Hey Jinglander,
Great question - and I love the title of your post. For many of these problems with "variables in the answer choice", I like to employ what I call a hybrid plug-in strategy:
Hybrid Plug-In
Instead of the simple "plug in numbers and then check them in the answer" strategy, which can be time-consuming when multiple variables and operations are present, you can use numbers just as placeholders to set up the algebra, and then go back to the algebra to solve in fewer steps.
In this case, let's pick small numbers for our variables and use them to set up the algebra:
Say the family has a child every two years, and the oldest is 6 years old. That means that j = 2 and t = 6. If they then have a child in 2 years, we'd calculate their number of children as 5 - they'd have kids of 0, 2, 4, 6, and 8.
The easiest way to calculate this algebraically is to add 2 to the oldest child's age and divide by 2 (the number of years-per-child). But that omits the fact that this is an "inclusive set". We know that a child every 2 years means that we're including each even number in the set for a total of 5 children. To accomplish that mathematically, we'd have to add the 1, giving us:
(6+2)/2 + 1
(age of the oldest + 2 years)/number of years-per-child + 1 for the inclusive set
(t + 2)/j + 1
The hybrid method helps you to double-check things like the (+1) by using math with numbers to make sure that you're comfortable with the setup, but then you're not stuck doing 6 different math problems (the original, A, B, C, D, and E).
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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