is the range of the numbers in S greater that 2?

[Mom4MBA]

This question is from OG

If S is a set of four numbers w,x,y,z, is the range of the numbers in S greater that 2?
1) w-z>2
2) z is the least number in S

OA is A

Had it been mentioned that S is an ordered pair of elements, the OA would have been justified. But the question does not tell us about the order, so shouldn't the answer be E.

[Rahul@gurome]

Solution
Range is the difference between the maximum and the minimum value of a given set of numbers or in other words the maximum of the differences between any two pair of numbers in the set.
First consider (1).
w-z>2.
It means that the difference between one pair of numbers in the set is more than 2.
So obviously range has to be more than this value.
Or we can say that range is more than 2.
(1) is sufficient.
Next consider (2).
It says z is the least number in S, but we need to know more about the least and the maximum value to answer the question.
(2) is not sufficient

The correct answer is (A).

[Mom4MBA]

Thanks Rahul.
I was missing on this point

in other words the maximum of the differences between any two pair of numbers in the set.

Now the answer is making sense.

[ssuarezo]

hi Rahul:

I still dont understand your reasoning. the maximum of the differences between any two pair of numbers in the set.
If I have 4, 3, 1, 8, then stm1 could be 4-1>2, but 8-4>3, so as Mom says, if the sets were ordered, it would make sense, but its not any pair in the set, as u said, range is the max value minus the min value. Did I miss something?

Solution
Range is the difference between the maximum and the minimum value of a given set of numbers or in other words the maximum of the differences between any two pair of numbers in the set.
First consider (1).
w-z>2.
It means that the difference between one pair of numbers in the set is more than 2.
So obviously range has to be more than this value.
Or we can say that range is more than 2.
(1) is sufficient.

Thanks
Silvia

[Mom4MBA]

Hi Silvia,

let the set be 4, 3, 1, 8

now difference between any two numbers of the set will be

4-3=1
3-1=2
4-8=-4
8-4=4
1-8=-7
3-8=-5
8-3=5
and so on

the range will be 8-1=7 (largest - smallest)

see the range is and always will be greater than the difference between any two numbers of the set
so if the difference between any two numbers is >2 then obviously the range will be >2
so statement 1 is sufficient, and the order is not important

[ssuarezo]

Thanks Mom (even if u r not my mom !) ..
it's more than clear now.

Hi Silvia,

see the range is and always will be greater than the difference between any two numbers of the set
so if the difference between any two numbers is >2 then obviously the range will be >2
so statement 1 is sufficient, and the order is not important

[lordspace]

Thanks Rahul & Mom for explanation of range.

I was going for answer E.

[RadiumBall]

Actually I still don't get this...so range is always the difference between the largest and the smallest numbers no matter any order...but who has told us that 'w' is the largest number and 'z' is the smallest number? I dont see how this was assumed...

[Geva@EconomistGMAT]

It's not assumed that they are the larges and the smallest. But consider the case where they are not the largest and the smallest: that just means that there is another term that is larger than W, or a term that is smaller than z. The range in such a case will grow even greater than just the difference between r and z. So whether r and z are the greatest and smallest pair, or some there's some other pair with an even greater difference, the range of the set is greater than 2.

[bigge2win]

None of these explanations still make any sense to me whatsoever. w-z>2, but that doesn't tell me anything about x and y. Isn't it possible that x-z can be greater than 0, but less than 2? Am I missing something very fundamental here?

[anuprajan5]

None of these explanations still make any sense to me whatsoever. w-z>2, but that doesn't tell me anything about x and y. Isn't it possible that x-z can be greater than 0, but less than 2? Am I missing something very fundamental here?

Think about the relative positioning of the variables.

If x and y are the outer numbers, then if w-z>2 and therefore the range will be greater than 2. Example if x,z,w,y (ascending) were 0,0,3,3, then y-x - the range is greater than 2.

If x and y are the inner numbers, then if w-z>2 and therefore the range will be greater than 2. Example if z,x,y,w (ascending) were 0,1,2,3, then w-z - the range is greater than 2.

If x and y are inner and outer then if w-z>2 and therefore the range will be greater than 2. Example if z,x,w,y (ascending) were 0,1,3,3, then y-z - the range is greater than 2.

Regards
Anup