Consecutive integers

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																		Consecutive integers
																		 Wed Apr 11, 2012 8:52 am
									
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In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?

A. 585

B. 580

C. 575

D. 570

E. 565

#85, OG 12

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																		 Wed Apr 11, 2012 9:13 am
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HG10 wrote:In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?

A. 585

B. 580

C. 575

D. 570

E. 565

#85, OG 12
x  , x+1, x+2, x+3, x+4 = 560

x+5, x+6, x+7, x+8, x+9 = ??

[GMAT Approach]we see that the difference between each term is 5. hence 5 x 5terms = 25 ==> 560 + 25= 585.

[Conventional method will be solve for x, ]

5x +10= 560

5x=550

x=110

5x+35= 550+35 = 585

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																		 Wed Apr 11, 2012 9:31 am
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In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?

A. 585

B. 580

C. 575

D. 570

E. 565 

HI I think you had some problem...

well you can also do what gmat_kolaveri did... 

There is another faster approach as well

the total of the 5 consecutive integers is 560.

Now divide 560 by 5 and you get the average as 112.

112 is the 3rd number as in case of odd number of numbers, the median and the mean are the same.

So the numbers are 110, 111, 112, 113 and 114.

The total of the last 5 integers are 115 + 116 + 117 + 118 + 119 which comes to 585...

Only calculation related to the division and the last addition...

The OA is A...

Hope this helped...

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Wed Apr 11, 2012 3:21 pm

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Thank you both for the solutions!

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																		 Wed Apr 11, 2012 3:28 pm
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Since they're consecutive, the 6th term is 5 more than the 1st term, the 7th term is 5 more than the 2nd term, etc.  Since we have five terms that are each 5 more than their corresponding term, the sum of the last five terms must be 5*5=25 more than the sum of the first five terms.

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Wed Apr 11, 2012 3:35 pm

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@Bill@VeritasPrep: Thank you for the alternative solution.

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																		 Wed Apr 11, 2012 4:22 pm
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HG10 wrote:In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?

A. 585

B. 580

C. 575

D. 570

E. 565

#85, OG 12
With evenly spaced integers:

Average = median = sum/number.

Sum = number*median.

In the problem at hand:

The median of the first five integers = sum/number = 560/5 = 112.

Each integer in the second set of five integers is 5 greater than the corresponding integer in first set of five integers.

Thus, the median of the last five integers = 112+5 = 117.

Thus, the sum of the last five integers = number*median = 5*117 = 585.

The correct answer is A.

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Last edited by GMATGuruNY on Wed Apr 11, 2012 6:18 pm; edited 1 time in total

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Troika Really wants to Beat The GMAT!

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Wed Apr 11, 2012 5:12 pm

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Thank you, Mitch

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