Last visit was: 19 Jul 2025, 16:59 It is currently 19 Jul 2025, 16:59
Close
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
Your Progress

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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
 [34]
4
Kudos
Add Kudos
30
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
 [13]
4
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
General Discussion
User avatar
Senthil7
Joined: 31 Mar 2016
Last visit: 05 Mar 2017
Posts: 323
Own Kudos:
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
GMAT 1: 670 Q48 V34
Posts: 323
Kudos: 211
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
rt1601
Joined: 12 Jul 2013
Last visit: 15 Jun 2017
Posts: 5
Own Kudos:
1
 [1]
Given Kudos: 84
Posts: 5
Kudos: 1
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Official Solution:


The range of a set is the difference between the largest and smallest elements of a set.

\(range_t=t_{max}-t_{min}\);

\(range_s=s_{max}-s_{min}\);

Question: \(range_{t \text{ and } s} \gt (t_{max}-t_{min})+(s_{max}-s_{min})\)?

(1) The largest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{max} \gt s_{max}\), so the largest element of combined set is \(t_{max}\) but we still don't know which is the smallest element of combined set:

If it's \(t_{min}\) then the question becomes is \(t_{max}-t_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(0 \gt s_{max}-s_{min}\) and the answer would be NO;

If it's \(s_{min}\) then the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\) and the answer would be sometimes NO and sometimes YES. Not sufficient.

(2) The smallest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{min} \gt s_{max}\), so the largest element of the combined set is \(t_{max}\) and the smallest element of the combined set is \(s_{min}\).

So the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\)? And that is given to be true, so the answer is YES. Sufficient.


Answer: B

Hi Bunuel,

Wont the hypothesis break down in the following screnario

T=[1,2,3,4,5]
S=[0,0,0,0]

so the answer to the question would be "E" cannot be determined.

Kindly let me know if i have misunderstood.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
742,792
 [2]
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rt1601
Bunuel
Official Solution:


The range of a set is the difference between the largest and smallest elements of a set.

\(range_t=t_{max}-t_{min}\);

\(range_s=s_{max}-s_{min}\);

Question: \(range_{t \text{ and } s} \gt (t_{max}-t_{min})+(s_{max}-s_{min})\)?

(1) The largest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{max} \gt s_{max}\), so the largest element of combined set is \(t_{max}\) but we still don't know which is the smallest element of combined set:

If it's \(t_{min}\) then the question becomes is \(t_{max}-t_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(0 \gt s_{max}-s_{min}\) and the answer would be NO;

If it's \(s_{min}\) then the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\) and the answer would be sometimes NO and sometimes YES. Not sufficient.

(2) The smallest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{min} \gt s_{max}\), so the largest element of the combined set is \(t_{max}\) and the smallest element of the combined set is \(s_{min}\).

So the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\)? And that is given to be true, so the answer is YES. Sufficient.


Answer: B

Hi Bunuel,

Wont the hypothesis break down in the following screnario

T=[1,2,3,4,5]
S=[0,0,0,0]

so the answer to the question would be "E" cannot be determined.

Kindly let me know if i have misunderstood.

For this case you still have an YES answer to the question for (2). The range of combined set is 5 and the sum of the ranges of T and S is 4 + 0 = 4.
avatar
digvijay99
Joined: 29 Nov 2016
Last visit: 02 Jun 2019
Posts: 1
Own Kudos:
2
 [1]
Given Kudos: 8
Posts: 1
Kudos: 2
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
what if
s =( 2,3,40) &
t= (41,41,41)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
742,792
 [1]
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
digvijay99
what if
s =( 2,3,40) &
t= (41,41,41)

In this case the range of combined set would be 41 - 2 = 39 and the sum of the ranges of S and T would be 38 + 0 = 38. So, for (2) you'll get the same YES answer to the question, we've got in the solution.

Does this make sense?
avatar
22jadhavajit
Joined: 28 Mar 2017
Last visit: 21 Aug 2018
Posts: 7
Own Kudos:
Given Kudos: 229
GMAT 1: 550 Q43 V23
GMAT 1: 550 Q43 V23
Posts: 7
Kudos: 6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
avatar
Canteenbottle
Joined: 10 Jan 2018
Last visit: 28 May 2019
Posts: 11
Own Kudos:
Given Kudos: 19
Location: United States (NY)
GMAT 1: 710 Q49 V38
GMAT 2: 770 Q51 V44
GPA: 3.36
GMAT 2: 770 Q51 V44
Posts: 11
Kudos: 9
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What about both S and T are single element set? Let S = {0} and T = {1} . T's smallest element is larger than S's biggest element . S and T can merge into {0,1} with range to be 1. The sum of the range of S and T is 1. So (2) is insufficient. What's wrong with this logic?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Canteenbottle
What about both S and T are single element set? Let S = {0} and T = {1} . T's smallest element is larger than S's biggest element . S and T can merge into {0,1} with range to be 1. The sum of the range of S and T is 1. So (2) is insufficient. What's wrong with this logic?

The range of a single-element set is 0.
avatar
AkarshS
Joined: 15 May 2018
Last visit: 10 Apr 2019
Posts: 8
Own Kudos:
3
 [2]
Given Kudos: 26
GMAT 1: 750 Q51 V40
GRE 1: Q166 V164
GPA: 3.97
WE:Consulting (Consulting)
GMAT 1: 750 Q51 V40
GRE 1: Q166 V164
Posts: 8
Kudos: 3
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let us take 2 sets:
1) S = {1,2,3}
2) T = {4,6}

This satisfies statement 2.
Range of S = 2
Range of T = 2
Total = 4
Range of S,T = 5

It satisfies, so far so good.

Now take t ={4,5}, with S remaining same. Now Range of S,T is 4 and not greater than the sum. Answer should be (E) I believe
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AkarshS
Let us take 2 sets:
1) S = {1,2,3}
2) T = {4,6}

This satisfies statement 2.
Range of S = 2
Range of T = 2
Total = 4
Range of S,T = 5

It satisfies, so far so good.

Now take t ={4,5}, with S remaining same. Now Range of S,T is 4 and not greater than the sum. Answer should be (E) I believe

In case S = {1, 2, 3} and T = {4, 5}.

The sum of ranges of sets S and T = 2 + 1 = 3, while the range of combined set is 4. So, you'd still have an YES answer. The correct answer to the question is B, as explained above.
avatar
Milind27
Joined: 03 May 2017
Last visit: 29 Jan 2020
Posts: 4
Own Kudos:
1
 [1]
Given Kudos: 1
Location: India
Concentration: General Management, Technology
Schools: HEC Montreal
Schools: HEC Montreal
Posts: 4
Kudos: 1
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

Let's say:
S: 2
T: 4,6

Range of (S,T) will not be greater than individual ranges.

Let;s say:
S:1
T:7,9

Range of (S,T) will be greater than individual ranges.

Please guide :)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Milind27
Hi Bunuel,

Let's say:
S: 2
T: 4,6

Range of (S,T) will not be greater than individual ranges.

Let;s say:
S:1
T:7,9

Range of (S,T) will be greater than individual ranges.

Please guide :)

S: 2 --> range = 0
T: 4,6 --> range = 2
Combined {2, 4, 6} --> range = 4.
avatar
shubhgmat
Joined: 09 Dec 2018
Last visit: 06 Sep 2020
Posts: 15
Own Kudos:
Given Kudos: 5
Location: India
GMAT 1: 650 Q47 V32
GPA: 3
Products:
GMAT 1: 650 Q47 V32
Posts: 15
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Very nice question that actually tests your DS skills.For option 1, you can very easily get lost with it you just assume that you do not have the sufficient info to get to the answer. Fortunately, i was able to get it right but could have got it wrong had the second scenario in option 1 given the answer as No.
User avatar
SharmaGyan
Joined: 25 Jan 2020
Last visit: 07 Jul 2021
Posts: 15
Own Kudos:
30
 [3]
Given Kudos: 8
Location: India
Schools: IIMC PGPEX'22
GMAT 1: 730 Q50 V39
GPA: 4
WE:Sales (Computer Software)
Schools: IIMC PGPEX'22
GMAT 1: 730 Q50 V39
Posts: 15
Kudos: 30
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To visualize the official explanation by our mythical master, please refer the diagram below:


Only way in which we can get a sure answer is when there is no overlap.
Attachments

Solution.png
Solution.png [ 10.2 KiB | Viewed 5211 times ]

avatar
Michele4
Joined: 23 Oct 2020
Last visit: 06 Jun 2021
Posts: 20
Own Kudos:
Given Kudos: 46
Posts: 20
Kudos: 5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Official Solution:


The range of a set is the difference between the largest and smallest elements of a set.

\(range_t=t_{max}-t_{min}\);

\(range_s=s_{max}-s_{min}\);

Question: \(range_{t \text{ and } s} \gt (t_{max}-t_{min})+(s_{max}-s_{min})\)?

(1) The largest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{max} \gt s_{max}\), so the largest element of combined set is \(t_{max}\) but we still don't know which is the smallest element of combined set:

If it's \(t_{min}\) then the question becomes is \(t_{max}-t_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(0 \gt s_{max}-s_{min}\) and the answer would be NO;

If it's \(s_{min}\) then the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\) and the answer would be sometimes NO and sometimes YES. Not sufficient.

(2) The smallest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{min} \gt s_{max}\), so the largest element of the combined set is \(t_{max}\) and the smallest element of the combined set is \(s_{min}\).

So the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\)? And that is given to be true, so the answer is YES. Sufficient.


Answer: B
@Bunel why 0 CANNOT BE GREATER THAN Smax- Smin??
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
742,792
 [1]
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Michele4
Bunuel
Official Solution:


The range of a set is the difference between the largest and smallest elements of a set.

\(range_t=t_{max}-t_{min}\);

\(range_s=s_{max}-s_{min}\);

Question: \(range_{t \text{ and } s} \gt (t_{max}-t_{min})+(s_{max}-s_{min})\)?

(1) The largest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{max} \gt s_{max}\), so the largest element of combined set is \(t_{max}\) but we still don't know which is the smallest element of combined set:

If it's \(t_{min}\) then the question becomes is \(t_{max}-t_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(0 \gt s_{max}-s_{min}\) and the answer would be NO;

If it's \(s_{min}\) then the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\) and the answer would be sometimes NO and sometimes YES. Not sufficient.

(2) The smallest element of \(T\) is bigger than the largest element of \(S\). Given: \(t_{min} \gt s_{max}\), so the largest element of the combined set is \(t_{max}\) and the smallest element of the combined set is \(s_{min}\).

So the question becomes is \(t_{max}-s_{min} \gt t_{max}-t_{min}+s_{max}-s_{min}\). Or: is \(t_{min} \gt s_{max}\)? And that is given to be true, so the answer is YES. Sufficient.


Answer: B
@Bunel why 0 CANNOT BE GREATER THAN Smax- Smin??

\(s_{max}\) is the greatest element of set S and \(s_{min}\) is the smallest t element of set S, so \(s_{max}>s_{min}\) (\(s_{max}-s_{min}>0\)).
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,627
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,627
Kudos: 742,792
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
Moderators:
Math Expert
102627 posts
Founder
41115 posts