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

Question

If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?
 
(1) x > y + z + 6
(2) y > w – z – 1

GMATinsight · Accepted Answer

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

Bunuel · Answer

Similar question: https://gmatclub.com/forum/if-s-is-a-se ... 66184.html

Cez005 · Answer

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?

er.arun88 · Answer

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..

T1101 · Answer

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!

GMATGuruNY · Answer

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. C

dictanobis · Answer

Why is statement 1 alone not sufficient? 
St. 1 says that x > y + z + 6. Which means, x is at least 6 greater than either y or z (or maybe even both).
This proves that range is >= 6!!

Please explain how this thought process is wrong

Bunuel · Answer

If x = -6, y = -7, z = -6, the range could be less than 5 or greater than 5 depending on w.

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

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

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