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

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If r, s, and w are positive numbers such that w = 60r + 80s  [#permalink]

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New post 12 Sep 2010, 06:25
2
6
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A
B
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D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:07) correct 33% (01:08) wrong based on 227 sessions

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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
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Re: Inequality DS  [#permalink]

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New post 12 Sep 2010, 06:46
1
1
If w = 60r + 80s and r+s = 1 then it means that w = 60r + 60s + 20s = 60(r+s) + 20s = 60 + 20s

(1) r > 0.5 so, since r + s = 1, we knows that s < 0.5.
so w = 60 + 20s < 60+ 20*0.5 = 60 + 10 = 0. So w < 70. SUFFICIENT

(2) This statement is the same as the first one. Indeed, r > s and r + s = 1 so s < 0.5.

Answer : D.
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Re: Inequality DS  [#permalink]

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New post 13 Sep 2010, 05:53
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


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).
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Re: Inequality DS  [#permalink]

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New post 13 Sep 2010, 06:19
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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


This is actually just a weighted average. Say at a company r is the fraction of employees who are men. Then s = 1-r would be the fraction of all employees who are women. If men earn $60/hr and women earn $80/hr, then w = 60r + 80s would then just be the average wage of all employees. If there are more male employees than female employees, then the average wage must be less than $70/hr, so each statement is sufficient alone.
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Re: If r, s, and w are positive numbers such that w = 60r + 80s  [#permalink]

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New post 29 Apr 2014, 20:51
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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



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
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Re: If r, s, and w are positive numbers such that w = 60r + 80s  [#permalink]

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New post 24 Dec 2018, 14:31
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Re: If r, s, and w are positive numbers such that w = 60r + 80s &nbs [#permalink] 24 Dec 2018, 14:31
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