Data Sufficiency

BTGmoderatorDC wrote: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

OA D

Source: Official Guide

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