If S is a set of four numbers x, y, z and w, is the range of the numbe

Range = Highest value - Lowest value of the set

Statement 1: x > y + z + 6
This statement doesn't give us the range of the values between any two numbers of set hence
NOT SUFFICIENT

Statement 2: y > w – z – 1
This statement doesn't give us the range of the values between any two numbers of set hence
NOT SUFFICIENT

Combining the two statements

Add the two inequalities
x+y > (y + z + 6)+(w – z – 1)

i.e. x-w > 5

Since the difference of the two numbers of the set is greater than 5 hence the Range of the set is bound to be greater than 5, Hence
SUFFICIENT

Answer: Option C

Similar question: https://gmatclub.com/forum/if-s-is-a-se ... 66184.html
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1) x-6>y+z
if x=-6, y=-7, z=-6, range could be 5<= or greater depending on w. Not suff.

2) y+1>w-z
if y=3, w=4,z=2, range could be 5<= or greater depending on x. Not suff.

1)&2)

Adding the inequalities:

x > y + z + 6
y > w – z – 1

x+y>y+z+6+w-z-1
x>6+w-1
x-w>5 and therefore range must be greater than 5 if 2 elements in the set are greater than 5.

Agree?

Hi

For x>6+w-1
x-w>5

How can we take w from RHS to LHS. without knowing the sign???
and nowhere it is mentioned that w is + or _ve..

We do not need to know!
We can subtract or add variables with inequalities regardless of their signs! The sign is only important when multiplying or dividing by a variable!

I received a DM asking me to comment.
Question stem, rephrased:
Among the four numbers, is there a difference greater than 5?

Statement 1:
No information about w.
The given inequality, rephrased in terms of differences:
x-y > z+6 OR x-z > y+6
Since z+6 and y+6 can each be ANY VALUE, the two differences on the left can also be any value.
INSUFFICIENT.

Statement 2:
No information about x.
The given inequality, rephrased in terms of differences:
w-z < y+1 OR w-y < z+1
Since y+1 and z+1 can each be ANY VALUE, the two differences on the left can also be any value.
INSUFFICIENT.

Inequalities with multiple variables can be added together.
Before adding, make sure the < > faces the same direction in each inequality.

Statements combined.
Adding together x-y > z+6 and y+1 > w-z, we get:
(x-y) + (y+1) > (z+6) + (w-z)
x+1 > 6+w
x-w > 5
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.


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