Which of the following is divisible by the first four positive even integer multiples of 31?
Which of the following is divisible by the first four positive even integer multiples of 31?
(i) 13020
(ii) 123752
(iii) 496496
Answer/Solution
i, ii and iii
Steps/Work
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=496, so (iii)=(4000+4)*124=4004*124, hence (iii) is divisible by 124.
124*(1000-2)=124000-248=123752, so (iii) is divisible by 124.
Finally, 13020-10*124=13020-12400=620=5*124, so (i) is divisible by 124.
Answer E.
124*4=496, so (iii)=(4000+4)*124=4004*124, hence (iii) is divisible by 124.
124*(1000-2)=124000-248=123752, so (iii) is divisible by 124.
Finally, 13020-10*124=13020-12400=620=5*124, so (i) is divisible by 124.
Answer E.