OG 13 40

[oquiella]

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


Answer: D


Please explain reasoning.

[MartyMurray]

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

The question is asking what amount has to be invested at rate of interest k in order to generate $500 in interest. Since if we know what k is we will be able to determine the amount needed to generate $500 in interest, the question can be rephrased as "What is the value of k?"

Statement 1 tells us the relationship between k and p. Since we can calculate that p = 10 from the fact that $5000 x p% = $500, using the information given in Statement 1 we can also calculate k.

Sufficient.

Statement 2 answers our rephrased question exactly.

Sufficient.

The correct answer is D.

[Brent@GMATPrepNow]

If $5000 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 amount of dollars ?

1) k = 0.8p
2) k = 8

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

[oquiella]

If $5000 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 amount of dollars ?

1) k = 0.8p
2) k = 8

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

So the answer did not have to yield $500 after computing? I thought the question was that it must equal $500 so I decided Statement 1 was insufficient because of the .08