Source: Official Guide for the GMAT 13th Ed. Problem Solving; #90 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #90

3

In an increasing sequence of 10 consecutive

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?

3 Explanations

4

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

1

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

2

Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

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