<p>The square of Billy's age is four times his grandmother's age. When Billy is 1.5 times as old as he is now, his grandmother will be 90. The ages of Billy and his grandmother are: (A) 16 and 64 (B) 22.5 and 78.75 (C) 15.5 and 60 (D) 18 and 81</p>
<p>I would suggest that the easiest way to solve this question would be to try out the options with the help of a calculator. The answer here is option D.</p>
<p>Now if you want the proper mathematical method, it is as follows.
Let Billy’s present age be x.
Therefore Grandma’s present age = (x^2)/4 From the first statement.</p>
<p>Billy will be one and a half times old as now after the number of years as many as half his present age. Right ?</p>
<p>Therefore Grandma will be 90 after x/2 years.
Add this x/2 to Grandma’s present age and equate it to 90.
Therefore (x^2)/4 + x/2 = 90
Write down this quadratic equation on paper to solve it better.
The values you get are 18 and -20. Since age cannot be negative, Billy’s age = x = 18 and Grandma’s age = (x^2)/4 = 18^2/4 = 324/4=81.</p>
<p>Hope that Helps.</p>
<p>Thanks deutschethinker. Cool!</p>
<p>why it’s not (A) 16^ 2 = 256 /4 = 64</p>
<p>^b/c it doesn’t satisfy the second requirement</p>
<p>It’s a rather silly problem. You can tell that the answer B was created solely to correspond to one of the criteria … after the fact. </p>
<p>Anyhow, the easiest clue to work with is “When Billy is 1.5 times as old as he is now, his grandmother will be 90.” So simply add 1/2 the age of Billy to the GM and see if it can reach 90.</p>
<p>(A) 16 and 64 = too small
(B) 22.5 and 78.75 Works as 11.25 + 78.75 is 90
(C) 15.5 and 60 = to small again
(D) 18 and 81 Works as 9 + 81 = 90</p>
<p>Although you could easily dismiss the answer B for its silliness, test the first condition and it ensures that D is the right answer. </p>
<p>Fwiw, it is best to leave the equations out of this one. And, if you happen to have developed the good habit of NOT using your calculator as a crutch, remember that </p>
<p>18 = 2<em>9 and 81 = 9</em>9 — which means you can easily check the first condition without squaring the age. Think 2<em>9</em>2<em>9 = 2</em>2<em>9</em>9</p>