Data Sufficiency

Nijeesh wrote:why can't it be C

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


this statements gives Y+Z=12, so let say 6+6=12 (length of longer ropes 6 and 6)

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

this gives us X+Y=11 or X+Z=11 , now X can be only 5..so 5+6=11

so shorter rope length is 5

another set of values
1) Y+Z=12, say 7+5=12 (longer ropes 7 and 5)
2) X+z=11, here we can't have X as 6 (to make X+Z as 11 we need X as 6 and Z=5 from (1) )since according to the given data..these are shorter ropes..

so only possible values are Y+Z=12, 6+6=12 (length of longer ropes 6 and 6)
X+Y=11 or X+Z=11 , so 5+6=11


is this not right ?

Stuart Kovinsky 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,

Hi,

you still only have 3 distinct equations for your 4 variables; you cannot create the 4th equation as you've attempted.

What you've done is a more complicated variation of taking:

y = x + 3

and

4 = 4

and combining them to get:

y + 4 = x + 7

and then using:

y = x + 3
and
y + 4 = x + 7

to solve for x and y; you'll end up with 0=0 if you try to solve those equations.

You'll find if you try to solve the equations you've set up, the same thing will happen; since the third equation is a combination of the first two, it's not distinct.

So, here's the rule:

to solve for a system of n variables, one requires n distinct, linear, equations.

This rule is THE most powerful tool for data sufficiency; the better you know it (and all the exceptions), the fewer calculations you'll have to make on DS questions.

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.