sapna44 wrote:
Last year a certain bond price with a face value of 5000 yielded 8% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
A. 4063
B. 5325
C. 5351
D. 6000
E. 6154
ronr34 wrote:
Hi Mike,
I found this question and I tried to approximate....
What I did was approximate the selling price as 6 instead of 6.5 and got something along the lines of 6666.
Luckily I chose the answer that was closes to it, but if I had approximated to 7 instead, I may have gotten stuck
between answers D and E.... Can you help with this?
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