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Can we solve this basis the mean?

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by [email protected] » Mon Jul 14, 2014 11:42 pm
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?



-165


-175


-195


-205


-215
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by [email protected] » Tue Jul 15, 2014 12:19 am
Hi shibsriz,

This question can be solved in a number of different ways, but it's built around an interest math pattern involving consecutive integers:

We know that we're dealing with 7 consecutive odd integers and that the sum of the 5 LARGEST is -185. This tells us that all of the integers are negative.

I'm going to call the 5 largest consecutive odds:

X, X+2, X+4, X+6 and X+8

These 5 integers sum to -185

We're asked for the sum of the 5 SMALLEST numbers in that sequence, so we'll need:

X, X+2, X+4 and the two integers that come BEFORE the X: X-2 and X-4

Compare these two sets of numbers:
X, X+2, X+4, X+6 and X+8
X, X+2, X+4, X-4 and X-2

What do they differ by? Look at the last two terms in each set....

The difference is 2(-10) = -20

So the sum of the 5 SMALLEST numbers in the sequence is -185 - 20 = -205

Final Answer: D

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by phanikpk » Tue Jul 15, 2014 12:30 am
Since the sum of five largest integers itself is a negative. Then the numbers has to be negative odd integers

And the sequence is as follows:
2n+1 2n+3 2n+5 2n+7 2n+9 2n+11 2n+13

Then the largest integers sum includes

Sum of 2n+5 2n+7 2n+9 2n+11 2n+13 = 10n+45

10n+45= -185

10n= -230

n= -23

So, the sequence is -45 -43 -41 -39 -37 -35 -33

So the sum of the smallest of five integers is -205
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by GMATGuruNY » Tue Jul 15, 2014 2:09 am
[email protected] 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?



-165


-175


-195


-205


-215
For any EVENLY SPACED SET:
sum = (number)(median).

Since the sum of the 5 largest integers = -185, the median of the 5 largest integers = sum/number = -185/5 = -37.
Thus, the 5 largest integers are as follows:
-41, -39, -37, -35, -33.

Adding to the set the 2 smallest integers, we get:
-45, -43, -41, -39, -37, -35, -33.

The median of the 5 smallest integers = -41.
Thus:
Sum of the 5 smallest integers = (number)(median) = (5)(-41) = -205.

The correct answer is D.
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by mcdesty » Tue Jul 15, 2014 1:23 pm
My scratch paper looked like this.
Attachments
Inte.jpg
I have made your mistakes before.
I am experienced - I have tutored calculus and linear algebra for over two years.
For a very modest fee, I will ensure that your GMAT journey is a smooth one: Daily assignments and careful micro management.
PM me so we can get started.
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by unknown13 » Tue Jul 15, 2014 11:04 pm
Hi
Got the answer as D
method used is
x,x+2,x+4,x+6,x+8,x+10,x+12
5 largest integer sum is
5x+40 = -185
5 smallest integer sum is
5x+20 = -185-20 = -205

thanks and regards
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by Matt@VeritasPrep » Wed Jul 16, 2014 10:43 am
One last trick on this one: instead of thinking of the five largest integers as x, x + 2, x + 4, x + 6, and x + 6, I'd think of them as

{x-4, x-2, x, x+2, x+4}

(This trick works well for consecutive integers, as the summation becomes easier.)

Then the sum of the five integers is 5x. Since 5x = -185, we have x = -37.

Now take a look at the five smallest integers: {x-8, x-6, x-4, x-2, x}. This is 5x - 20, or -185-20, or -205. Done!
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