Last year a certain bond with a face value of $5,000 yielded 8 percent

Dear ronr34,
I'm happy to help.

Remember, one criterion for approximation is that the answer choices be far apart and well-spaced. Here, the answers are not particularly far apart, so we are much more restricted in the kinds of approximating we can do. Here's how I would think about it.

First of all, 8% of $5000 is $400. For this part, it should be easy to calculate the exact value.

Now, 6.5% of the selling price is $400.
Let x = selling price
0.065*x = 400
To be honest, the answers are close enough together that I don't want to approximate 6.5 to either 6 or 7. Here's what I am going to do. First, I will multiply both sides by 100.
6.5*x = 40,000
Now, here is think is the big key to solving this problem easily --- change the decimal 6.5 to the fraction 13/2. In 90% of all cases, fractions are MUCH MUCH EASIER for calculation than are decimals!!
(13/2)*x = 40,000
13*x = 80,000

x = 80,000/13

Well, 13*6 = 78, so 13 goes into 80 six times, with a remainder of 2. That means, x is more than 6000. That's enough to isolate (E).

A totally different strategy --- backsolving. Once we know 6.5% of x is $400, plug in answer choices to see where we are. Normally, I would recommend starting with (C) --- see:
https://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/
Here, though, many of the answers are warthog-ugly numbers, but the question is handing us answer (D) on a golden platter as an ideal candidate for backsolving. (Incidentally, that's a very handy trick to have up your sleeve --- four ugly number answer choices, and one nice round number: chances are extremely good that backsolving with that one nice round number will help you find the answer quickly.)

What's 6.5% of $6000?

Well, 1% of $6000 is $60.
Six times that means: 6% of $6000 is $360.
Now, divide the 1% line in half --- 0.5% of $6000 is $30.
Now, add the last two lines --- 6.5% of $6000 is $390.

Thus, if x = 6000, then 6.5% of it is not big enough. We need something bigger than $6000, and the only choice is (E).

Does all this make sense?
Mike





Does all this make sense?
Mike