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

Question

Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest. If that interest was approximately 6.5 percent of the bond's selling price,approximately what was the bond's selling price?

A. $4,063
B. $5,325
C. $5,351
D. $6,000
E. $6,154

A. $4,063
B. $5,325
C. $5,351
D. $6,000
E. $6,154

mikemcgarry · Accepted Answer

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 :-)

Bunuel · Answer

Interest = 0.08*5000 = 0.065*selling price --> selling price = 0.08*5000/0.065 --> selling price = ~6,154

Answer: E.

Skag55 · Answer

I got confused with the wording "bond's selling price" :evil:

I started wondering "Who sold it? Do we need to find how much it was bought? What quantity?" :oops:

It could just ask "What's 6.5 % of the interest earned?". I hate when I get stuck in these kind of things in quant and end up wasting my time in one simple question!

ronr34 · Answer

Thanks Mike!!!! Great answer, I hope I still have enough time to try and work it into my toolbox....

BrainLab · Answer

8% from 5000=400 -> 400=\frac{6,5}{100}*S  (Selling price) =  \frac{400*20}{1.3} , here we can estimate...  \frac{40}{13} ~3, so  400/1.3  ~ 3000 (actually more) 3000*2=6000 we need an answer choice which is slightly more than 6000, hence Answer E

bhamini1 · Answer

I have a query.It says approx 6.5 of the bond's selling price ,but above 6.5% has been considered.Why is that?can anybody explain.

mikemcgarry · Answer

Dear bhamini1 , I'm happy to respond. :-)

My friend, the person who posted the question made a mistake. Whoever posted the question omitted the word " percent " after the 6.5. About 90% of the questions posted on GMAT Club are posted by students, and students don't always do a perfect job of posting a question. My friend, one of the most important skills to have, on the GMAT and in the business world, is critical thinking . See this blog article: Doing GMAT Critical Reasoning You cannot simply believe everything is mistake-free and meant to be trusted as is. If you interpret everything literally as if the world is a perfect place, then unscrupulous people in the business world will cheat you out of everything. You have to be cunningly clever to succeed on the GMAT and in the business world. My friend, I want to support your success in every way I can. Does all this make sense? Mike :-)

ScottTargetTestPrep · Answer

We are given that a certain bond with a face value of $5,000 yielded 8% of its face value in interest. Thus, we can determine the interest as follows:
 
5,000 x 0.08 = 400
 
We also know that the $400 of interest was approximately 6.5% of the bond's selling price. Thus, we can create the following equation, where p = the bond’s selling price:
 
400 = 0.065 x p
 
400/0.065 = p
 
400,000/65 = p
 
6,154 ≈ p
 
Answer: E

sashiim20 · Answer

Interest  = \frac{8*5000}{100} = 400

Given Interest is  6.5  percent of the bond's selling price.

400 =\frac{6.5}{100} * SP

SP = \frac{400 * 100}{6.5} =\sim 6,154

Answer E

BrentGMATPrepNow · Answer

Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest  
8% of $5,000 =  $400  
So, interest =  $400

If that interest was approximately 6.5 percent of the bond's selling price,approximately what was the bond's selling price?  
Let x = the bond's selling price
So,  $400  = 6.5% of x
In other words:  $400  = 0.065x
Solve: x = 400/0.065 ≈ 6154

Answer: E

Cheers, 
Brent

Archit3110 · Answer

5000*8/100= 6.5/100 * SP
SP= 6154
IMO E

CAMANISHPARMAR · Answer

face value of $5,000 yielded 8 percent of its face value in interest = $400 (interest)

Selling price = (400 * 100)/6.5 (which equals approx more than 6000) Since only one option E is a possibility;that's the correct answer

CrackverbalGMAT · Answer

Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest. If that interest was approximately 6.5 percent of the bond's selling price,approximately what was the bond's selling price?

A. $4,063
B. $5,325
C. $5,351
D. $6,000
E. $6,154

A. $4,063
B. $5,325
C. $5,351
D. $6,000
E. $6,154

Interest from certain bond = 8 % of 5000 = 400$

It's given that the interest was approximately 6.5 percent of the bond's selling price

i.e 400 = 6.5 % of Bond's SP.

Now you have 2 options.

1. Either you can solve for Bond's SP directly from the above equation i.e Bond's SP = (400/6.5)*100

2. Analyse the answer options and use back solving method to get the answer.

Since the answer options are arranged in the increasing order, it's better to start with the middle options.
Let's start with option D as its very easy to find 6.5 % of 6000
1 % of 6000 = 60
.5 % of 6000 = 60/2 =30
So 6.5 % of 6000 = (6*1 + .5 )% of 6000 = 6*60 +30 = 360 + 30 = 390.
Please note: Above calculations should be done in mind to save time.

Since $390 <$ 400, your answer should be greater than 6000 and we have left with only one option i.e Option E.

Option E is the correct answer.

Thanks,
Clifin J Francis,
GMAT QUANT SME

Kinshook · Answer

Given:Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest.
Asked: If that interest was approximately 6.5 percent of the bond's selling price,approximately what was the bond's selling price?

The bond's selling price = $5000*8/6.5 = $6154

IMO E

Posted from my mobile device

GmatKnightTutor · Answer

8% of $5000 is $400

If $400 is equal to ~6.5% of the selling price, we're essentially trying to figure out what ~100% of the selling price is to answer this question.

$400 = ~6.5%
$x = ~100%

We can make the following "approximate" expression:

6.5x = 400 (100)

x =  400 (100) / 6.5  
x =  400 (1000) / 65 
x =  80 (1000) / 13 
x =  (80/13) (1000)

If we divide 80 by 13 we're left with ~6.15

~6.15 x 1000 = ~6150 which is closest to $6154 out of the answer choices.

(E) is your answer.

totaltestprepNick · Answer

E https://www.youtube.com/watch?v=gKYKQCkb4vg Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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