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

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

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New post 03 Nov 2008, 22:13
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If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5

(2) r > s
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Re: DS : is x < 70 ? [#permalink]

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New post 03 Nov 2008, 22:31
D.

Going on a call....will post the explanation later.

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Re: DS : is x < 70 ? [#permalink]

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New post 03 Nov 2008, 23:48
amitdgr wrote:
If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5
(2) r > s


x = 60r + 80s
x = 60r + 60s + 20s
x = 60 (r + s) + 20s
x = 60 + 20s

is s <0.5?

E. will explain later as well.

a quick question: what is the use of W?
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Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
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Re: DS : is x < 70 ? [#permalink]

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New post 03 Nov 2008, 23:50
scthakur wrote:
D.

Going on a call....will post the explanation later.


D?

I am really curious about your selection of D.

Probably you presummed +ve numbers as integers.

waiting for your explanation.
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Re: DS : is x < 70 ? [#permalink]

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New post 04 Nov 2008, 00:10
GMAT TIGER wrote:
amitdgr wrote:
If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5
(2) r > s


x = 60r + 80s
x = 60r + 60s + 20s
x = 60 (r + s) + 20s
x = 60 + 20s

is s <0.5?

E. will explain later as well.

a quick question: what is the use of W?


Thanks GMAT TIGER ... I did not rephrase the question, thats why I had problem

The question says --- r,s are Positive numbers

The question boils down to "is s <0.5?" as you showed....


(1) r > 0.5
if r + s = 1, then most definitely r and s have to be less than 1.
if r = 0.6 then s = 0.4 and s < 1
even if r = 0.9, s will be 0.1 and s< 1 .... sufficient

(2) r > s
if r + s = 1, then most definitely r and s have to be less than 1.
if r = 0.6 then s = 0.4 and s < 1
even if r = 0.9, s will be 0.1 and s< 1 .... sufficient

Thence D :)
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Re: DS : is x < 70 ? [#permalink]

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New post 04 Nov 2008, 00:17
x = 60r + 80s = 80(r+s) - 20r = 80 - 20r.

From stmt1: r > 0.5 and 20r > 10
or -20r < -10
or 80-20r < 80-10
or, x < 70. Sufficient.

From stmt2:
r > s and since r + s = 1, r > (1-r) or 2r > 1 or r > 0.5 and this is the same as stmt1 and hence sufficient.

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Re: DS : is x < 70 ? [#permalink]

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New post 04 Nov 2008, 08:13
amitdgr wrote:
GMAT TIGER wrote:
amitdgr wrote:
If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5
(2) r > s


x = 60r + 80s
x = 60r + 60s + 20s
x = 60 (r + s) + 20s
x = 60 + 20s

is s <0.5?

E. will explain later as well.

a quick question: what is the use of W?


Thanks GMAT TIGER ... I did not rephrase the question, thats why I had problem

The question says --- r,s are Positive numbers

The question boils down to "is s <0.5?" as you showed....

(1) r > 0.5
if r + s = 1, then most definitely r and s have to be less than 1.
if r = 0.6 then s = 0.4 and s < 1
even if r = 0.9, s will be 0.1 and s< 1 .... sufficient

(2) r > s
if r + s = 1, then most definitely r and s have to be less than 1.
if r = 0.6 then s = 0.4 and s < 1
even if r = 0.9, s will be 0.1 and s< 1 .... sufficient

Thence D :)


Since r + s = 1, (1) r > 0.5 and (2) r > s, what the **** I was looking for?

I completely forgot (r + s) = 1 after rephrasing. :twisted: :evil:



Sorry guys, I am on break for a while for those silly mistakes.. :shocked
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Re: DS : is x < 70 ? [#permalink]

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New post 04 Nov 2008, 08:30
yup D it is..

we know that X will always be less <70..

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Re: DS : is x < 70 ? [#permalink]

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New post 05 Nov 2008, 04:19
amitdgr wrote:
If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5

(2) r > s


The question <=> Is x < 70 <=> Is 60r + 80s < 70 <=> Is 60r + 80(1-r) < 70 <=> Is -20r < - 10 <=> Is r > 0.5

(1) suff
(2) insuff

Answer is A

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Re: DS : is x < 70 ? [#permalink]

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New post 05 Nov 2008, 09:00
amitdgr wrote:
If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5

(2) r > s



D

The only way x is >=70 is if s is .5 or more. We know from either (1) or (2) that is not the case, since r+s=1

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Re: DS : is x < 70 ? [#permalink]

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New post 05 Nov 2008, 12:20
D.
when both r & s are 0.5 each x=70.

If r increases, it will tip the scale >70 and if s increases , it wil tip towards >70.

1) r>0.5 -> s<0.5, so x<70--suff
2) r>s --means the same--suff

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Re: DS : is x < 70 ? [#permalink]

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New post 05 Nov 2008, 15:09
D

x = 60+20s
x<70
s<0.5

1. r+s = 1 --> r>0.5
2. r+s =1 and s< 0.5 --> r>s

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Re: DS : is x < 70 ?   [#permalink] 05 Nov 2008, 15:09
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