Another useful tip to remember for these problem solving (a.k.a. discrete quantitative) questions is: If there are variables in the answer choices, plug in a workable number. This is helpful especially for those of you who would rather do arithmetic than algebra. If you choose applicable numbers for the variables, you can turn an algebra problem into an arithmetic problem, and it may streamline your work. Be on the lookout for any problem that contains variables in the answer choices. Lets see what this looks like in an example.
Now, this problem is not hard algebraically if you want to do it that way, but plugging in numbers will definitely be simpler and is especially helpful if you don’t have a clue how to set up this problem.
So, we only have one variable in this problem: f, so lets pick a value that we could use for the length of the string. An easy value would be 10 or 100, but here is an important step. If we look at the answer choices, we can see that if we are going to test them, we need a nice number divisible by 4 if we wanted to work more quickly on choices B and E. So it would be good to pick a number like 40. (If you don’t see this initially, it’s fine… The technique will work if you choose any number, but it is helpful if you look ahead.)
So, lets say this string is 40 feet long. If we cut it according to the problem, we will have one piece at 10 feet and the other at 30 feet. Now, the question asks what is the length of the longer piece. Well, with the number that we picked, the longer piece is 30?
All we have to do now is plug in our chosen value of 40 for f into the answer choices and see which one produces 30.
In choice A, we get 80. That’s not 30, so it’s out. In choice B we get 10. So that’s out. Choice C we get 78, no good. Choice D we get 120, way to high. So hopefully its going to work out for E! Indeed it does… We get 30 for choice E. This matches our scenario so it is the answer. The length of the longest side is 30.
What’s good about this strategy is that you don’t have to spend time trying to come up with an algebraic equation to express the problem. All you have to do is pick a workable number and plug in. From there it’s just arithmetic to match your prediction. So, remember this tip for test day. When you see variables in the answer choices, try to plug in a workable number.
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