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.
Numbers
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Frankenstein
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ikaplan
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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.
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.
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GMATGuruNY
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When integers are evenly spaced, the average = the median.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?
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.
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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].
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