The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?
Choose the correct choice from the following options:	A) 26	B) 17	C) 25	D) 33	E) 50
Four consecutive odd numbers: k-2, k, k+2, k+4   Three consecutive even numbers: n-2, n, n+2   k-2+k+k+2+k+4=n-2+n+n+2   4k+4=3n   4(k+1)=3n   k+1=(3/4)n   k=(3/4)n-1   All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:   We know,   101&lt;n&lt;208   104&lt;=n&lt;=204   Count=(204-104)/4+1=100/4+1=25+1= 
<gadget id="calculator">25+1</gadget>
<output>26</output>
26   26ns: 26.
<result>A</result>
The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?