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This question is testing the
following divisibility rules:
- A number is divisible by 3 if the sum of
its digits is divisible by 3.
- A number is divisible by 4 if its last two
digits are divisible by 4.
- A number is divisible by 5 if its last digit
is a 0 or a 5.
- A number is divisible by 6 if it's divisible
by both 2 (even numbers are divisible by 2) and 3 (see first rule above).
Since this is a "which of the following"
question, let's evaluate Choices (5) and (4) first, and then work our
way up. Before beginning, however, note that not all of the rules need
to be evaluated one by one. For instance, we know simply by glancing at
the answer choices that they are all divisible by 5 (all end in a 0) and
by 2 (all are even). Furthermore, if a choice is divisible by 3, it must
also be divisible by 6. This is because we have already confirmed divisibility
by 2 by skimming the answer choices. This means that only the divisibility
rules for 3 and 4 need to be tested. Let's begin:
Choice (E): 4730 = 4 + 7 + 3 + 0 = 14; 14 is
not divisible by 3. Eliminate.
Choice (D): 4560 = 4 + 5 + 6 + 0 = 15; 15 is divisible by 3.
The last two digits in 4560 are 60; 60 is divisible by 4.
Choice (D) is the correct answer. At this point
we would choose our answer and move on, but let's evaluate the remaining
choices:
Choice (C): 3870 = 3 + 8 + 7 + 0 = 18; 18 is
divisible by 3, but 70 is not divisible by 4.
Choice (B): 3140 = 3 + 1 + 4 + 0 = 8; 8 is not divisible by 3, although
40 is divisible by 4.
Choice (A): 3020 = 3 + 0 + 2 + 0 = 5; 5 is not divisible by 3, although
20 is divisible by 4.
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