y=12-z=> 12-1-x

now put in 2
x+12-1-x=11 ...cant solve it for x...

so answer is E ..

cgc wrote: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.

for rope x + y + z = a

1. x + y = 12

2. y + z = 11

c. can you combine the two equations to create another separate equation? For example...
y = 12 -x
(12-x) + z = 11


Are these not distinct equations to satisfy the equation/variable rule?

Please help explain.

thanks,

Long ones combined 12

Short one combined 11

so i 6 and 6 for long

and 5.1 and 5.9 for short one so 5.1 is the shortest

Option c

I am missing anything?

I got this question today with the BTG daily math emails, I'm not sure if I'm right but i would love her the experts thoughts on it.

If we can only 1 answer for the problem, then the statement or statements are Sufficient,

if We have a>b>c

from statement 1: a+b= 12 the rope isn't more than 18, L<18
from statement 2: b+c= 11 isn't shorter than 16, L>16.5
From both we know that the rope is 16.5<L<18 the difference is 1.5

and we also know that A-c =1, B is 0.5 between A and C,
if we pick numbers A=5.25
b:5.75
C:6.25
We satisfied that A+B=12
AND B+C=11

and total is 17.25 between the range 18-16.5

so I think the right answer is C unless we can find other solutions.


Regards

Kassim

I'm totally Wrong the values could also be

A=5.30
b:5.70
C:6.30

I don't know why I thought for a while it could be solved.

Regards

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.

AD BCE
A. Not Sufficient as it gives no info about the total length > X+Y = 12
D. Since is not sufficient hence D is ruled out.

B. Not sufficient as it gives no ifo about the total length > Y+Z = 11
C. Combining both we get > X-Z = 1 but still we have 2 variables but no other info
E. Which is the correct answer

U r missing that all the three are of unequal sizes

Ganesh hatwar wrote:

cgc wrote: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.

for rope x + y + z = a

1. x + y = 12

2. y + z = 11

c. can you combine the two equations to create another separate equation? For example...
y = 12 -x
(12-x) + z = 11


Are these not distinct equations to satisfy the equation/variable rule?

Please help explain.

thanks,

Long ones combined 12

Short one combined 11

so i 6 and 6 for long

and 5.1 and 5.9 for short one so 5.1 is the shortest

Option c

I am missing anything?

x+y = 12
y+z = 11

there is no way we can solve for z (the shortest piece here)

Ans: E