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

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.
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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

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,

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
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