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

While our mind tends to assume that the series is arranged from lowest to largest value, there is no explicit mention of this in the question.

Statement 1 : x > w + 4
The essence of this question is the uncertainty whether the series is arranged in Ascending order or Descending order i.e
we have two cases
case 1:: x<w -- Series is arranged in Ascending order
Range is Greatest number - smallest number = w - x
then rephrase the stem as "Is (w-x < 4)?
statement 1--> x> w+ 4
or x-w >4
or w - x < -4
this provides us with a 'Yes' to the rephrased question.

But, for case2 ::x>w -- Series is arranged in Descending Order
Range is Greatest number - smallest number = x - w
the rephrased question becomes "is (x-w) < 4 ? "
statement 1---> x-w >4
We get an answer "No" to the rephrased question

Since we cannot determine from statement 1 which case to choose from, statement 1 is insufficient .


Statement 2:: y – 5 > z
or y > z+5.
Clearly insufficient as no information about the greatest and smallest number is given to find out the range.

Combining statement (1) & (2)
This tells us that 'y' is certainly greater than 'z'. This further tells us that the series is arranged in Descending order. So statement 1 & 2 together gives us the information to select case 2(previously explained) and hence come to a definite answer.

"C"

X>w holds good for my understanding.. but unable to grasp the case when x<w...

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Target question: Is the range of the numbers in S less than 4?
ASIDE: Range = (greatest value) - (least value)

KEY CONCEPT: If the range of a set containing 2 values = k, then adding additional values to the set cannot decrease the range.
For example, the set {3, 10} has a range of 7
If we add more values to the set, we cannot make the range less than 7

Statement 1: x > w + 4
Subtract w from both sides to get: x - w > 4
This us tells us that the range of the set {x, w} is already greater than 4
So, if we add y and z, the range of the set {w, x, y, z} MUST be greater than 4
So, the answer to the target question is NO, the range is NOT less than 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y – 5 > z
Add 5 to both sides to get: y > z + 5
Subtract z from both sides to get: y - z > 5
This us tells us that the range of the set {y, z} is already greater than 5
So, if we add w and x, the range of the set {w, x, y, z} MUST be greater than 5
So, the answer to the target question is NO, the range is NOT less than 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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Hi ,

Could you please explain me on what basis you have assumed that series of VARIABLES given are arrange in ascending and descending order.

We don't need to actually arrange the variables in ascending order. We just need to recognize that we CAN always arrange variables in ascending or descending order.

In you solution you have assume that x is the smallest number and w is the largest number but its not stated in the ques.... one ca assume that Y is the smallest number and W is the largest.... In that case How will the statement 1

I believe you're referring to statement 1 (x > w + 4)
We can rewrite this as: w + 4 < x
Also know that w < w + 4, we can write: w < w + 4 < x
In other words, w < x
So, among those TWO values (w and x), we can be certain that w is smaller, and x is bigger.

Likewise, statement 2 indirectly tells us that z < y
So, among those TWO values (z and y), we can be certain that z is smaller, and y is bigger.

So, as you can see, we can make some conclusions about PAIRS of variables.

We know from statement 1 that x>w but we do not know anything about y and Z.
Similarly from statement 2 we know that y>z, and we do not know anything about x and w.
How can we infer that x<y<z<w from statement1 and statement2 alone. Unless we assume that x,y,z, and w is - x<y<z<w, I think the answer is E. what am I missing here?