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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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X>w holds good for my understanding.. but unable to grasp the case when x<w...

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
kumarparitosh123 wrote:
X>w holds good for my understanding.. but unable to grasp the case when x<w...

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app


hello kumarparitosh123,

Thanks a lot for pointing out the fault in my reasoning. Have edited my explanation and +1 to you for helping me learn through my mistake.
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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should not the answer will be "E" ?

As the range in a set is difference of smallest number and the highest number and by using both the statement we can not deduce which is highest and which one is smallest
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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Bunuel wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S less than 4?

(1) x > w + 4
(2) y – 5 > z


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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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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How can we assume that the sequence/set is in ascending or descending order?
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
BrentGMATPrepNow wrote:
Bunuel wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S less than 4?

(1) x > w + 4
(2) y – 5 > z


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.
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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vishumangal wrote:
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.
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
BrentGMATPrepNow wrote:
vishumangal wrote:
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
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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vishumangal wrote:
BrentGMATPrepNow wrote:
vishumangal wrote:
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.
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
BrentGMATPrepNow wrote:
vishumangal wrote:
BrentGMATPrepNow wrote:
vishumangal wrote:
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?
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If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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anupam87 wrote:

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?


If the correct answer is E, then it should be possible to find sets of values for the variables that yield conflicting answers to the target question.
Try doing that and see what happens.

Cheers,
Brent
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
Concepts like these hurt my brain :shh:
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
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