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

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Manager
Joined: 06 Apr 2010
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If r, s, and w are positive numbers such that w = 60r + 80s  [#permalink]

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12 Sep 2010, 07:25
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65% (01:58) correct 35% (01:53) wrong based on 235 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
Intern
Joined: 18 Jul 2010
Posts: 40

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12 Sep 2010, 07:46
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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.

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Joined: 06 Aug 2010
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13 Sep 2010, 06:53
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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13 Sep 2010, 07:19
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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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29 Apr 2014, 21:51
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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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24 Dec 2018, 15:31
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If r, s, and w are positive numbers such that w = 60r + 80s   [#permalink] 24 Dec 2018, 15:31
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