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

 It is currently 19 May 2019, 23:39

### 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

# Set S contains five different positive integers a, b, c, d, and e, whe

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Feb 2017
Posts: 165
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

07 Aug 2018, 10:32
1
11
00:00

Difficulty:

95% (hard)

Question Stats:

19% (01:40) correct 81% (01:54) wrong based on 158 sessions

### HideShow timer Statistics

Set S contains five different positive integers a, b, c, d, and e, where a < b < c < d < e. Is c − b equal to d − c?
1) The mean of S is equal to the median of S
2) When any element of S is divided by 5, the remainder is 4

_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than \$)
Intern
Joined: 24 Oct 2017
Posts: 25
Location: United States (IA)
GMAT 1: 700 Q47 V38
GPA: 3.39
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

07 Aug 2018, 13:02
Why is A not sufficient? S Contains only positive integers and from A we know that the integers are evenly spaced. Is there something I'm missing or overlooking? Thank you

Posted from my mobile device
Manager
Joined: 29 Sep 2017
Posts: 118
Location: United States
Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

07 Aug 2018, 19:56
3
Saurabhminocha wrote:
Why is A not sufficient? S Contains only positive integers and from A we know that the integers are evenly spaced. Is there something I'm missing or overlooking? Thank you

Posted from my mobile device

Consider 2 sets of numbers:

Set 1:
a = 2
b = 3
c = 5
d = 7
e = 8
Sum = 25
Mean = 5
Median = 5
In this case, A works as mean = median and c-b = d-c = 2

Set 2:
a = 2
b = 3
c = 5
d = 6
e = 9
Sum = 25
Mean = 5
Median = 5
I changed the bolded numbers. Now mean = median, but d-c = 1 and c-b = 2.

Hence, A is not sufficient. I guess I should ask you this: what implies that numbers are evenly spaced? Just because numbers are positive and have a mean = median, it does not mean they are evenly spaced.
_________________
If this helped, please give kudos!
Intern
Joined: 08 Jul 2016
Posts: 38
Location: Singapore
GMAT 1: 570 Q43 V25
GMAT 2: 640 Q42 V36
WE: Underwriter (Insurance)
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

11 Aug 2018, 09:19
can you post the OE please?
Senior Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 298
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

16 Dec 2018, 15:51
1
for statement 1) The mean of S is equal to the median of S, we can conclude:
$$(a+b+c+d+e)/5 = c$$
$$a+b+c+d+e = 5c$$
$$a+b+d+e = 4c$$

the only constrain is that a<b<c<d<e,
so if we let c = 19,
then $$a+b+d+e = 19*4 = 76$$, which can be (1,2,20,53) or (1,3,20,52) or others.

so statement 1 is not sufficient.

for statement 2) When any element of S is divided by 5, the remainder is 4:
we have to choose numbers with unit digit of 4 or 9 so that the remainder remains 4 when divided by 5.

the set can be (4,9,14,19,24) or (4,9,14,99,199) or others.

so statement 2 is not sufficient.

if we tried combining:

let c = 19, and try choosing numbers with unit digit of 4 or 9 and their sum is $$4*19=76$$

set can be (4,9,19,24,39) where (d-c) not equal (c-b)
or can be (4,9,19,29,34) where (d-c) equal (c-b).

so still insufficient

so the answer is E.
_________________
..Thanks for KUDOS
Manager
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

23 Dec 2018, 08:03
Raksat wrote:
Set S contains five different positive integers a, b, c, d, and e, where a < b < c < d < e. Is c − b equal to d − c?
1) The mean of S is equal to the median of S
2) When any element of S is divided by 5, the remainder is 4

chetan2u Requesting your expert inputs.
Why is 1) and 2) together not sufficient?

1) tells us that mean and median = c

2) tells us that all numbers are of the type 5k+4
I'm unable to proceed from this point.
_________________
We learn permanently when we teach,
We grow infinitely when we share.
Senior Manager
Joined: 25 Sep 2018
Posts: 252
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

23 Dec 2018, 08:17
ScottTargetTestPrep Can you please provide an explaination?
_________________
Why do we fall?...So we can learn to pick ourselves up again

If you like the post, give it a KUDOS!
Math Expert
Joined: 02 Aug 2009
Posts: 7672
Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

24 Dec 2018, 02:43
Darshi04 wrote:
Raksat wrote:
Set S contains five different positive integers a, b, c, d, and e, where a < b < c < d < e. Is c − b equal to d − c?
1) The mean of S is equal to the median of S
2) When any element of S is divided by 5, the remainder is 4

chetan2u Requesting your expert inputs.
Why is 1) and 2) together not sufficient?

1) tells us that mean and median = c

2) tells us that all numbers are of the type 5k+4
I'm unable to proceed from this point.

Ok ..
it means are b and d equidistant from c, or whether c is the average of b, c and d.
(I) statement I tells us mean=median=c.
So if a and e are equidistant from c, Ans will be yes otherwise no..
But we can't say anything about d and e.
3,4,5,6,7.. 5 is mean and median ..Ans is yes..
1,2,5,6,11...5 is median and mean ...Ans is No
Insufficient

(II) statement II tells us that 4 is the remainder when divided by 5 ..
As correctly mentioned by you the numbers are 5k+4..
But we do not know anything about numbers..
9,14,19,24,29...yes
9,14,24,29,34...no
Insufficient

Combined..
We can still have many ways..
We can decrease the first two, a and b, and just increase only the largest e..
9,14,19,24,29..... mean=median=19...yes
4,9,19,24,29.... Mean=median=19......no
Still insufficient..
Or
The numbers are 5(k-x)+4; 5(k-y)+4, 5k+4; 5(k+a)+4; 5(k+b)+4..
Mean and median is 5k+4..
So 5a+5b-5x-5y=0...a+b=x+y
We are looking for y=b, which cannot be guaranteed here.
E
_________________
Manager
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

Updated on: 24 Dec 2018, 05:09
chetan2u wrote:
Darshi04 wrote:
Raksat wrote:
Set S contains five different positive integers a, b, c, d, and e, where a < b < c < d < e. Is c − b equal to d − c?
1) The mean of S is equal to the median of S
2) When any element of S is divided by 5, the remainder is 4

chetan2u Requesting your expert inputs.
Why is 1) and 2) together not sufficient?

1) tells us that mean and median = c

2) tells us that all numbers are of the type 5k+4
I'm unable to proceed from this point.

Ok ..
it means are b and d equidistant from c, or whether c is the average of b, c and d.
(I) statement I tells us mean=median=c.
So if a and e are equidistant from c, Ans will be yes otherwise no..
But we can't say anything about d and e.
3,4,5,6,7.. 5 is mean and median ..Ans is yes..
1,2,5,6,11...5 is median and mean ...Ans is No
Insufficient

(II) statement II tells us that 4 is the remainder when divided by 5 ..
As correctly mentioned by you the numbers are 5k+4..
But we do not know anything about numbers..
9,14,19,24,29...yes
9,14,24,29,34...no
Insufficient

Combined..
We can still have many ways..
We can decrease the first two, a and b, and just increase only the largest e..
9,14,19,24,29..... mean=median=19...yes
4,9,19,24,29.... Mean=median=19......no
Still insufficient..

E

chetan2u Many thanks for your inputs.

This is pretty much how I solved it. I was wondering if there is any algebraic method / using variables to solve and arrive at a conclusive answer, rather than using numbers (trial/error).

Or is it recommended to solve mean/median questions using real numbers?

Posted from my mobile device
_________________
We learn permanently when we teach,
We grow infinitely when we share.

Originally posted by Darshi04 on 24 Dec 2018, 02:49.
Last edited by Darshi04 on 24 Dec 2018, 05:09, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7672
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

24 Dec 2018, 04:39
Darshi04 wrote:
chetan2u wrote:
Raksat wrote:
Set S contains five different positive integers a, b, c, d, and e, where a < b < c < d < e. Is c − b equal to d − c?
1) The mean of S is equal to the median of S
2) When any element of S is divided by 5, the remainder is 4

Ok ..
it means are b and d equidistant from c, or whether c is the average of b, c and d.
(I) statement I tells us mean=median=c.
So if a and e are equidistant from c, Ans will be yes otherwise no..
But we can't say anything about d and e.
3,4,5,6,7.. 5 is mean and median ..Ans is yes..
1,2,5,6,11...5 is median and mean ...Ans is No
Insufficient

(II) statement II tells us that 4 is the remainder when divided by 5 ..
As correctly mentioned by you the numbers are 5k+4..
But we do not know anything about numbers..
9,14,19,24,29...yes
9,14,24,29,34...no
Insufficient

Combined..
We can still have many ways..
We can decrease the first two, a and b, and just increase only the largest e..
9,14,19,24,29..... mean=median=19...yes
4,9,19,24,29.... Mean=median=19......no
Still insufficient..

E

chetan2u Many thank for your inputs.

This is pretty much how I solved it. I was wondering if there is any algebraic method / using variables to solve and arrive at a conclusive answer, rather than using numbers (trial/error).

Or is it recommended to solve mean/median questions using real numbers?

Posted from my mobile device

A solution which is a bit more algebraic is...
The numbers are 5(k-x)+4; 5(k-y)+4, 5k+4; 5(k+a)+4; 5(k+b)+4..
Mean and median is 5k+4..
So 5(k-x)+4 + 5(k-y)+4 + 5k+4 + 5(k+a)+4 + 5(k+b)+4 = 5*(5k+4)..
5*(5k+4)-5x-5y+5a+5b=5*(5k+4)......
So 5a+5b-5x-5y=0......
a+b=x+y
We are looking for y=b, which cannot be confirmed as it will depend on a and x too..
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6152
Location: United States (CA)
Re: Set S contains five different positive integers a, b, c, d, and e, whe  [#permalink]

### Show Tags

28 Dec 2018, 12:04
Raksat wrote:
Set S contains five different positive integers a, b, c, d, and e, where a < b < c < d < e. Is c − b equal to d − c?
1) The mean of S is equal to the median of S
2) When any element of S is divided by 5, the remainder is 4

We need to determine whether c – b = d – c in a set of five positive integers a, b, c, d, and e where a < b < c < d < e.

Statement One Only:
The mean of S is equal to the median of S.

Knowing the mean of a set is equal to the median of the set is not sufficient to determine the answer to the question.

For example, if a = 1, b = 2, c = 3, d = 4 and e = 5, then c – b = d – c since c – b = 1 and d – c = 1.

However, if a = 1, b = 2, c = 4, d = 5 and e = 8, then c – b  d – c since c – b = 2 and d – c = 1.

Statement Two Only:

When any element of S is divided by 5, the remainder is 4.

That is, each element is in the form of 5k + 4 where k is a nonnegative integer. However, knowing each element in a specific format is not sufficient to determine the answer to the question.

For example, if a = 4, b = 9, c = 14, d = 19 and e = 24, then c – b = d – c since c – b = 5 and d – c = 5.

However, if a = 4, b = 9, c = 19, d = 24 and e = 39, then c – b  d – c since c – b = 10 and d – c = 5.

Statements One and Two Together:

Knowing both statements are still not sufficient to answer the question. We can use the same two examples in statement two since both have their respective means equal to their medians and both have elements in the form of 5k + 4.

Answer: E
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Set S contains five different positive integers a, b, c, d, and e, whe   [#permalink] 28 Dec 2018, 12:04
Display posts from previous: Sort by

# Set S contains five different positive integers a, b, c, d, and e, whe

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.