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# M26-24

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Math Expert
Joined: 02 Sep 2009
Posts: 47898

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16 Sep 2014, 01:25
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65% (hard)

Question Stats:

64% (01:46) correct 36% (01:34) wrong based on 59 sessions

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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

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16 Sep 2014, 01:25
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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: $$(x+4)+(x+6)+(x+8)+(x+10)+(x+12)=-185$$

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

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

$$5x+20=-205$$

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Joined: 11 Sep 2013
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27 Nov 2014, 16:02
3
5
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

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04 Feb 2015, 00:55
Can you please explain this step of the solution:

(5x+20)+20=-185

I'm having a difficult time understanding how this 20 appears
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Joined: 17 Sep 2014
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04 Feb 2015, 01:13
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
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21 Aug 2015, 20:29
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
Joined: 02 Sep 2009
Posts: 47898

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22 Aug 2015, 05:00
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??
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08 Jul 2016, 07:59
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

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Joined: 27 Apr 2015
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13 Sep 2016, 08:56
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
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27 Oct 2016, 09:58
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
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29 Mar 2017, 19:45
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
Joined: 02 Sep 2009
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29 Mar 2017, 23:06
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.
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30 Mar 2017, 00:40
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.
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18 Jul 2017, 02:42
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

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Math Expert
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18 Jul 2017, 03:06
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.
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12 May 2018, 10:01
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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.
Re: M26-24 &nbs [#permalink] 12 May 2018, 10:01
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# M26-24

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