If $5,000 invested for one year at p percent simple annual

Question

If $5,000 invested for one year at p percent simple annual interest yields $500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?

(1) k = 0.8p
(2) k = 8

ID: 100894

Bunuel · Accepted Answer

SOLUTION

If $5,000 invested for one year at p percent simple annual interest yields $500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?

Simple interest = Principal * Interest rate * Time , so we have that  $500=$5,000*\frac{p}{100}*1 , which gives  p=10%

(1) k = 0.8p -->  k=8%  -->  $500=Principal *\frac{8}{100}*1 . Sufficient to calculate Principal.
(2) k = 8.  $500=Principal *\frac{8}{100}*1 . Sufficient to calculate Principal.

Answer: D.

BrentGMATPrepNow · Answer

The great thing about DS questions is that we aren't required to perform calculations if we know that we COULD perform those calculations. Here's what I mean:

Target question:  What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ?

Given : If $5000 invested for one year at p percent simple annual interest yields $500  
 IMPORTANT : There's ONLY ONE possible value of p that will yield $500 interest after 1 year (if $5000 is invested). So, we COULD perform some calculations to determine that ONE VALUE of p.

Statement 1 : k = 0.8p  
Since we COULD determine the value of p, we COULD also determine the value of k Using the fact that k = 0.8p). 
Once we know the ONE value of k,  we COULD determine how much money needs to be invested to get $500 in interest after 1 year . 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : k = 8  
Perfect! 
Once we know the value of k,  we COULD determine how much money needs to be invested to get $500 in interest after 1 year.  
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers, 
Brent

cyberjadugar · Answer

Hi,

Difficulty level: 600

SI (Simple Interest) =  \frac{PRT}{100} ,
where, P = Principal,
R = Rate in percentage,
T = Time

Thus,  500 = \frac {5000*p*1}{100} 
or p = 10%

New Principal invested depends on value of k

Using (1),
k=0.8*p=8%
 P=\frac {100SI}{RT}
=\frac {100*500}{8*1} . Sufficient.

Using (2),
k=8%
 P=\frac {100SI}{RT}
=\frac {100*500}{8*1} . Sufficient.

Answer (D),

Regards,

JeffTargetTestPrep · Answer

Since interest amount = principal x interest rate x time, we have:

500 = 5000 x p/100 x 1

500 = 50 x p

p = 10

Let A = principal that yields $500 interest at k percent simple annual interest rate in one year, so we have:

500 = A x k/100 x 1

50000/k = A

So if we know the value of k, we can determine the value of A.

Statement One Alone:

k=0.8p

Since p = 10, then k = 0.8(10) = 8. Since we know the value of k, we can determine the value of A (without actually determining it). Statement one alone is sufficient.

Statement Two Alone:

k=8

Since we know the value of k, we can determine the value of A (without actually determining it). Statement two alone is sufficient.

Answer: D

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=kwS6PHP7CtY Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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