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If a and b are odd integers such that a  b > 7, what is [#permalink]
25 Dec 2004, 08:29
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If a and b are odd integers such that a  b > 7, what is the smallest possible positive difference between a and an even number less than b?
A) 7
B) 8
C) 9
D) 10
E) 11
HIGHLIGHT BELOW TO SEE OA:
(C) There is a lot of information in this question, so take it a step at a time. a and b are odd, and a  b > 7, so a > b. There is no clear way to go forward here, so try some values for a and b, and see what happens. Since you are trying to find the smallest possible positive difference between a and an even number less than b, try and make a and b as close together as possible. If a = 11, then the largest number b can be is 3, since 11  3 is 8. The largest even number less than b is 2, so the positive difference between a and this number is 11  2 = 9. Immediately you know that answer choices (D) and (E) are too large, and can be discarded. And since you are finding the difference between a (an odd number), and an even number, the difference must be odd. So you can get rid of all the even answer choices (B) and (D) . This leaves you with (A) and (C), so guessing is a good option if you get stuck here.
Alternatively, use logic. If a  b > 7, then a > b + 7. Since a and b are both odd integers, the smallest possible positive difference between a and b must be 8. Since b is odd, the largest even number less than b must be b  1, that is, it is 1 further away from a than b is. So the minimum possible positive difference between a and this number is one greater than 8, or 9.
This is a good question. Check it out.
