Last visit was: 17 Jun 2024, 00:24 It is currently 17 Jun 2024, 00:24
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93696
Own Kudos [?]: 632376 [10]
Given Kudos: 82322
Senior Manager
Joined: 09 Mar 2017
Posts: 364
Own Kudos [?]: 835 [0]
Given Kudos: 646
Location: India
Concentration: Marketing, Organizational Behavior
WE:Information Technology (Computer Software)
Manager
Joined: 02 Nov 2015
Posts: 133
Own Kudos [?]: 58 [0]
Given Kudos: 121
GMAT 1: 640 Q49 V29
Manager
Joined: 02 Nov 2015
Posts: 133
Own Kudos [?]: 58 [1]
Given Kudos: 121
GMAT 1: 640 Q49 V29
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
1
Kudos
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
Senior Manager
Joined: 09 Mar 2017
Posts: 364
Own Kudos [?]: 835 [0]
Given Kudos: 646
Location: India
Concentration: Marketing, Organizational Behavior
WE:Information Technology (Computer Software)
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.
Intern
Joined: 25 Mar 2016
Posts: 31
Own Kudos [?]: 13 [1]
Given Kudos: 2
Location: India
Concentration: Finance, General Management
WE:Other (Other)
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
1
Kudos
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
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [4]
Given Kudos: 799
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
4
Kudos
Top Contributor
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

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE
Intern
Joined: 01 Nov 2017
Posts: 4
Own Kudos [?]: 1 [1]
Given Kudos: 20
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
1
Kudos
How can we assume that the sequence/set is in ascending or descending order?
Manager
Joined: 27 Jun 2015
Posts: 96
Own Kudos [?]: 47 [0]
Given Kudos: 57
GRE 1: Q158 V143
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

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE

Hi ,

Could you please explain me on what basis you have assumed that series of VARIABLES given are arrange in ascending and descending order.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [0]
Given Kudos: 799
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
Top Contributor
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.
Manager
Joined: 27 Jun 2015
Posts: 96
Own Kudos [?]: 47 [0]
Given Kudos: 57
GRE 1: Q158 V143
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
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [1]
Given Kudos: 799
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
1
Kudos
Top Contributor
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.
Manager
Joined: 23 Dec 2011
Posts: 66
Own Kudos [?]: 89 [0]
Given Kudos: 131
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?
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30567 [1]
Given Kudos: 799
If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
1
Kudos
Top Contributor
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
Manager
Joined: 23 Sep 2021
Posts: 132
Own Kudos [?]: 54 [0]
Given Kudos: 257
GRE 1: Q163 V157
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
Non-Human User
Joined: 09 Sep 2013
Posts: 33616
Own Kudos [?]: 838 [0]
Given Kudos: 0
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]
Moderator:
Math Expert
93697 posts