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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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Bunuel
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If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink] New post   17 Sep 2017, 03:14
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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
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D
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TaN1213
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If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink] New post   Updated on: 17 Sep 2017, 05:53
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


statement 1 : x > w + 4
or x-w > 4 ------> difference of first number in the series and the last number is positive and > 4.This tells us that x>w
So this is a series arranged in descending order.
So range would be greatest number - smallest number i.e. (x-w)
So stem asks "is (x-w)<4"
So the answer is No with statement 1.
Sufficient

Statement 2:: y – 5 > z
or y - z> 5.
States that y>z ----> again implies that series is in descending order.
Secondly, if the difference between intermediate numbers in a set of four arranged in descending order, is greater than 4 then surely the difference between the largest and smallest number must be greater than 5. Even if the stem would have stated distinct integers, the range wouldn't have still been less than 4.
This provides an answer No, the range is not less than 4.
Sufficient

"D"

Originally posted by TaN1213 on 17 Sep 2017, 04:03.
Last edited by TaN1213 on 17 Sep 2017, 05:53, edited 2 times in total.
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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] New post   17 Sep 2017, 04:11
TaN1213 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


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"

Hi tan1213,
Can you pls help me in understanding the Part 1 of statement 1..
I am unable to hold the case ... I mean can u pls take any number and then use it ..

Thanks in advance !!!!

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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] New post   17 Sep 2017, 04:12
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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] New post   17 Sep 2017, 05:35
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] New post   18 Sep 2017, 10:45
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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] New post   14 Jan 2019, 11:21
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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] New post   14 Jan 2019, 23:39
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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] New post   12 May 2020, 09:59
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] New post   12 May 2020, 10:06
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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] New post   12 May 2020, 10:23
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] New post   12 May 2020, 10:53
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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] New post   23 May 2020, 14:04
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] New post   23 May 2020, 14:26
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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] New post   09 Jun 2022, 23:06
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] New post   22 Jun 2023, 10:53
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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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