In an increasing sequence of 10 consecutive

Tanvir Taher

Recognize that you're dealing with consecutive integers

1 2 3 4 5 6 7 8 9 10

Therefore 1+2+3+4+5 = 15 / 6+7+8+9+10 = 40

40-15 = 25 -- no matter where you start adding, you know that the difference between 2 sets of added consecutive numbers is always going to be 25.

To prove this, let's use the numbers from the question.

110+111+112+113+114 = 560

115+116+117+118+119 = 585

560 + 25 = 585

Edit: I realize this isn't necessarily traditional GMAT Quant thinking -- this isn't based on any real methodology apart from number sense.

Mar 12, 2015 • Comment

Awesome shortcut!

IMHO, another approach (but longer :( ) could be:

Since is a sequence of consecutive integers, and each group of numbers has an odd # of elements:

I * 5 = sum ( G , H , I , J , K)
N * 5 = sum ( L , M , N , O , P)

The sum of five consecutive numbers, divided by 5, will be equal to the value of the median (an also the average), which will match the third value (middle value) of that sequence.

So, 560 / 5 (we can use the "dividing by 5 technique": http://gmat.magoosh.com/lessons/309-dividing-by-5

560 / 5 = 112 = I

I + 5 = N = 117

So, being 117 the median of the second sequence of consecutive numbers , multiplying it by the # of elements will bring us to the sum of that 5 numbers.

N * 5 = sum ( L , M , N , O , P)

117 * 5 = 585

Jan 26, 2015 • Comment

Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment