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# If a and b are odd integers such that a - b > 7, what is

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Director
Joined: 29 Oct 2004
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If a and b are odd integers such that a - b > 7, what is [#permalink]

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25 Dec 2004, 09:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.
Manager
Joined: 28 Aug 2004
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26 Dec 2004, 00:13
Since a & b are odd, b-1 is even. Odd - even = odd. So eliminate choices B & D.

I will translate "positive difference between a and an even number less than b" into

a - (b -1)

and backsolving:

A) a - (b-1) = 7; a-b = 6 not good
C) a - (b-1) = 9; a-b = 8 OK
E) a - (b-1) = 11; a-b = 10 OK

but C is smaller than E.

Good question!
Director
Joined: 31 Aug 2004
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01 Jan 2005, 15:26
The difference between 2 odd numbers is always an even number so the smallest value of a - b = 8
so a - x (where x = b-1) = 8+1 = 9
01 Jan 2005, 15:26
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