komal wrote:The average (arithmetic mean) of the multiples of 6 that are greater than 0 and less than 1,000 is
A. 499
B. 500
C. 501
D. 502
E. 503
OA : C Source : Kaplan Online
Some facts we should know about any set of evenly spaced, consecutive integers:
1. Average = median = (biggest + smallest)/2
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Average = median = (9+1)/2 = 5.
2. Number of integers = (biggest - smallest)/(difference between each successive pair of integers) + 1
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Difference between each successive pair = 1.
Number of integers = (9-1)/1 + 1 = 9.
{2, 4, 6, 8}
Difference between each successive pair = 2
Number of integers = (8-2)/2 + 1 = 4
{3, 6, 9}
Difference between each successive pair = 3
Number of integers = (9-3)/3 + 1 = 3.
3. Sum = (average) * (number of integers)
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Average = (9+1)/2 = 5
Number of integers = (9-1)/1 + 1 = 9.
Sum = 5*9 = 45
{2, 4, 6, 8}
Average = (8+2)/2 = 5.
Number of integers = (8-2)/2 + 1 = 4
Sum =5*4 = 20.
{3, 6, 9}
Average = (9+3)/2 = 6.
Number of integers = (9-3)/3 + 1 = 3.
Sum = 6*3 = 18.
A harder example:
What is the sum of all the multiples of 7 between 1 and 100?
Range is 7 to 98.
Average = (98+7)/2. (This is also the value of the median.)
Number = (98-7)/7 + 1.
Sum = average * number = (98+7)/2 * ((98-7)/7 + 1) = (105/2)*14 = 735.
Hope this helps!
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
Featured Course
