The number of multiples of 10 which are less than 1000, which can be written as a sum of four consecutive integers is
Choose the correct option:
A) 22	B) 50	C) 88	D) 76	E) 18
Answer: Option A   Sol:   We can write 10 = 1 + 2 + 3 + 4. So we have to find how many multiples of 10 can be written in this manner.   Let the first of the four numbers be n. So   n + (n+1) + (n+2) + (n+3) = 10k   4n + 6 = 10k   2n + 3  4  + 6= 
<gadget id="calculator"> 4  + 6</gadget>
<output>10</output>
10k   2n + 3 = 5k   n  2  + 3= 
<gadget id="calculator"> 2  + 3</gadget>
<output>5</output>
5k   n= 5k−325k−32 = 2k – 1 + k–12k–12   So n is intezer for k = an odd number. So for k = 1, 3, 5, .... 99 we can write a number as a sum of four consecutive intezers.   So there are 50 numbers.   Answer:50
<result>B</result>
The number of multiples of 10 which are less than 1000, which can be written as a sum of four consecutive integers is