The sum of four consecutive even numbers is 'X+26' and there are four consecutive odd numbers, of which the 2nd lowest number is three more than the 2nd highest even number. If the sum of the lowest numbers in both series is 37, then find the value of \(\frac{X}{2}\).

(a) 25
(b) 50
(c) 75
(d) 20
(e) 40

The value of 2 X ​ is 25, based on the calculations from the sums of the consecutive even and odd numbers. We found X to be 50, which leads to our final answer. Therefore, the correct answer is (a) 25.
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Answered by Anonymous | 2025-07-14

To solve this problem, we need to work with consecutive even and odd numbers and set up equations based on the information provided.
Let's start with the consecutive even numbers. Let the smallest of these four consecutive even numbers be n . Therefore, the four consecutive even numbers can be expressed as:

n
n + 2
n + 4
n + 6

The sum of these four numbers is given as X + 26 :
n + ( n + 2 ) + ( n + 4 ) + ( n + 6 ) = X + 26
Simplifying, we have:
4 n + 12 = X + 26
4 n = X + 14 (Equation 1)
Now, let's focus on the four consecutive odd numbers. Let the smallest of these be m . Therefore, the four consecutive odd numbers can be written as:

m
m + 2
m + 4
m + 6

According to the problem, the second lowest odd number is three more than the second highest even number. Therefore:
m + 2 = ( n + 4 ) + 3
Simplifying, we have:
m + 2 = n + 7
m = n + 5 (Equation 2)
We're also told that the sum of the lowest numbers in both series is 37:
n + m = 37
Substitute m = n + 5 from Equation 2:
n + ( n + 5 ) = 37
Simplifying, we get:
2 n + 5 = 37
2 n = 32
n = 16
Using Equation 2, m = n + 5 = 21 .
Now, plug n = 16 into Equation 1 to find X :
4 ( 16 ) = X + 14
64 = X + 14
X = 50
Finally, we are asked to find 2 X ​ :
2 X ​ = 2 50 ​ = 25
Thus, the answer is (a) 25.

Answered by IsabellaRoseDavis | 2025-07-21