udaymathapati wrote:
If r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1, is w < 70?
(1) r > 0.5
(2) r > s
Given: r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1 Target question: w < 70STRATEGY: Always be on the lookout for opportunities to rephrase the target question. In many cases, a little work up front will make analyzing the statements much easier. Since we're told that r + s = 1, we might recognize that we can manipulate the equation w = 60r + 80s to take advantage of this information.
We can write: w = (60r + 60s) + 20s
Then factor the first part to get: w = 60(r + s) + 20s
Substitute to get: w = 60(
1) + 20s
In other words: w = 60 + 20s, which means the target question becomes:
Is 60 + 20s < 70?We can make things even easier by subtracting 60 from both sides to get:
Is 20s < 10?And we can divide both sides by 20 to get:
Is s < 0.5?REPHRASED target question
Is s < 0.5?Aside: the video below has tips on rephrasing the target question Statement 1: r > 0.5 We already know that
r + s = 1 So, for example, if r = 0.5, then s = 0.5
Similarly, if r > 0.5, we can be certain that
s < 0.5In other words, the answer to the REPHRASED target question is
YES, s is less than 0.5Statement 1 is SUFFICIENT
Statement 2: r > sIf
r + s = 1, we can subtract s from both sides to get:
r = 1 - sNow take statement 2 and replace
r with
1 - s to get:
1 - s > sFrom here, we can add s do both sides of the inequality to get:
1 > 2sDivide both sides by 2 to get:
0.5 > sOnce again, the answer to the REPHRASED target question is
YES, s is less than 0.5Statement 2 is SUFFICIENT
Answer: D
VIDEO ON REPHRASING THE TARGET QUESTION: