Which of the following is divisible by the first four positive even integer multiples of 31?
(i) 13020
(ii) 123752
(iii) 496496  Choose the correct choice from the following options:
A) None  B) iii only  C) ii and iii only  D) i and ii only  E) i, ii and iii
A positive integer x is divisible by the first four integer multiples of 31 if and only if it is divisible by their least common multiple, 3*4*31=124.   124*4= 
<gadget id="calculator">124*4</gadget>
<output>496</output>
496, so (iii)=(4000+4)*124=4004*124, hence (iii) is divisible by 124.   124*(1000-2)=124000-248= 
<gadget id="calculator">124000-248</gadget>
<output>123_752</output>
123752, so (iii) is divisible by 124.   Finally, 13020-10*124=13020-12400= 
<gadget id="calculator">13020-12400</gadget>
<output>620</output>
620=5*124, so (i) is divisible by 124.   Answer i, ii and iii.
<result>E</result>
Which of the following is divisible by the first four positive even integer multiples of 31?
(i) 13020
(ii) 123752
(iii) 496496