Larry invested $20,000 in an investment that earned an annual

Question

Larry invested  $20,000  in an investment that earned an annual interest of  r  percent when compounded quarterly. On the same day, Mark invested  $20,000  in an investment that earned an annual interest of  q  percent compounded semi-annually. Did Mark earn more interest than Larry at the completion of one year of their investments?

(1)  \frac{q}{200} > \frac{r}{400}

(2) Peter, whose investment of  $20,000  earned an annual interest of  q  percent compounded annually, earned more interest than Larry at the end of one year of the investment.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Problem Solving Butler  
  Sentence Correction Butler  
  Reading Comprehension Butler  
  Integrated Reasoning Butler

EshaFatim · Answer

going with option E.

In statement 1, there's no exact relation between q and r. Also, after testing some values based on   \frac{q}{200}>\frac{r}{400}   =>  q>\frac{r}{2} , there are variations in the results, where Larry earns more at times and Mark earns more at times. So, for inconsistent results, statement 1 is not sufficient.

statement 2 holds the similar cause.

so IMO option E. If there's a better tactical or quantitative approach than please enlighten me. I feel like there could be better way/s to reach the conclusion.

pierjoejoe · Answer

Larry (1+r/4)^4
Mark (1+q/2)^2

(1) 2q>r --> q>r/2 
substituting into Mark
Larry (1+r/4)^4
Mark (1+q/2)^2 = (1+r/4)^2

now if q = r/2 (or slightly bigger) than, (1+r/4)^2 is for sure less than (1+r/4)^4 MARK<LERRY, but if (given q>r/2) q = 2r
Larry (1+r/4)^4
Mark (1+q/2)^2 = (1+r)^2
than MARK > LERRY

INSUFFICIENT

(2) this one is telling us that Peter investiment (compounded one year) is greater than Larry investiment (compounded 4 times)

(1+q) > (1+r/4)^4

we know that Mark investiment is 
(1+q/2)^2

I also know (but i have to check this from my old finance courses ahah) that the higher the compounding, the higher the interest earned, given a certain interest rate. 
thus if (1+q/2)^2> (1+q) 
and (1+q) > (1+r/4)^4
we also know that Mark investiment will yield a greater investiment
SUFFICIENT

IMO B

EshaFatim · Answer

Hi  pierjoejoe ,
for my better understanding, could you please explain how you landed on the following expression?

(1+\frac{q}{2})^2> (1+q)

pierjoejoe · Answer

https://www.desmos.com/calculator/ydfvfdb4cj take a look at this plot i made. as you can see for any x (1+\frac{q}{2})^2> (1+q) as long as the interest rate is positive and the compounding (n) the greater than 1. in general, when you compound more in a year, given a fixed interest rate, you will earn more interest than someone who compounded less times. at least that's what i remember. don't take my words for granted lol

Matthyrou · Answer

(1+q/2)^2= 1+q+q^2/4 (so no matter q it's greater than 1+q)

Krunaal · Answer

(1 + \frac{r}{400})^4 > (1+ \frac{q}{200})^2  ?

Statement 1

\frac{q}{200} > \frac{r}{400}

This tells us that the interest added per period for Mark, is greater than the interest added per period for Larry. However, this does not immediately imply that Mark earned more interest, because Larry has more compounding periods (4) than Mark (2).  INSUFFICIENT

Statement 2

This statement tells us that Peter, with annual compounding, earned more than Larry, who had quarterly compounding.  P > L

Since annual compounding yields less interest than semi-annual compounding (given the same rate) , this implies that Mark, with semi-annual compounding at q%, must have earned  even more  than Peter.  M > P

Thus, if Peter earned more than Larry, Mark must also have earned more than Larry.  M > L   SUFFICIENT

Answer B.

akshatv45 · Answer

Statement 1 - q/200 > r/400. Lets say q/200 = 2 and r/400 = 1

then is (1 + q/200)^2 > (1+ r/400)^4 ?

substituting values, we get

(1+2)^2 > (1+1)^4 ?

=> 9 > 16 ?

The answer is NO. So Statement 1 is not Sufficient.

Statement 2 says - (1+q/100) > (1+ r/400)^4

We need to check how is (1+q/100) related to (1+q/200)^2

(1 + q/200)^2 = 1 + q^2/40000 + 2q/200 = 1 + q/100 + q^2/40000 so > (1+q/100)

Hence B —> statement 2 is sufficient.

NoeticImbecile · Answer

Hello, can you elaborate upon: " now if q = r/2 (or slightly bigger) than, (1+r/4)^2 is for sure less than (1+r/4)^4 MARK<LERRY, but if (given q>r/2) q = 2r" 
 and also how did you arrive at:- 
 "Mark (1+q/2)^2 = (1+r)^2"

Larry invested $20,000 in an investment that earned an annual

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Larry invested $20,000 in an investment that earned an annual

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards