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07 Sep 2019, 09:12
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B
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There are N consecutive even integers in descending order. The first integer is N and the average of the first five is 1594 more than the last integer. Find the value of N.
(A) 700
(B) 800
(C) 600
(D) 750
(A) 700
(B) 800
(C) 600
(D) 750
07 Sep 2019, 11:08
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Let's take an example to understand the problem.
Ex 1: Let there be 4 (N-above) consecutive even numbers in descending order and first number is 4 (N-above)
So, the series is 4, 2, 0, -2 -> consecutive even numbers in descending order.
Note the the last number is negative of 2nd number from starting
Ex 2: Let there be 6 (N-above) consecutive even numbers in descending order and first number is 6 (N-above)
So, the series is 6, 4, 2, 0, -2, -4 -> consecutive even numbers in descending order
Note the the last two numbers are negative of 2nd and 3rd number from starting respectively
Actual Question: Using the logic above last 5 numbers will be negative of 2nd, 3rd, 4th, 5th and 6th number from starting respectively
Series will be N, N-2, N-4, N-6, N-8..... -(N-10), -(N-8), -(N-6), -(N-4), -(N-2)
So, Average of first 5 numbers will be the middle term (as they are in arithmetic sequence) -> N-4
Given that: the average of the first five is 1594 more than the last integer.
N-4 = 1594 + (-(N-2))
N-4 = 1594 - N + 2
2N = 1600 => N = 800
So, Answer will be B.
Hope it helps!
Ex 1: Let there be 4 (N-above) consecutive even numbers in descending order and first number is 4 (N-above)
So, the series is 4, 2, 0, -2 -> consecutive even numbers in descending order.
Note the the last number is negative of 2nd number from starting
Ex 2: Let there be 6 (N-above) consecutive even numbers in descending order and first number is 6 (N-above)
So, the series is 6, 4, 2, 0, -2, -4 -> consecutive even numbers in descending order
Note the the last two numbers are negative of 2nd and 3rd number from starting respectively
Actual Question: Using the logic above last 5 numbers will be negative of 2nd, 3rd, 4th, 5th and 6th number from starting respectively
Series will be N, N-2, N-4, N-6, N-8..... -(N-10), -(N-8), -(N-6), -(N-4), -(N-2)
So, Average of first 5 numbers will be the middle term (as they are in arithmetic sequence) -> N-4
Given that: the average of the first five is 1594 more than the last integer.
N-4 = 1594 + (-(N-2))
N-4 = 1594 - N + 2
2N = 1600 => N = 800
So, Answer will be B.
Hope it helps!
