If r, s, and w are positive numbers such that w = 60r + 80s

1 and 2 are exactly the same, so the answer is either (D) or (E).

For #1: If r = 0.5, then w = (60*0.5) + (80*0.5) = 30 + 40 = 70. As r gets bigger, w gets smaller (because it's composed of a bigger fraction of 60 and a smaller fraction of 80 - eg, if r = 0.9, s = 0.1 and w = 54+8 = 62), so w is definitely less than 70.

Since 1 and 2 are the same, the answer is (D).

Sol: Given r,s and w are positive nos and w=60r+80s and r+s=1
We need to know whether w<70 or not

Given r+s=1 so 60r+60s=60---> The given expression for w = 60r+60s+20s or w=60+20s
The question becomes is 60+20s<70 or s<1/2

St 1: If r>0.5 then s<0.5 because r+s=1. Sufficient
St 2: r>s. Okay it is given that r+s=1 so as r increases, s decreases and r=s=0.5. Since r>s therefore r has to greater than 0.5 and hence s < 0.5

Ans is D

Given: r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1

Target question: w < 70
STRATEGY: 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 < 0.5
In other words, the answer to the REPHRASED target question is YES, s is less than 0.5
Statement 1 is SUFFICIENT

Statement 2: r > s
If r + s = 1, we can subtract s from both sides to get: r = 1 - s
Now take statement 2 and replace r with 1 - s to get: 1 - s > s
From here, we can add s do both sides of the inequality to get: 1 > 2s
Divide both sides by 2 to get: 0.5 > s
Once again, the answer to the REPHRASED target question is YES, s is less than 0.5
Statement 2 is SUFFICIENT

Answer: D

VIDEO ON REPHRASING THE TARGET QUESTION:

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