yellowho wrote:I. The least/smallest integer is odd
II. None of the integers is divisible by 5
III. One of the integers has 3 as its units digit
If the sum of 4 consecutive integers is divisible by 5, which of the following must be true?
A) I only
B) II only
C) III only
D) I and III
E) None of the above
How are people breaking this down? Especially III.
For the sum to be a multiple of 5, the units digit of the sum must be 0 or 5. Thus, we need to determine which combinations of consecutive digits will yield a sum whose units digit is 0 or 5.
1+2+3+4 = 10. This works.
2+3+4+5 = 14. Doesn't work.
3+4+5+6 = 18. Doesn't work.
4+5+6+7 = 22. Doesn't work.
5+6+7+8 = 26. Doesn't work.
6+7+8+9 = 30. This works.
7+8+9+0 = 24. Doesn't work.
8+9+0+1 = 18. Doesn't work.
9+0+1+2 = 12. Doesn't work.
0+1+2+3 = 6. Doesn't work.
Only the following combinations work: 1, 2, 3, 4 and 6, 7, 8, 9.
Now onto the answer choices:
I. The smallest integer doesn't have to be odd. The correct answer choice cannot include I. Eliminate A and D.
II. Since any integer that has a units digit of 1, 2, 3, 4, 6, 7, 8, or 9 is not a multiple of 5, it must be true that none of the integers is divisible by 5. The correct answer choice must include II. Eliminate C and E.
The correct answer is
B.
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