Numbers

Hi,
Let the numbers be n,n-1,n-2,n-3
-----------------n-4,n-5,n-6,n-7
Clearly, every number in the second row is 4 less than its corresponding number from the top row. So, sum of them will be 4*(-4) less than the sum of top row
So, x - 16 = 298 => x= 314.

This is how I solved this one: since the integers are consecutive and their sum is 298, I divide the sum with the number of integers to get the idea about the approximate value of the number.

298:4= 74,5

so I know that the integers are +/- 75

Next, I make a potential list of integers: 73, 74, 75, 76 and sum the last digits- since the sum of the last digits ends with 8 it is a good sign that I am on the right path.

Having in mind that the sequence is decreasing and that 298 was the sum of the last 4 integers, the other integers are 77, 78, 79 and 80.
When you sum these integers you will get 314.

thanks

ntamhane wrote:In a decreasing sequence of 8 consecutive integers, the sum of the last 4 integers is 298. what is the sum of the first 4 integers in the decreasing sequence?

When integers are evenly spaced, the average = the median.
Thus, the median of the last four integers = 298/4 = 74.5.
Thus, of the last four integers, the two largest are 76 and 75, implying that the first four integers are 80,79,78,and 77.

When integers are evenly spaced, Average = (biggest + smallest)/2 and Sum = Number * Average.

Thus, the sum of the first four integers = 4 * (80+77)/2 = 314.

Great Explanation GMatGuruNY