GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2018, 15:46

### 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

# M13-26

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 48067

### Show Tags

16 Sep 2014, 00:49
1
7
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:04) correct 48% (01:27) wrong based on 111 sessions

### HideShow timer Statistics

Is the range of a combined set $$(S, T)$$ is bigger than the sum of ranges of sets $$S$$ and $$T$$ ?

(1) The largest element of $$T$$ is bigger than the largest element of $$S$$.

(2) The smallest element of $$T$$ is bigger than the largest element of $$S$$.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 48067

### Show Tags

16 Sep 2014, 00:50
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.

_________________
Current Student
Joined: 06 Mar 2014
Posts: 256
Location: India
GMAT Date: 04-30-2015

### Show Tags

09 Oct 2014, 15:07
1
Is there any way, we can present the above statements with some examples?

Some other way in which we don't have to resort to variables such as tmax and tmin.
Intern
Joined: 22 Jun 2014
Posts: 22
Concentration: General Management, Finance
GMAT 1: 700 Q50 V34
GRE 1: Q800 V600
GPA: 3.68

### Show Tags

22 Oct 2014, 19:06
imagine the two sets as two line segments in a straight line. the lines can overlap each other, one inside another or be in different place altogether. to answer the question, we need to know if the lines overlap or there is a finite distance between them?
The 1st point says the right end of line t is on the right side of right end of line s - this doesn't answer our question. The 2nd point says left end of line t is on the right side of right end of line s --> there is a finite distance between the lines. We just got our answer
Senior Manager
Joined: 31 Mar 2016
Posts: 400
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

### Show Tags

31 Aug 2016, 04:46
I think this is a high-quality question and I agree with explanation.
Current Student
Joined: 12 Jul 2013
Posts: 7

### Show Tags

23 Oct 2016, 06:19
Bunuel wrote:
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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 48067

### Show Tags

23 Oct 2016, 06:40
rt1601 wrote:
Bunuel wrote:
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.

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.
_________________
Intern
Joined: 29 Nov 2016
Posts: 3

### Show Tags

16 Jun 2017, 21:52
what if
s =( 2,3,40) &
t= (41,41,41)
Math Expert
Joined: 02 Sep 2009
Posts: 48067

### Show Tags

17 Jun 2017, 04:30
digvijay99 wrote:
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?
_________________
Intern
Joined: 28 Mar 2017
Posts: 10
GMAT 1: 550 Q43 V23

### Show Tags

25 Mar 2018, 15:57
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 10 Jan 2018
Posts: 11
Location: United States (NY)
Schools: Tuck '21
GMAT 1: 710 Q49 V38
GMAT 2: 770 Q51 V44
GPA: 3.36

### Show Tags

17 Apr 2018, 08:18
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?
Math Expert
Joined: 02 Sep 2009
Posts: 48067

### Show Tags

17 Apr 2018, 13:52
Canteenbottle wrote:
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.
_________________
Intern
Joined: 15 May 2018
Posts: 8
GMAT 1: 750 Q51 V40
GRE 1: Q166 V164
GPA: 3.97
WE: Consulting (Consulting)

### Show Tags

11 Jun 2018, 00:24
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
Math Expert
Joined: 02 Sep 2009
Posts: 48067

### Show Tags

11 Jun 2018, 05:39
AkarshS wrote:
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.
_________________
Intern
Joined: 09 Jan 2018
Posts: 3

### Show Tags

01 Aug 2018, 07:41
What if it is a single set elements . It didnt talk about number of elements .
Re: M13-26 &nbs [#permalink] 01 Aug 2018, 07:41
Display posts from previous: Sort by

# M13-26

Moderators: chetan2u, Bunuel

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.