Carol is three times Alice’s age but only twice as old as Betty. Alice is twenty-four years younger than Carol. How old is Betty?  Choose the correct choice from the following answers:
A) 26 B) 19 C) 22 D) 18 E) 24
Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.   We're told 3 facts about the relative ages of 3 people:   1) Carol's age is 3 times Alice's age   2) Carol's age is 2 times Betty's age   3) Carol is 24 years older than Alice   We're asked for BETTY'S age.   From the answer choices and the information provided, Carol can't be that old (The difference of 12 years = 3 times; that relationship can only occur when the numbers are relatively small). Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.   IF....   Betty = 18   Then Carol = 2(18) = 36   Then Alice = 36 - 24= 
<gadget id="calculator">36 - 24</gadget>
<output>12</output>
12 AN18 36/3= 12   All of these values mesh perfectly with the facts and with one another, so Betty MUST be 18   18
<result>D</result>
Carol is three times Alice’s age but only twice as old as Betty. Alice is twenty-four years younger than Carol. How old is Betty?