GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 04:07

### 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

# The range of the numbers in set S is x, and the range of the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 172
The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

14 Dec 2012, 02:47
1
50
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:29) correct 26% (01:34) wrong based on 2173 sessions

### HideShow timer Statistics

The range of the numbers in set S is x, and the range of the numbers in set T is y. If all of the numbers in set T are also in set S, is x greater than y?

(1) Set S consists of 7 numbers.
(2) Set T consists of 6 numbers.
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

14 Dec 2012, 02:50
9
10
The range of the numbers in set S is x, and the range of the numbers in set Tis y. If all of the numbers in set T are also in set S, is x greater than y?

(1) Set S consists of 7 numbers. Nothing about set T. Not sufficient.
(2) Set T consists of 6 numbers. Nothing about set S. Not sufficient.

(1)+(2) It's quite easy to get two different answers. For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 7}, then x=6=y. not sufficient.

_________________
##### General Discussion
Retired Moderator
Joined: 29 Oct 2013
Posts: 245
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

07 Apr 2014, 00:55
2
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

07 Apr 2014, 01:11
5
9
MensaNumber wrote:
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!

Good observation.

We are told that all of the numbers in set T are also in set S, which means that set T is a subset of set S. As you corrected noted the range of a subset cannot be greater than the range of a whole set, thus y (the range of T) cannot be greater than x (the range of S), hence the following relationship must be true: $$x\geq{y}$$.

Similar questions to practice:
s-is-a-set-containing-9-different-numbers-t-is-a-set-contai-101912.html
if-set-s-consists-of-the-numbers-w-x-y-z-is-the-range-of-158973.html
r-is-a-set-containing-8-different-numbers-s-is-a-set-128119.html
a-is-a-set-containing-7-different-numbers-b-is-a-set-contai-102809.html
s-w-x-y-z-is-the-range-of-s-greater-than-101718.html
set-a-contains-20-numbers-and-set-b-contains-40-numbers-is-132330.html
if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html

Hope this helps.
_________________
Retired Moderator
Joined: 29 Oct 2013
Posts: 245
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

07 Apr 2014, 02:10
Thanks for validating that observation. Thanks also for providing additional practice questions. Really appreciated!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

29 Sep 2016, 06:08
3
1
We are given that the range of the numbers in set S is x and that the range of the numbers in set T is y. We also know that all of the numbers in set T are included in set S. We must determine whether x is greater than y or, in other words, whether the range of set S is greater than the range of set T. Recall that the formula for the range of a set of numbers is: range = largest number – smallest number.

Statement One Alone:

Set S consists of 7 numbers.

Without knowing anything about the values of the numbers in set S or anything about set T, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Set T consists of 6 numbers.

Without knowing anything about the values of the numbers in set T or anything about set S, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that set S contains 7 numbers and that set T contains 6 numbers. We also know from the given information that all of the numbers in set T are also in set S. However, we still do not have enough information to determine whether the range of set S is greater than the range of set T. Let’s test a few cases to illustrate.

Case #1

set T = {1,2,3,4,5,6}

y = range of set T = 6 – 1 = 5

set S = {1,2,3,4,5,6,7}

x = range of set S = 7 – 1 = 6

In the above case, x is greater than y.

Case #2

set T = {1,2,3,4,5,6}

y = range of set T = 6 – 1 = 5

set S = {1,2,3,4,5,6,6}

x = range of set S = 6 – 1 = 5

In above case, x = y.

_________________

# Jeffrey Miller | Head of GMAT Instruction | Jeff@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

SVP
Joined: 24 Jul 2011
Posts: 2122
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

22 Dec 2016, 12:01
1
1
Statement (1):
Set S consists of 7 numbers. We do not know how many numbers are in set T, other than they can at most be 7. If the range of set S is x, is is possible to define set T in such a way that it has less elements than set S, and the lowest and highest of these elements in set T is higher and lower respectively than the highest and lowest in set S. It is also possible to define set T in such a way that it is exactly similar to set S, in which case the ranges are equal. Therefore this statement alone is insufficient.

Statement (2):
This is similar to statement (1), except here we are given the number of elements in set T. So we know the number of elements in set S is six or greater, and includes all the elements in set T. Using similar logic as in statement (1), we can see that this statement too is insufficient.

Combining both the statements:
Set S has 7 elements and set T has six. We can still have the following two cases:
The lowest of set T is higher than that of set S and all other elements of set T are same as those of set S. In this case the range of set S is higher than that of set T.
The lowest and highest of set T and set S are the same. In this case the ranges are the same.

Therefore even combining both the statements is insufficient.

Another similar question for practice: http://gmatclub.com/forum/set-a-contain ... l#p1083950
_________________

Awesome Work | Honest Advice | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
SVP
Joined: 23 Feb 2015
Posts: 2005
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

24 Jan 2017, 19:39
Bunuel wrote:
MensaNumber wrote:
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!

Good observation.

We are told that all of the numbers in set T are also in set S, which means that set T is a subset of set S. As you corrected noted the range of a subset cannot be greater than the range of a whole set, thus y (the range of T) cannot be greater than x (the range of S), hence the following relationship must be true: $$x\geq{y}$$.

Similar questions to practice:
s-is-a-set-containing-9-different-numbers-t-is-a-set-contai-101912.html
if-set-s-consists-of-the-numbers-w-x-y-z-is-the-range-of-158973.html
r-is-a-set-containing-8-different-numbers-s-is-a-set-128119.html
a-is-a-set-containing-7-different-numbers-b-is-a-set-contai-102809.html
s-w-x-y-z-is-the-range-of-s-greater-than-101718.html
set-a-contains-20-numbers-and-set-b-contains-40-numbers-is-132330.html
if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html

Hope this helps.

But, how do we be sure that set S consists more numbers than set T? If i say that all the members of gmatclub can sit in the chair of stedium S, should i assume or infer that there are more chair in this stedium than the number of the members of gmat club? MAY be yes ( more chair than member)or may not be (equal number of chair and member of gmat club). If something is used as MAY, why do we take it seriously or exactly? Thank you...
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

25 Jan 2017, 05:15
iMyself wrote:
Bunuel wrote:
MensaNumber wrote:
Hi Bunuel, So 'y' can never be larger than 'x', can it? Thanks!

Good observation.

We are told that all of the numbers in set T are also in set S, which means that set T is a subset of set S. As you corrected noted the range of a subset cannot be greater than the range of a whole set, thus y (the range of T) cannot be greater than x (the range of S), hence the following relationship must be true: $$x\geq{y}$$.

Similar questions to practice:
s-is-a-set-containing-9-different-numbers-t-is-a-set-contai-101912.html
if-set-s-consists-of-the-numbers-w-x-y-z-is-the-range-of-158973.html
r-is-a-set-containing-8-different-numbers-s-is-a-set-128119.html
a-is-a-set-containing-7-different-numbers-b-is-a-set-contai-102809.html
s-w-x-y-z-is-the-range-of-s-greater-than-101718.html
set-a-contains-20-numbers-and-set-b-contains-40-numbers-is-132330.html
if-s-is-a-set-of-four-numbers-w-x-y-and-z-is-the-range-o-166184.html

Hope this helps.

But, how do we be sure that set S consists more numbers than set T? If i say that all the members of gmatclub can sit in the chair of stedium S, should i assume or infer that there are more chair in this stedium than the number of the members of gmat club? MAY be yes ( more chair than member)or may not be (equal number of chair and member of gmat club). If something is used as MAY, why do we take it seriously or exactly? Thank you...

If I understood you correctly, then answer to your question is that a set can be considered to be a subset of itself. For example, {1, 2, 3} is a subset of {1, 2, 3}.
_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4987
GMAT 1: 770 Q49 V46
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

30 Aug 2017, 14:05
Top Contributor
The range of the numbers in set S is x, and the range of the numbers in set T is y. If all of the numbers in set T are also in set S, is x greater than y?

(1) Set S consists of 7 numbers.
(2) Set T consists of 6 numbers.

Target question: Is x greater than y?

Given: The range of the numbers in set S is X. The range of the numbers in set T is Y. All of the numbers in set T are also in Set S

Statement 1 contains no information about set T, so statement 1 is NOT SUFFICIENT
Statement 2 contains no information about set S, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several conflicting scenarios that satisfy BOTH statements. Here are two:
Case a: set S = {1, 1, 1, 1, 1, 1, 4}, which means X = 3, and set T = {1, 1, 1, 1, 1, 1}, which means Y = 0. In this case, X IS greater than Y
Case b: set S = {1, 1, 1, 1, 1, 1, 1}, which means X = 0, and set T = {1, 1, 1, 1, 1, 1}, which means Y = 0. In this case, X is NOT greater than Y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

RELATED VIDEO FROM OUR COURSE

_________________
If you enjoy my solutions, you'll love my GMAT prep course.

Non-Human User
Joined: 09 Sep 2013
Posts: 15597
Re: The range of the numbers in set S is x, and the range of the  [#permalink]

### Show Tags

03 May 2020, 10:22
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: The range of the numbers in set S is x, and the range of the   [#permalink] 03 May 2020, 10:22