1981 AHSME Problems/Problem 12
If , , and are positive numbers and , then the number obtained by increasing by and decreasing the result by exceeds if and only if
Solution (Answer Choices)
Answer Choice : It is obviously incorrect because if is and we increase by % and then decrease %, will be around .
Answer Choice : If is and is , it should be equal but instead we get is more than . This is therefore also incorrect.
Answer Choice : Obviously incorrect since if is larger than , this is always valid since is less than which is obviously false.
Answer Choice : If is and is , it should be equal but instead we get is less than . Therefore, is also incorrect.
Answer Choice : If is and is , it should be equal, and if we check our equation, we get = . Therefore, our answer is