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silverflamein: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Oct 19, 2011 7:12 pm

by silverflamein » Wed Oct 19, 2011 9:30 pm

The average of 5 consecutive integers starting with x is a. What is the average of 9 consecutive integers that start with x+3 ?

A - x+a
B - a+5
C - 2x
D - 2a
E - 2x+a

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Wed Oct 19, 2011 9:49 pm

Let x=1.
5 consec int - (1,2,3,4,5)
Avg = a =3.

Now if first number is x+3 = 4
We have (4,5,6,7,8,9,10,11,12)
And Avg = 8 (or) a+5 B

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Wed Oct 19, 2011 9:54 pm

x, x+1, x+2, x+3, x+4

5x+10 = 5a
5x = 5a-10
x = a-2

Sum of 9 consecutive integers = 9x+3+4+5+6+7+8+9+10+11 =9x+9(3+11)/2 [sum of AP]
=>9x + 63

average = (9x+63)/9 = x+7 = a-2 +7 [because x=a-2]
avg = a+5

B is the correct option

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 19, 2011 9:57 pm

silverflamein wrote:The average of 5 consecutive integers starting with x is a. What is the average of 9 consecutive integers that start with x+3 ?

A - x+a
B - a+5
C - 2x
D - 2a
E - 2x+a

With evenly spaced integers, the average = the median.

Let x=1.
The integers are 1,2,3,4,5.
a = 3.

Given x+3 = 1+3 = 4:
The integers are 4,5,6,7,8,9,10,11,12.
Average = 8. This is our target.

Now we plug x=1 and a=3 into the answers to see which yields our target of 8.

Only answer choice B works:
a+5 = 3+5 = 8.

The correct answer is B.

Last edited by GMATGuruNY on Thu Oct 20, 2011 7:15 am, edited 2 times in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Oct 19, 2011 11:57 pm

silverflamein wrote:The average of 5 consecutive integers starting with x is a. What is the average of 9 consecutive integers that start with x+3 ?

Average of 5 consecutive integers starting with x will be the 3rd integer = (x + 2)
Hence, (x + 2) = a

Average of 9 consecutive integers starting with (x + 3) will be the 5th integer = (x + 3) + 4 = (x + 7) = (a + 5)

The correct answer is B

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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

by rohit_gmat » Thu Oct 20, 2011 3:28 am

used mitch's method as shown above..

but while finding the avg did - 4+12/2 = 8

(but i wasted a lil time at first coz i did 4+13/2 then i was stuck

so be careful

)

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