How many 4-digit numbers are completely divisible by 7? Select.
A) 1354  B) 1286  C) 1178  D) 1224  E) None
Solution: 4- digit numbers divisible by 7 are: 1001, 1008, 1015….. 9996.   This is an A.P. in which a=1001, d=7, l=9996.   Let the number of terms be n.   Then Tn=9996. .'. a+(n-1)d=9996   =&gt; 1001+(n-1)7= 9996   =&gt;(n-1)7=8995   =&gt;(n-1)= 8995/7= 
<gadget id="calculator">8995/7</gadget>
<output>1_285</output>
1285=&gt; n=1286.   .'. number of terms =1286.   Answer 1286
<result>B</result>
How many 4-digit numbers are completely divisible by 7?