mciatto wrote:
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.
Project DS Butler: Day 12: Data Sufficiency (DS24)
For DS butler Questions Click HereLet 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.