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M26-24

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Bunuel
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M26-24 [#permalink] New post   16 Sep 2014, 01:25
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If set A consists of 7 consecutive odd integers and the sum of the 5 largest integers in set A is -185, what is the sum of the 5 smallest integers in set A?

A. -165
B. -175
C. -195
D. -205
E. -215
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Bunuel
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Re M26-24 [#permalink] New post   16 Sep 2014, 01:25
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Official Solution:

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

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


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

Given: \((x+4)+(x+6)+(x+8)+(x+10)+(x+12)=5x+40=-185\)

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

Given that \(5x+40=-185\), the value of \(5x+20\) will be 20 units smaller, resulting in -205.


Answer: D
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Raihanuddin
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Re: M26-24 [#permalink] New post   27 Nov 2014, 16:02
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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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Re: M26-24 [#permalink] New post   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.
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Re: M26-24 [#permalink] New post   21 Aug 2015, 20:29
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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.

Please assist.
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Bunuel
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Re: M26-24 [#permalink] New post   22 Aug 2015, 05:00
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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.

Please assist.


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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Re: M26-24 [#permalink] New post   13 Sep 2016, 08:56
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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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M26-24 [#permalink] New post   13 Sep 2019, 05:37
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pankajpatwari wrote:
The sum is -ve so shudn't we take numbers as x, x-2,x-4,x-6,x-8,x-10,x-12?? In that case the 5 largest numbers are x,x-2,x-4,x-6 and x-8 and their sum equals -185. hence 5x-20=-185 and x=-31. Accordingly the sum of 5 smallest numbers comes out to be -195.

Where m i going WRONG??



First of all, it does not matter whether you take 7 integers to be x, x + 2, ..., x + 12 or x-12, x-10, ..., x.

Next, from x + x - 2 + x - 4 + x - 6 + x - 8 = -185 it follows that x = -33, not -31. If you plug x = -33, you'll get the correct answer.
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Re: M26-24 [#permalink] New post   29 Mar 2017, 19:45
here sum is negative https://gmatclub.com/chat 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 ??
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Re: M26-24 [#permalink] New post   29 Mar 2017, 23:06
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soniyanibhani wrote:
here sum is negative https://gmatclub.com/chat 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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Re: M26-24 [#permalink] New post   27 Jul 2019, 18:57
The sum is -ve so shudn't we take numbers as x, x-2,x-4,x-6,x-8,x-10,x-12?? In that case the 5 largest numbers are x,x-2,x-4,x-6 and x-8 and their sum equals -185. hence 5x-20=-185 and x=-31. Accordingly the sum of 5 smallest numbers comes out to be -195.

Where m i going WRONG??
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Re: M26-24 [#permalink] New post   14 Oct 2019, 12:12
Bunuel,

arent`t odd/even numbers positive only?
how can they sum to a negative number?

thank you
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Bunuel
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Re: M26-24 [#permalink] New post   14 Oct 2019, 20:51
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adymyr2 wrote:
Bunuel,

arent`t odd/even numbers positive only?
how can they sum to a negative number?

thank you


An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an integer that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.
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Re: M26-24 [#permalink] New post   29 Mar 2023, 01:21
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M26-24 [#permalink] New post   24 Jul 2023, 18:50
If set A consists of 7 consecutive odd integers and the sum of the 5 largest integers in set A is -185, what is the sum of the 5 smallest integers in set A?
A={x,x+2,x+4,x+6,x+8,x+10,x+12}
=>x+4+x+6+x+8+x+10+x+12=-185<=>5x+40=-185<=>x=-45
=>x+x+2+x+4+x+6+x+8=5x+20=-45*5+20=-205 =>D
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Re: M26-24 [#permalink]
24 Jul 2023, 18:50
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