3 no. leave remainders of 43, 47 & 49 on division by N. The sum of the three no.'s leaves a remainder 9 on division by N. What are the values N can take?
Choose the most appropriate option.
A) 34 B) 35 C) 38 D) 67 E) More than one value is possible
In this question, the sum of the three numbers should leave a remainder  43 + 47 + 49= 
<gadget id="calculator"> 43 + 47 + 49</gadget>
<output>139</output>
139. Or, it should be of the form N * k + 139, where K is an integer.   However, it leaves a remainder 9, or it is of the form N * m + 9.   N * k + 139= N * m + 9   N * (m - k) = 130   Or, N should be a factor of 130. Since the remainders left on division by N are 43, 47 and 49, N should be greater than 49.   The only factors of 130 that are greater than 49 are 65 and 130. So, N can take 2 values – 65 or 130   More than one value is possible
<result>E</result>
3 no. leave remainders of 43, 47 & 49 on division by N. The sum of the three no.'s leaves a remainder 9 on division by N. What are the values N can take?