Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 02:28 ### 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.  # M26-24

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56261

### Show Tags

1
8 00:00

Difficulty:   65% (hard)

Question Stats: 65% (01:51) correct 35% (01:58) wrong based on 240 sessions

### HideShow timer Statistics A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185 what is the sum of the 5 smallest integers of set A?

A. -165
B. -175
C. -195
D. -205
E. -215

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

### Show Tags

1
3
Official Solution:

A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185 what is the sum of the 5 smallest integers of set A?

A. -165
B. -175
C. -195
D. -205
E. -215

Say 7 consecutive odd integers are: $$x$$, $$x+2$$, $$x+4$$, $$x+6$$, $$x+8$$, $$x+10$$, $$x+12$$.

Question: $$x+(x+2)+(x+4)+(x+6)+(x+8)=5x+20=$$?

Given: $$(x+4)+(x+6)+(x+8)+(x+10)+(x+12)=-185$$

$$(x+4)+(x+6)+(x+8)+(x+10)+(x+12)=5x+40=-185$$

$$(5x+20)+20=-185$$

$$5x+20=-205$$

_________________
Manager  S
Joined: 11 Sep 2013
Posts: 140
Concentration: Finance, Finance

### Show Tags

9
6
Average of largest 5 = -185/5 =-37
So the largest numbers are -41, -39, -37, -35, -33

Now if we consider smallest 5, we have to eliminate last 2 numbers, which are -35 and -33

Notice here that the numbers are equally spaced.
So the average of smallest number will just shift 2 place to the left.
Avg= -41
Therefore, total = -41*5= -205
Intern  Joined: 12 Aug 2014
Posts: 3

### Show Tags

1
Can you please explain this step of the solution:

(5x+20)+20=-185

I'm having a difficult time understanding how this 20 appears
Intern  Joined: 17 Sep 2014
Posts: 2

### Show Tags

wpereira3 wrote:
Can you please explain this step of the solution:

(5x+20)+20=-185

I'm having a difficult time understanding how this 20 appears

From previous step -

(5x+20)+20=-185 is the same as (5x+40)=-185
Verbal Forum Moderator Joined: 15 Apr 2013
Posts: 181
Location: India
Concentration: General Management, Marketing
GMAT Date: 11-23-2015
GPA: 3.6
WE: Science (Other)

### Show Tags

1
Dear Buenel,

You have mentioned in the solution that

5x+20 is the "sum of five smallest" but isn't it the "Sum of five Largest" because we are dealing with negative numbers (i.e. X is negative)

If this is the case then the answer would be -175.

Math Expert V
Joined: 02 Sep 2009
Posts: 56261

### Show Tags

1
WillGetIt wrote:
Dear Buenel,

You have mentioned in the solution that

5x+20 is the "sum of five smallest" but isn't it the "Sum of five Largest" because we are dealing with negative numbers (i.e. X is negative)

If this is the case then the answer would be -175.

Our 7 consecutive odd integers are: $$x$$, $$x+2$$, $$x+4$$, $$x+6$$, $$x+8$$, $$x+10$$, $$x+12$$.

Let me ask you a question, which 5 of them are the smallest? Aren't those $$x$$, $$x+2$$, $$x+4$$, $$x+6$$ and $$x+8$$? What difference does it make whether x is negative or positive??
_________________
Senior Manager  S
Joined: 08 Jun 2015
Posts: 421
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38 GPA: 3.33

### Show Tags

Raihanuddin wrote:
Average of largest 5 = -185/5 =-37
So the largest numbers are -41, -39, -37, -35, -33

Now if we consider smallest 5, we have to eliminate last 2 numbers, which are -35 and -33

Notice here that the numbers are equally spaced.
So the average of smallest number will just shift 2 place to the left.
Avg= -41
Therefore, total = -41*5= -205

Brilliant Liked your approach !
_________________
" The few , the fearless "
Intern  Joined: 27 Apr 2015
Posts: 1

### Show Tags

A relatively easier method to lessen calculation:

Let the consecutive odd numbers be n-6, n-4, n-2, n, n+2, n+4, n+6

Given, n-2 + n + n+2 + n+4 + n+6 = -185
=> 5n = -195

Therefore, n-6 + n-4 + n-2 + n + n+2 = 5n -10 = -195 - 10 = -205. Thus solved Intern  B
Joined: 21 Jan 2015
Posts: 8
GMAT 1: 570 Q41 V28 GMAT 2: 600 Q42 V31 GPA: 3.47

### Show Tags

we can have another approach. If we question how many number is added in terms of number line, we will get 12 (largest-lowest) and 8 (2nd largest-2nd lowest). so in total 20 will be added and since all are negative number so the sum will be (-185-20)= -205
Intern  Joined: 23 Jan 2017
Posts: 2

### Show Tags

here sum is negative right.means Sum of largest number should not be last 5 but a,a+4,........Then answer is -165 Where am I wrong??? I mean clearly a is negative,and in negative numbers smaller is larger.Please reply ??
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

### Show Tags

soniyanibhani wrote:
here sum is negative right.means Sum of largest number should not be last 5 but a,a+4,........Then answer is -165 Where am I wrong??? I mean clearly a is negative,and in negative numbers smaller is larger.Please reply ??

The integers are: {x, x+2, x+4, x+6, x+8, x+10, x+12} = {-45, -43, -41, -39, -37, -35, -33}.

The five largest there are {x+4, x+6, x+8, x+10, x+12} = {-41, -39, -37, -35, -33}. The sum = -185.
The five smallest there are {x, x+2, x+4, x+6, x+8} = {-45, -43, -41, -39, -37}. The sum = -205.

Hope it's clear.
_________________
Intern  Joined: 23 Jan 2017
Posts: 2

### Show Tags

Bunuel wrote:
soniyanibhani wrote:
here sum is negative right.means Sum of largest number should not be last 5 but a,a+4,........Then answer is -165 Where am I wrong??? I mean clearly a is negative,and in negative numbers smaller is larger.Please reply ??

The integers are: {x, x+2, x+4, x+6, x+8, x+10, x+12} = {-45, -43, -41, -39, -37, -35, -33}.

The five largest there are {x+4, x+6, x+8, x+10, x+12} = {-41, -39, -37, -35, -33}. The sum = -185.
The five smallest there are {x, x+2, x+4, x+6, x+8} = {-45, -43, -41, -39, -37}. The sum = -205.

Hope it's clear.

Oh yes.I got it. Thanks a lot. I am so fool.
Manager  S
Joined: 04 Jun 2015
Posts: 78

### Show Tags

Why I am not getting the same answer if I take the series 2n+1, 2n+3, 2n+5....., 2n+13
Given 5 largest sum, so that will be from 2n+5 to 2n+13
10n+45 = -185
n = 22

Asked - Sum of first five, so that will from 2n+1 to 2n+9
10n + 25 = -195

_________________
Sortem sternit fortem!
Math Expert V
Joined: 02 Sep 2009
Posts: 56261

### Show Tags

Sash143 wrote:
A set A consists of 7 consecutive odd integers. If the sum of 5 largest integers of set A is -185 what is the sum of the 5 smallest integers of set A?

A. -165
B. -175
C. -195
D. -205
E. -215

Why I am not getting the same answer if I take the series 2n+1, 2n+3, 2n+5....., 2n+13
Given 5 largest sum, so that will be from 2n+5 to 2n+13
10n+45 = -185
n = 22

Asked - Sum of first five, so that will from 2n+1 to 2n+9
10n + 25 = -195

From 10n + 45 = -185 it follows that n = -23, not 22. In this case 10n + 25 = -205.
_________________
Intern  B
Joined: 14 Mar 2018
Posts: 1

### Show Tags

1
I used easy numbers to plug in and solve. I started at -1,-3,-5,-7,-9,-11,-13. The smallest 5 numbers are -1,-3,-5,-7,-9. The largest 5 numbers are -5,-7,-9,-11,-13. Therefore, -1,-3 and -11,-13 are the only different numbers in those two sets. The difference between those 4 numbers are 20. Then I just add 20 to 185 and I got 205. Done.
Manager  S
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87

### Show Tags

let seven consecutive integers are:
$$x-6, x-4, x-2, x, x+2, x-4, x-6$$
as given: $$x-2 + x + x+2 + x-4 + x-6 = -185$$
$$5x+10=-185$$
$$x=-39$$

so sum of smallest 5 integers is:
$$x-6 + x-4 + x-2 + x + x+2 = 5x-10 = 5(-39)-10 = -205$$ (D)
_________________
Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas
Intern  Joined: 21 Aug 2018
Posts: 1
Location: India
GPA: 3.6

### Show Tags

how 5x+20 comes Re: M26-24   [#permalink] 22 Aug 2018, 08:01
Display posts from previous: Sort by

# M26-24

Moderators: chetan2u, Bunuel  