If *r* > 0, then for all *p* and *q* such that *pq* does not equal 0 and such that *pr* > *qr*, we have:

- –
*p*> –*q* - –
*p*>*q* - 1 >
*q*/*p* - 1 <
*q*/*p* - none of these

*Since r* is not equal to 0, we can divide by *r*, and since *r* > 0 we know *pr* > *qr* implies *p* > *q*. We have three possibilities to consider, so let’s try specific values.

__Note__*:* *p* < 0 and *q* > 0 is impossible since *p* > *q*.

p | q |
p | q |
a |
b |
c |
d |
|||||

–p > –q |
–p > q |
1 > q/p |
1 < q/p |
|||||||||

+ | + | 6 | 3 | F | F | T | F | |||||

+ | – | 6 | -3 | F | F | T | F | |||||

– | – | -3 | -6 | F | T | F | T |

Since none of the conditions (a), (b), (c), or (d) holds for every possibility of *p* and *q*, we conclude that (e) is the correct response.